Objectives for Chapter 10 – Energy, Work and Simple Machines Student Targets

403. I can identify kinetic energy as a function of velocity. 2. An object that has kinetic energy must be a. moving b. falling c. pretty d. elevated e. at rest

3. Which gives the correct relationship for kinetic energy? a. KE = mv c. KE = mv/2 b. KE = mv2 d. KE = mv2/2

4. An object that has kinetic energy must have (A) acceleration. B) a force applied to maintain it. C) momentum. D) none of the above

404. I can calculate gravitational potential energy* and kinetic energy. 5. What’s the KE of a 100,000kg spaceship orbiting at 8,000m/s? a) 4 x 1013 J b) 3.2 x 1012 J c) 4 x 108J 406. I can identify that energy is transferred between different forms. 7. An arrow in a bow has 70 J of potential energy. Assuming no loss of energy due to heat or poor accounting procedures, how much kinetic energy will the arrow have after its shot and traveling in air? a. 140 J b. 70 J c. 50 J d. 35 J e. 0 J

407. I can solve problems using conservation of mechanical energy.

408. I can apply the mathematical definition of work as the product of Force and displacement. 10. How much net work is done by gravity on a rock that weighs 50 N that you carry horizontally across a 10 m room? a. 500 J b. 500 W c. 10 J d. 5 J e. 0 J 11. It takes a net work of 40 J to push a box of physics papers 4 meters across a floor. Assuming the push is in the same direction as the box moved, what is the magnitude of the net force on the box of physics papers? a. 4 N b. 10 N c. 40 N d. 160 N e. none of these 12. T/F When there is an angle between the force and the displacement, W = F d cosθ. 13. Clarice has a mass of 78 kg and climbs the schools stairs in 23.0 seconds. The school stairwell contains 41 stairs that are 18 cm tall each. How much work against gravity did Clarice do climbing up the stairs? a. 5641 J b. 576 J c. 564127J d. 245 J e. 764 J

409. I can identify situations of net positive work, negative work, zero work. 14. When friction slows down a ball, friction is doing: a) Positive Work b) Negative work c zero work

410. I can identify work as a change in energy. 15. The amount of potential energy possessed by an elevated object is equal to A) the distance it is lifted. B) the work done in lifting it. C) the force needed to lift it. D) the value of the acceleration due to gravity. E) the power used to lift it.

OPRF Physics Custom Objectives Note: any objectives involving calculation of one variable imply the calculation of any other variable in the equation, depending on the given information. 10/11.1 Calculate power. 16. How much power is required to do 100 J of work on a 35 kg object in 2 seconds? a. 17.5 W b. 3500 W c. 200 W d. 50 W e. 100 W 17. Power equals work multiplied by time.

a. True b. False

10.4 State SI units for work, energy, spring constant, and power. 21. The unit of energy is the watt.

a. True b. False 22. The unit of power is the watt.

a. True b. False 23. The unit of work is the Joule.

a. True b. False 11.5 Calculate answers for hypothetical energy scenarios using the idea of proportionality. (e.g., if you double the velocity, what happens to the energy, etc) 24. If you lift two loads of equal weight up one story, how much work do you do compared to lifting just one load up one story? A) Four times as much B) One quarter as much C) Twice as much D) One half as much E) The same amount 25. If Nellie Newton pushes an object with three times the force for twice the distance, she does A) three times the work. B) six times the work. C) four times the work. D) the same work. 26. How much farther will a car traveling at 200 km/s skid than the same car traveling at 100 km/s? A) The same distance B) Five times as far C) Half as far D) Four times as far E) Twice as far 27. If a student pushes an object with twice the force for twice the distance, she does a. the same work b. twice the work c. four times the work d. eight times the work 28. How much MORE kinetic energy will a car traveling at 100 km/hr have then the same car traveling at 50 km/hr? a. five times as much b. four times as much c. twice as much d. the same e. half as much

Mechanical advantage Calculate the mechanical advantage of a lever that moves a 12,000N object 0.20m when a person applies a force of 910N over a distance of 3.00m. Calculate the ideal mechanical advantage for the system. A student takes the following data for a spring. Find the work done on the spring and the spring constant.

Displacement Force

0.0 0.0

0.3 137.5

0.5 275.0

0.8 412.5

1.0 550.0

1.3 687.5

1.5 825.0

1.8 962.5

2.0 1100.0

2.3 1237.5

2.5 1375.0

2.8 1512.5

3.0 1650.0

2) Two men, Joel and Jerry, push against a wall. Jerry stops after 10 min, while Joel is able to push for 5.0 min longer. Compare the work they do. A) Joel does 75% more work than Jerry. B) Joel does 50% more work than Jerry. C) Jerry does 50% more work than Joel. D) Neither of them do any work. Answer: D Diff 2 4) Matthew pulls his little sister Sarah in a sled on an icy surface (assume no friction), with a force of

60.0 Newtons at an angle of 37.0° upward from the horizontal. If he pulls her a distance of 12.0 m, the

work he does is A) 0.333 kJ B) 720 J C) 575 J D) 433 J E) 185 J Answer: C Diff: 2 5) A simple pendulum, consisting of a mass m and a string of length L, swings upward, making an

angle Ө with the vertical. The work done by the tension force is

A) zero. B) mgL.

C) mgL cos Ө.

D) mgL sin Ө.

E) mgL tan Ө.

Answer: A Diff: 2 6) A 4.0 kg box of fruit slides 8.0 m down a ramp, inclined at 30.° from the horizontal. If the box slides at a constant velocity of 5.0 ml s, the work done by gravity is A) +78. J. B) 0.16 kJ. C) -78. J. D) zero.

E) -0.16 kJ. Answer: B Diff: 2 7) An auto is coasting on a level road. It weighs 10. kN. How much work is done by gravity as it moves horizontally 150. meters? Answer: zero (displacement is perpendicular to the force) Diff: 2 8) If there is no motion, can work be done on a system? A) yes, provided an outside force is applied B) yes, since motion is only relative C) no, since a system which is not moving has no kinetic energy D) no, because of the way work is defined Answer: D Diff:1 Choose from the following list: (a) friction (b) J/s (c) dyne.cm (d) N.m (e) 550 ft.lb/s (f) mgy (g) 1/2 mv2 (h) dimensionless (i) Nlm (j) 3.6 MJ (k) ft.lb (I) -kx (m) weight (n) ft.lb Is 9) Match joule to one of the choices above. Answer: (d) N m Diff: 1

10) Which of the following is not a unit of work? A) Kg-m/s B) J C) Kw-h D)N-m E) W-s Answer: A Diff: 1 11) When you lift a 12 ounce beverage can from the table top to your mouth, you do approximately how much work? A) 1 Calorie B) 1 Wall C) 1 Kw-h D) 1 Joule E) 1 erg Answer: D Diff:2 19) Which is usually larger: the kinetic coefficient of friction or the static coefficient of friction? A) kinetic coefficient of friction B) static coefficient of friction C) neither Answer: B Diff: 1 20) The angle of repose depends on the weight of the object on the hill. Answer: FALSE Diff: 2 21) The coefficients of friction for plastic on wood are µs = 0.50 and µk= 0.40. How much horizontal force would you need to apply to a 3.0-lb plastic calculator to start it moving from rest? A) 1.2 N B) 2.7 N C) 1.5 N D) 0.15 N E) 0.50 N

Answer: C Diff:2 22) The number of forces acting on a car parked on a hill is ..Name them. Answer: Three. Gravity, road on tires, and air pressure. Diff:3 Choose from the following list: (a) friction (b)J/s (c) dyne-cm (d) N.m (e) 550 ft-lb/s (f) mgy (g) 1/2mv2 (h) dimensionless (i) N/m (j) 3.6 MJ (k) ft.lb (I) -kx (m) weight (n) ft-lb / s 12) Match erg to one of the choices above. Answer: (c) dyne.cm Diff:1 13) You throw a ball straight up. Compare the sign of the work done by gravity while the ball goes up with the sign of the work done by gravity while it goes down. A) Work up is -, and the work down is -. B) Work up is +, and the work down is +. C) Work up is -, and the work down is +. D) Work up is +, and the work down is-. Answer: C Diff:2 5.2 Work Done by a Variable Force 1) A 10. kg mass, hung onto a spring, causes the spring to stretch 2.0 cm. The spring constant is

A) 5.0 N/cm B) 49 N/cm C) 0.20 N/cm D) 20. N/m E) 0.0020 N/cm Answer: B Diff:2

2) Describe the type of spring "constant" needed to produce a constant restoring force like curve (a) above. A) k must vary as the stretch squared. B) k must be a real constant. C) k must vary inversely with stretch. D) k must vary proportional to stretch. E) none of these Answer: C Diff:2 3) Which of the graphs above illustrates Hooke's Law? A) graph a B) graph b C) graph c

D) graph d Answer: B Diff 2 4) Which of the graphs above represents a spring which gets less stiff the more it is stretched? A) graph a B) graph b C) graph c D) graph d Answer: D Diff: 2 5) The area under the curve, on a Force-position (F-x) graph, represents A) work. B) efficiency. C) kinetic energy. D) power. E) friction. Answer: A Diff 1

6) The force that a squirrel exerts on a nut it has found is observed over a 10. second interval, as shown on the graph above. How much work did the squirrel do during that 10. s? A) 12.5 J B) 50. J C) 25. J D) 22. J E) zero

Answer: C Diff: 2 7) The force that a squirrel exerts on a nut it has found is observed over a 10. second interval, as shown on the graph above. What was the average power exerted by the squirrel? A) zero B) 1.3 W C) 2.5 W D) 2.2 W E) 5.0 W Answer: C Diff: 2 8) The resultant force you exert while pressing a key on the keyboard of your new computer, for a 1.0-s period, is plotted on the graph, shown.

How much work did you do during this 1-s interval? A) zero B) 50. J C) -25. J D) 12.5 J E) 22. J Answer: A Diff: 2 9) Consider a 0.002 gram mass hung from a spring. When an additional 15. kg is added, the equilibrium position changes by 20. cm. (a) What is the spring constant? (b) How much energy does the spring store? (c) If 30. kg are added, by how much will the equilibrium position change?

Answer: (a) 0.74 x 103 N/m (b) 15. J (c) 40. cm Diff:3 10) Daisy raises 10 kg to a height of 2.5 meters in 2.0 seconds. (a) How much work did she do? (b) How much power was expended? (c) If she raises it in 1.0s rather than 2.0s, how do the work and power change? Answer: (a) 0.25 kJ (b) 0.13 kW (c) same work but power doubles Diff:3 11) Consider a plot of the displacement (x) vs. applied force (F) for an ideal elastic spring. The slope of the curve would be A) the spring constant. B) the reciprocal of the spring constant. C) the acceleration of gravity. D) the reciprocal of the acceleration of gravity. Answer: B Diff:2 12) Consider an ideal elastic spring. The spring constant is A) inversely proportional to the applied force. B) inversely proportional to the displacement. C) proportional to displacement from equilibrium. D) proportional to the mass attached to the spring. E) none of the other answers. Answer: E Diff: 1 5.3 The Work-Energy Theorem: Kinetic Energy 1 ) A driver, traveling at 22. m/ s, slows down her 1500. kg car to stop for a red light. What work is done by the friction force against the wheels? Answer: 3.6 x 105 Joules Diff:2

(a) friction (b)J/s (c) dyne-cm (d) N.m (e) 550 ft-lb/s (f) mgy (g) 1/2mv2 (h) dimensionless (i) N/m (j) 3.6 MJ (k) ft.lb (I) -kx (m) weight (n) ft-lb/s 2) Match kinetic energy to one of choices above. Answer: (g) 1/2 mv2 Diff: 1 3) The work energy theorem says A) the net work done is equal to the initial kinetic energy less the final energy. B) the net work done plus the final kinetic energy is the initial kinetic energy. C) the net work done plus the initial kinetic energy is the final kinetic energy. D) the net work done minus the initial kinetic energy is the final kinetic energy. E) final kinetic energy plus the net work done is the initial kinetic energy. Answer: C Diff: 2 4) Car J moves twice as fast as car K, and car J has half the mass of car K. The kinetic energy of car J, compared to car K is A) 4 to 1. B) 2 to 1. C) the same. D) 42 to 1. E) 1 to 2. Answer: B Diff: 2 5) If both the mass and the velocity of a ball are tripled, the kinetic energy is increased by a factor of

A) 18. B) 81. C) 6. D) 9. E) 27. Answer: E Diff: 2 6) Is more work required to increase a car's speed from rest to 30 mph, or from 50 mph to 60 mph? Answer: 50 to 60 mph Diff:2 7) Kinetic energy is proportional to speed. Answer: FALSE Diff: 1 8) A brick and a pebble fall from the roof of an apartment building under construction. At some point the brick is moving at a speed of 3.0 m/ 5 and the pebble's speed is 5.0 m/s. If both objects have the same kinetic energy, what is the ratio of the brick's mass to the rock's mass? A) 25 to 9.0 B) 3.0 to 5.0 C) 5.0 to 3.0 D) 12.5 to 3.0 E) 12.5 to 4.5 Answer: A Diff: 2 9) A truck weighs twice as much as a car, and is moving at twice the speed of the car. Which statement is true about the truck's kinetic energy (K) compared to that of the car? A) The truck has 4 times the K of the car. B) All that can be said is that the truck has more K. C) The truck has twice the Kof the car. D) The truck has 8 times the K of the car.

E) The truck has -.J2 times the K of the car. Answer: D Diff: 2 10) What is the minimum energy needed to lift 1.0 kg to a height of 200. km and to give it a speed of 8.0 km/ s? (Neglect the small decrease of "g" over that distance.) A) 34. TJ B) 34. kJ C) 34. MJ D) 34. GJ E) 34. J Answer: C Diff: 2 5.4 Potential Energy NOTE: The following question(s) refer(s) to the Cyclone, the famous roller coaster ride at Coney Island, shown in the sketch. Assume no friction.

1 ) How much work was required to bring the 1000-kg roller coaster from point P to rest at point Q at the top of the 50. m peak? A) 50. kJ B) 0.25 MJ C) 32. kJ D) 0.49 MJ E) 75. kJ Answer: D

Diff: 2 Choose from the following list: (a) friction (b)J/s (c) dyne-cm (d) N.m (e) 550 ft-lb/s (f) mgy (g) 1/2mv2 (h) dimensionless (i) N/m (j) 3.6 MJ (k) ft.lb (I) -kx (m) weight (n) ft-lb/s 2) Match potential energy to one of the choices above. Answer: (f) mgy Diff: 1 3) Match spring constant to one of the choices above. Answer: (i) N I m Diff: 1 4) Consider 10. kg in circular orbit 200. km above the Earth's surface, moving at 7.6 km/s. (a) What is its kinetic energy in Joules? (b) Assuming g is a constant 9.80 m/s2 in that 200. km above the surface (actually g decreases only several percent in that distance), what potential energy is required to put that 10 kg in orbit? (c) Assuming an energy cost of 10¢/kw-h, what would be the minimum cost to put 10. kg in orbit (however present rockets are incredibly inefficient)? Answer: (a) 2.9 x 108J (b) 2.0 x 107J (c) $8.60 Diff: 3

Choose from the following list: (a) friction (b)J/s (c) dyne-cm (d) N.m (e) 550 ft-lb/s (f) mgy (g) 1/2mv2 (h) dimensionless (i) N/m (j) 3.6 MJ (k) ft.lb (I) -kx (m) weight (n) ft-lb/s 5) Match Hooke's Law to one of the choices above. Answer: (I)-kx Diff 1 6) A 200-g mass attached to the end of a spring causes it to stretch 5.0 cm. If another 200-g mass is added to the spring, the potential energy of the spring will be A) twice as much.

B) √ times as much. C) the same. D) 4 times as much. E) 3 times as much. Answer: D Diff:2

7) On the accompanying diagram of a pendulum, at what position is the potential energy maximum? A) A B) B C) C Answer: C Diff:2 8) On the accompanying diagram of a pendulum, at what position is the kinetic energy maximum? A) A B) B C) C Answer: A Diff: 2 9) A spring is characterized by a spring constant of 60. N/ m. How much potential energy does it store, when stretched by 1.0 cm? A) 600. J B) 6.0 µJ C) 60. J D) 0.3 J E) 0.003 J Answer: E Diff: 2 10) Assuming negligible friction, what spring constant would be needed by the spring in a "B-B gun" to fire a 10. gram pellet to a height of 100 meters if the spring is initially compressed 10. cm? A) 20. N/cm B) 20. N/m C) 200. N/m 0) 2.0 x 103 N/cm E) 2.0 x 10-3 N/m

Answer: A Diff: 2 11) If a spring- operated gun can shoot a pellet to a height of 100.m on Earth, how high could the pellet rise if fired on the moon? A) 3600. m B) 16.7m C) 600.m D) 3.60 km E) 100.m Answer: C Diff: 2 12) You and your friend want to go to the top of the Eiffel Tower. Your friend takes the elevator straight up. You decide to walk up the spiral stairway, taking longer to do so. Compare the gravitational potential energy (U) of you and your friend, after you both reach the top. A) It is impossible to tell, since the times and distances are unknown. B) Your friend's U is greater than your U, because she got to the top faster. C) Both of you have the same amount of potential energy. D) Your U is greater than your friend's U, because you traveled a greater distance in getting to the top. Answer: C Diff 2 13) On a plot of F vs. x, what represents the work done by the force F? A) the slope of the curve B) the length of the curve C) the area under the curve 0) the product of the maximum force times the maximum x E) the maximum F times minimum x Answer: C Diff: 2

5.5 The Conservation of Energy 1 ) A simple pendulum, consisting of a mass m, is attached to the end of a 1 yd length of string. If the mass is held out horizontally, and then released from rest, its speed at the bottom of the swing is about A) 2. m/s. B) 4. m/s. C) 1.3 m/s. D) 10. m/s. E) 30. m/s. Answer: B Diff: 2 Choose from the following /ist: (a) friction (b)J/s (c) dyne-cm (d) N.m (e) 550 ft-lb/s (f) mgy (g) 1/2mv2 (h) dimensionless (i) N/m (j) 3.6 MJ (k) ft.lb (I) -kx (m) weight (n) ft-lb/s 2) Match conservative force to one of the choices above. Answer: (m) weight Diff: J 3) Match non-conservative force to one of the choices above . Answer: (a) friction Diff: J

4) A simple pendulum, with a 4.4 kg mass and length 75. cm, is released from rest at an angle of 50◦. (a) To what height does the mass swing on the other side? (b) What is the speed of the mass at the bottom of the swing? Answer: (a) 27. cm (b) 2.3 m/s Diff:3 NOTE: The following question(s) refer(s) to the Cyclone, the famous roller coaster ride at Coney Island, shown in the sketch. Assume no friction.

5) If the roller coaster leaves point Q from rest, how fast is it traveling at point R? A) 0.98 km/s B) 31 m/s C) 22 m/s 0) 0.49 km/s E) 51 m/s Answer: B Diff: 2 A ball is released from rest, at the left side of the loop-the-loop, at the height, h, shown.

6) If the radius of the loop is R, what minimum height h allows the ball not to fall off the track at the top of the loop?

a) 3.5R b) 2.5R c) 2.0R d) √ e) 3.0 R

Answer: B Diff: 2 7) If the radius of the loop is R, what vertical height does the ball rise to, on the other side, neglecting friction? A) R B) 2R C) less than R D) greater than 2R Answer: 0 Diff: 2 8) What distinguishes a conservative force from a non-conservative force? Answer: Work done by a conservative force is independent of the object's path and the work only depends upon the initial and final positions. Diff: 2 9) A "machine" multiplies (increases) A) time. B) energy. C) work. D) force. E) power. Answer: D Diff: 1

10) You slam on the brakes of your car in a panic, and skid a certain distance on a straight, level road. If you had been traveling twice as fast, what distance would the car have skidded, under the same conditions? A) It would have skidded 4 times farther. B) It would have skidded twice as far. C) It would have skidded. √ times farther. D) It is impossible to tell from the information given. Answer: A Diff: 2 11) A toy rocket, weighing 10. N, blasts off from ground level. At the exact top of its trajectory, its energy is 140.J. To what vertical height does it rise? A) 1.4m B) 14.m C) 12.m D) 0.12 km E) 1.4 km Answer: B Diff: 2 12) A boy releases his 2.0 kg toy, from rest, at the top of a sliding-pond inclined at 20' above the horizontal. What will the toy's speed be after sliding 4.0 m along the sliding-pond? The coefficient of kinetic friction is 0.20. A) 3.0 m/s B) 4.4 m/s C) 2.2 m/s D) 5.2 m/s E) 3.5 m/s Answer: D Diff:2 13) Problems involving a non-conservative force cannot be solved because there is no definable potential energy.

Answer: FALSE Diff: 1 14) A 4-kg mass moving with speed 2 m/s, and a 2-kg mass moving with a speed of 4 m/s, are gliding over a horizontal frictionless surface. Both objects encounter the same horizontal force, which directly opposes their motion, and are brought to rest by it. Which statement correctly describes the situation? A) Both masses travel the same distance before stopping. B) The 2-kg mass travels twice as far as the 4-kg mass before stopping. C) The 2-kg mass travels farther, but not necessarily twice as far. D) The 4-kg mass travels twice as far as the 2-kg mass before stopping. E) The 4-kg mass loses more kinetic energy than the 2-kg mass. Answer: B Diff: 2 NOTE: The following question(s) refer(s) to the Cyclone, the famous roller coaster ride at Coney Island, shown in the sketch. Assume no friction.

15) If the roller coaster leaves point Q from rest, what is its speed at point S (at the top of the 25. m peak) compared to its speed at point R? A) zero B) 1/√ C) √ D) 2 E) 4

Answer: B Diff: 2 16) How fast must the coaster be moving at P in order to coast to a stop at Q? A) 9.8 m/s B) 33. m/s C) 22. m/s D) 0.49 km/s E) 0.98 km/s Answer: B Diff: 2 17) The total mechanical energy of a system A) can never be negative. B) is equally divided between kinetic energy and potential energy. C) is either all kinetic energy or all potential energy, at anyone instant. D) is constant only if conservative forces act. Answer: D Diff:2 18) A leaf falls from a tree. Compare its kinetic energy K to its potential energy U. A) K increases, and U decreases. B) K decreases, and U increases. C) K decreases, and U decreases. 0) K increases, and U increases. E) K and U remain constant. Answer: A Diff:1 19) A 30. N stone is dropped from a height of 10. m, and strikes the ground with a velocity of 13.m/s. What average force of air friction acts on it as it falls? A) 7.2 N B) 2.9 N C) 1.2 N D) 4.1 N

E) 0.13 KN Answer: D Diff: 2 20) Is it possible for a system to have negative potential energy? A) Yes, as long as the total energy is positive. B) Yes, since the choice of the zero of potential energy is arbitrary. C) No, because this would have no physical meaning. D) No, because the kinetic energy of a system must equal its potential energy. Answer: B Diff: 2 21) King Kong falls from the top of the Empire State Building, through the air (air friction is present), to the ground below. How does his kinetic energy (K) just before striking the ground compare to his potential energy (U) at the top of the building? A) K is equal to U. B) It is impossible to tell. C) K is less than U. D) K is greater than U. Answer: C Diff:2 22) A skier, of mass 60. kg, pushes off the top of a hill with an initial speed of 4.0 mI s. How fast will she be moving after dropping 10.m in elevation? A) 0.20 km/s B) 15. m/s C) 10. m/s D) 0.15 km/s E) 49. m/s Answer: B Diff:2 23) A container of water is lifted vertically 3.0 m, then returned to its original position. If the total weight is 30. N, how much work was done?

A) 0.18 kJ B) 45 J C) 90 J D) No work was done. E) 0.90 kJ Answer: D Diff 2 24) A 1.0 kg flashlight falls to the floor. At the point during its fall when it is 0.70 m above the floor, its potential energy exactly equals its kinetic energy. How fast is it moving? A) 3.7 m/s B) 6.9 m/s C) 14 m/s D) 45 m/s E) 9.8 m/s Answer: A Diff 2 5.6 Power 1) How many joules of energy are used by a 2.0 hp motor that runs for 1.0 hr? Answer: 5.4 MJ Diff: 2 Choosefrom the following list: (a) friction (b)J/s (c) dyne-cm (d) N.m (e) 550 ft-lb/s (f) mgy (g) 1/2mv2 (h) dimensionless (i) N/m (j) 3.6 MJ (k) ft.lb (I) -kx (m) weight (n) ft-lb/s

2) Match efficiency to one of the choices above. Answer: (h) dimensionless Diff: 1 3) Match watt to one of the chocies above. Answer: (b) J I s Diff: 1 4) Match fps unit of power to one of the choices above. Answer: (n) ft.lb I s Diff: 1 5) Match hp to one of the choices above. Answer: (e) 550 ft.lbsl s Diff: 1 6) 1left five 100. watt bulbs burning in my basement for two weeks. If electricity costs me 10.¢/kw-h, how much did the electricity cost (to the nearest dollar) to leave these bulbs on and how many joules of electrical energy did they consume? Answer: $17. and 6.05 x 108 Joules Diff: 3 7) Compared to yesterday, you did 3 times the work in one-third the time. To do so, your power output must have been A) the same as yesterday's power output. B) one-third of yesterday's power output. C) 3 times yesterday's power output. D) 9 times yesterday's power output.

E) 34 times yesterday's power output. Answer: D Diff: 2 8) As plant engineer, Donna purchases an electrical motor which has an output of 1500.hp. If it requires 1.20 Megawatts of electricity, what is the efficiency of the motor? Answer: 93.3% Diff: 2 9) My 5.0 hp mower would be equivalent to an electric mower rated at what power? A) 2.8 W B) 0.25 KW C) 2.8 KW D) 3.7 KW E) 0.78 KW Answer: D Diff: 2 10) Place a P or an E after each unit, indicating whether it is a unit of power or energy:

Watt ft-lb/ s joule

Erg Newton-meter ft-lb

kw-h horsepower calorie

kg-m2/s watt-s kg-m2/s2

Answer: P P E E E E EPE PEE Diff:2 11) One horsepower is equal to A) 550. watts. B) 746. watts. C) 746.). D) 550.). E) 550. kW-h.

Answer: B Diff:1 12) My battery charger uses 12. watts. At 6.0 cents per kilowatt-hour, how much does it cost to charge batteries for 24. hours? A) 0.28 cents B) 1.4 cents C) 0.74 cents D) 1.7 cents E) 2.3 cents Answer: D Diff: 2 13) A roofer lifts supplies a height of 20. m with a hand-operated winch. How long would it take him to lift a 200. kg load, if the winch has an efficiency of 90%, and the rate at which the winch can do work is 0.80 hp? Answer: 73. seconds Diff: 2 14) A horse-power is equal to 550 A) JIs. B) Kw-h. C) ft-Ib/minute. D) ft-Ib/s. E) J/hour. Answer: D Diff: 1 15) Water flows over a waterfall 20.m high, at the rate of 4.0 x 104 kg/s. If this water powers an electric generator with a 40% efficiency, how many watts of electric power can be supplied? Answer: 3.1MW Diff: 2 Choose from the following list:

(a) friction (b)J/s (c) dyne-cm (d) N.m (e) 550 ft-lb/s (f) mgy (g) 1/2mv2 (h) dimensionless (i) N/m (j) 3.6 MJ (k) ft.lb (I) -kx (m) weight (n) ft-lb/s 16) Match kW-h to one of the choices above. Answer: (j) 3.6 MJ Dif!: 1 17) A family goes on vacation for one week, but forgets to tum off an electric fan that consumes electricity at the rate of 200 watts. If the cost of electricity is $0.120/kW-h, how much does it cost to run the fan? Answer: $4.03 Diff: 2 18) Lisa runs up 4 flights of stairs in 22. seconds. She weighs 510. Newtons. If each flight rises 310. cm: (a) What is her change in potential? (b) What average power (watts) was required during the 22. s? (c) What minimum horsepower motor would be required to do this? Answer: (a) 6.32 kJ (b) 287. watts (c) 0.385 hp Diff:3 19) A cyclist does work at the rate of 500.W while riding. With how much average horizontal force does the wheel push when she is traveling at 10. m/s?

Answer: 50. N Diff:2 20) To accelerate your car at a constant acceleration, the car's engine must A) maintain a constant power output. B) develop ever-decreasing power. C) develop ever-increasing power. D) maintain a constant turning speed. Answer: C Diff: 2 21) Assuming muscles are 20% efficient, at what rate is a 60. kg boy using energy when he runs up a flight of stairs 10.m high, in 8.0 s? Answer: 3.7 kW Diff: 2

Review questions 3) Spock has landed on a newly discovered planet and is instructed to determine its gravitational strength. He constructs a simple pendulum with a length of 700.mm and observes 20. Full swings in 1 minute and 16.7 seconds. What does he deduce the "acceleration of gravity" to be from this? Answer: g; 1.88 m/ s2 Diff:2

5) Simple pendulum A swings back and forth at twice the frequency of simple pendulum B. Which statement is correct?

A) Amplitude of pendulum A is twice that of B. B) Amplitude of B is twice of A. C) Amplitude cannot be determined from data given. D) Amplitude of A is 1.41 that of B.

Answer: C Diff: 1

8) Simple pendulum A swings back and forth at twice the frequency of simple pendulum B. Which statement is correct?

A) Pendulum B is twice as long as A. B) Pendulum B is twice as massive as A.

C) The length of Bis. 2 times the length of A.

D) The mass of Bis. 2 times the mass of A.

E) The length of A is. 2 times the length of B. Answer: C Diff:2

9) Grandfather clocks often are built so that each one-way swing of the pendulum is a second. How long is the length of a simple pendulum for a 2.00 second period?

A) 0.993 m B) 24.8 cm C) 101.cm D) 0.500 m E) 500. cm

Answer: A Diff:2 16) A mass swinging on the end of a massless string undergoes SHM. Where is the instantaneous acceleration of the mass greatest?

A) A and C B) B C) C D) A and D E) A and B

Answer: D Diff: 2

9) Give at least one example of each of the following:

(a) longitudinal standing wave.

(b) transverse standing wave. Answer: (a) sound wave resonating in an organ pipe

(b) vibrating string on a violin Diff:2

Chapter 15 Sound 8. I can recognize that sound is a longitudinal wave with pressure variations that are transmitted to detectors.

6. SOUND waves are actually produced by: a. radio stations b. vibrating objects c. soft objects d. none of these

7. If my dog Greta is barking at some people walking past our house, I hear her sound waves because:

a. there is a source, medium, and house

b. there is a source, medium, and window

c. there is a source, medium, and detector

d. there is a source, medium, and protector

9. I can recognize which wave characteristic most closely relates to pitch and/or loudness.

8. Which characteristic is most closely related to loudness? a. pitch b. amplitude c. wavelength d. frequency

10. I can relate the temperature of air to the velocity at which sound will travel.

9. Sound will travel faster in air if the air is: a. Warmer b. Colder c. makes no difference

11. I can describe/recognize what beats are and/or calculate the apparent beat frequency between two frequencies.

10. Beats occur when two tuning forks at equal frequencies are sounded together. a. True b. False

11. Sound beats can be described as the apparent ________ of two sound waves that are being observed at the same time.

a. Changing of the frequency b. Changing of the loudness c. Soundness of the loudness d. Changing of the sounding board

12. I can calculate and describe the amount of audible Doppler shift for sound waves.

12. A car is moving to the right at 20m/s, and its horn emits a pitch of 400 Hz. If you are standing and the car approaches you, what frequency do you hear? (Assume the temperature of the air is 20C)

a. 425 Hz b. 423 Hz c. 388 Hz d. 120 Hz

13. Because of the Doppler effect, an observer will hear a sound moving away from her as being higher in

pitch. a. True b. False

13. I can calculate the velocity of sound given the resonance lengths of open/closed tubes.

14. A tuning fork produces a fundamental resonance w/ a closed tube 8.3 cm long. Assuming room temp is 20C, what is the lowest possible frequency of the tuning fork?

a. 2072 Hz b. 456 Hz c. 1033 Hz d. 114 Hz

15. I can describe some of the relationships between the components of musical instruments and the sounds that they produce.

15. A string instrument, which has a node at each end of the string, resonates with any whole number of quarter wavelengths.

a. True b. False

16. I can describe and calculate relationships involving loudness and decibels

16. Compared to a quiet conversation (30dB), a loud conversation (60db) would be a. 30x intensity b. 1000x intensity c. 2x intensity d. 3000x intensity

1 ) Sound vibrations with frequencies less than 20 Hz are called A) infrasonics. B) ultrasonics. C) supersonics. D) infrared. Answer: A Diff: 1 2) Sound vibrations with frequencies greater than 20,000 Hz are called A) infrasonics. B) ultrasonics. C) supersonics. D) megasonics. Answer: B Diff: 1 3) The pitch of sound is related to its A) loudness. B) velocity. C) amplitude. D) intensity. E) frequency. Answer: E Diff:l 4) Which of the following is a false statement? A) Sound waves are longitudinal pressure waves. B) Sound can travel through vacuum. C) The transverse waves on a vibrating string are different from sound waves. D) Light travels very much faster than sound. E) "Pitch" (in music) and frequency have approximately the same meaning. Answer: B Diff: 1 5) What is the audible range of sound frequencies? Answer: 20. Hz to 20. kHz

Diff:l 17) Total constructive interference occurs when two waves with similar frequency and wavelength A) are completely out of phase. B) are completely in phase. C) have 90 degrees phase difference. D) have a phase difference of -90 degrees. Answer: B Diff:l 18) The natural frequencies for a stretched string of length L, and wave speed v, are nv/(2L) where N equals A) 0, 1, 2, 3, . B) 2, 4, 6, 8, . C) 1, 2, 3, 4, . D) 0, 1, 3, 5, . E) 1, 3, 4, 5, . Answer: C Diff:2 2) What is the ratio of the speed of sound in air at 0 C to the speed at 100C?

Answer: 0.86 Diff:2 4) The wavelength in air of a sound wave of frequency 0.50kHz is A) 0.68 m. B)0.75m. C) 2.0 m. D) 1.5m. Answer: A Diff: 2 5) What is the speed of sound in air at freezing temperature? A) 331mph B) 650 m/s C) 331 m/s D) 650mph E) 1.8 m. F) 1100m/s

Answer: C Diff: 1 8) After seeing a flash of lightning, if one counts the seconds before hearing the thunder, one can estimate the distance to the flash. How many seconds delay (b) per kilometer? Answer: (b) 3. seconds per km Diff: 2 9) When sound passes from air into water A) its wavelength does not change. B) its frequency does not change. C) its velocity does not change. Answer: B Diff:l 11 ) Sound traveling in air at 23. C enters a cold front where the air temperature is 2.°C. If the sound

frequency is 1500. Hz, determine the speed in the warmer air and in the colder air. Answer: 345. m/s; 332. m/s Diff:2 12) If you were to inhale a few breaths from a helium gas balloon, you would probably experience an amusing change in your voice. You would sound like Donald Duck or Alvin the Chipmunk. What is the cause of this curious high-pitched effect? A) The helium causes your vocal cords to tighten and vibrate at a higher frequency. B) For a given frequency of vibration of your vocal cords, the wavelength of sound is less in helium than it is in air. C) Your voice box is resonating at the second harmonic, rather than at the fundamental frequency. D) Low frequencies are absorbed in helium gas, leaving the high frequency components, which result in the high, squeaky sound. E) Sound travels faster in helium than in air at a given temperature. Answer: E DifJ: 2 13) If you hear thunder 5.0 s after seeing a flash of lightning, the distance to the lightning strike is About

A) 2.2km. B) 0.60 km. C) 1.7 km.

D) 0.90km. E) 1.2 km.

Answer: C Diff: 2 14) On a day when the speed of sound in air is 340. m/s, a bat emits a shriek whose echo reaches it 25.0 ms later. How far away was the object that reflected back the sound? Answer: 4.25m Diff:2 15) As the temperature of the air increases, what happens to the velocity of sound? (Assume that all other factors remain constant.) . A) It increases. B) It decreases. C) It does not change. D) It increases when atmospheric pressure is high and decreases when the pressure is low. Answer: A Diff:l 2) Which of the following is most closely identified with loudness of a musical note? A) frequency B) velocity C) pitch D) amplitude E) phase Answer: D Diff:l 4) How many times more intense is an 80. db sound than a 60. db sound? A) 10 B) 20 C) 2.0 D) 1.33 E) 100 Answer: E Diff: 2 8) The decibel level of sound is related to its A) wavelength. B) intensity.

C) velocity. D) frequency. E) pitch. Answer: B Di!!: 1 9) Which of the following increases as a sound becomes louder? A) period B) wavelength C) amplitude D) velocity E) frequency Answer: C Diff:l 2) An unknown tuning fork is sounded along with a tuning fork whose frequency is 256. Hz and a beat frequency of 3. Hz is heard. What is the frequency of the unknown tuning fork? A) It must be 256 Hz. B) It must be 259 Hz. C) It could be either 253 Hz or 259 Hz; there is no way to tell. D) It must be 253 Hz. Answer: C Diff: 2 3) In order to produce beats, the two sound waves should have A) slightly different amplitudes. B) the same frequency. C) the same amplitude. D) slightly different frequencies. Answer: d Diff: 1 5) Given 4 tuning forks of frequency 446,440, 443,and 449 Hz, how many different beat frequencies could be produced and what are they? Answer: Three beat frequencies: 3, 6, 9 Hz Diff: 2 8) If the phase angle between sound waves from two different point sources is 180, what kind of

interference will occur? A) destructive B) constructive

C) either constructive or destructive Answer: A Diff:l 9) Consider the standing wave on a guitar string and the sound wave generated by the guitar as a result of this vibration. What do these two waves have in common? A) They have the same velocity. B) They have the same wavelength. C) They have the same frequency. D) They have nothing in common. Answer: C Diff: 1 13) Two pure tones are sounded together and a particular beat frequency is heard. What happens to the beat frequency if the frequency of one of the tones is increased? A) It does not change. B) It decreases. C) It could either increase or decrease. D) It increases. Answer: C Diff 1 1 ) The Doppler shift explains A) how sonar works. B) why the siren on a police car changes its pitch as it races past us. C) the phenomenon of beats. D) why a sound grows quieter as we move away from the source. E) why it is that our hearing is best near 3000 Hz. Answer: B or A (some sonar uses Doppler shift to find speeds) Diff: 1 3) Suppose you hear a car approaching and its horn is heard as a 3037. Hz tone. After passing, you hear 2430. Hz. (b) What is the speed of sound if the outside temperalure is 19.'C? (c) How fast was the car moving, in meters per second? Answer: (b) 342. mls (c) 38.0 mls Diff:3

4) Middle C has a frequency of 262. Hz. What is the frequency of C an octave higher? A) 2.10 kHz B) 786. Hz C) 0.524 kHz D) 270. Hz E) 2.62 kHz Answer: C Diff:l 5) The change in the frequency of a wave due to the motion of the source (or observer) is known as A) the Bell effect. B) the Mach effect. C) the Doppler effect. D) interference. E) diffraclion. Answer: C Diff:l 7) A sound source (normal frequency of 1000 Hz) approaches a stationary observer at one-half the speed of sound. The observer hears a frequency of A) 2000 Hz. B) 500 Hz. C) 250 Hz. D) 1500 Hz. E) 1414 Hz. Answer: A Dif/: 2 9) A train moving 30. m/ s approaches a station and sounds its whistle and passengers standing at the station hear a pitch of 440. cycles/ second. What pitch will be heard when the train is at rest at the station? (assume the air temperature is 20. C)

Answer: 402. Hz oiff: 2 2) Two violin strings, vibrating at 880.Hz and 876.Hz respectively, will cause a beat frequency of A) 4. Hz. B) 8. Hz. C) 878. Hz. D) 1.76kHz. Answer: A Diff: 1

3) A trombone or a trumpet can be considered a(n) A) open organ pipe. B) closed organ pipe. Answer: A Diff:l 4) A closed organ pipe has a 5th harmonic frequency of 1230.Hz at 20: c. (a) What is the length of the organ tube? (b) What is the 1st harmonic of the pipe? (c) If one end of the pipe were opened, what would be the 1st harmonic? Answer: (a) 35.0cm (b) 246.Hz (c) 123.Hz Diff: 3 7) A sound wave of pure frequency can under certain circumstances cause a glass goblet to shatter. This would be an example of A) constructive interference. B) resonance. C) destructive interference. D) overtones. E) the Doppler effect. Answer: B and A Di!!: 1 10) Which of the following properties of a sound wave is most closely identified with the "pitch" of a musical note? A) amplitude B) wavelength C) frequency D) phase E) intensity Answer: C Diff:l 11) A closed organ pipe of length 0.750m is played when the speed of sound in air is 340. m/ s. What is the fundamental frequency? A) 228 Hz B) 113 Hz C) 570. Hz D) 57.0 Hz E) 171. Hz Answer: B Oiff: 2

12) Only odd harmonics can be produced in a(n) organ pipe. A) closed B) narrow C) open D) wide Answer: A Oiff: 2 Choose from the following: (a) meters (b) rad/s (e) seconds (f) N/m (c) degrees (g) g/cm (d) Hertz (h) m/s 13) Beat frequency has which of the units shown above? Answer: (e) Hertz Oiff 1 14) What is the beat frequency of two sounds that have equal amplitudes and frequencies of 440. Hz and 444. Hz? Answer: 4. Hz Oiff:2 12) A car is moving toward you as you stand on a corner in 20. C air. The car's horn is designed to

blow at a frequency of 400. Hz tone. How fast is the car moving if the air is steadily blowing 10. m/ s toward you in the same direction that the car is moving? A) 20. m/s B) 30. m/s C) 28. m/s D) 10. m/s E) 40. m/s Answer: E Diff: 2

Chapter 24 Physical Optics: The Wave Nature of Light

24.1 Young's Double-Slit Experiment

1 ) Two light sources are said to be coherent if they

A) are of the same frequency.

B) are of the same frequency, and maintain a constant phase difference.

C) are of the same frequency and amplitude.

0) are of the same amplitude, and maintain a constant phase difference.

Answer: B

Diff: 2

2) The path difference for destructive interference is rrIA/2 where

A) m = 1, 2, 3, 4, .

B) m = 0, 2, 4, 6, .

C) m = 2, 4, 6 , 8, .

0) m = 0, 1,2,3, .

E) m= 1, 3, 5, 7, .

Answer: E

Diff:2

3) A double-slit experiment uses light of wavelength 633. nm with a slit separation ofO.lOOmm

and a screen placed 2.0 m away.

(a) What is the linear width of the central fringe?

(b) What is the lateral distance between 1st and 2nd order fringes?

(c) What is the angular separation between the central maximum and the 1st order maximum?

Answer: (a) 1.3cm

(b) 1.3cm

(c) 6.33 milliradian

Diff: 3

4) What is the "small angle approximation" and for what angles is it appropriate?

Answer: sin(e) = e when e « 1 radian (I.e., 57. degrees)

Diff: 2

5) If two light waves are coherent, which of the following is NOT necessary?

A) They must have the same frequency.

B) They must have the same wavelength.

C) They must have the same amplitude.

0) They must have the same velocity.

E) They must have a constant phase difference at every point in space.

Answer: C

Diff: 2

412

Test Item File

14) A double convex lens has faces of radii 18.0 em and 20.0 em. When an object is placed 24.0 cm

from the lens, a real image is fonned 32.0 em from the lens. Determine:

(a) the focal length of the lens.

(b) the index of refraction of the lens material.

Answer: (a) 13.7 em

(b) n ~ 1.69

Diff: 3

15) A double convex (convex-convex) thin lens has radii of curvature 46. cm, and is made of glass

of index of refraction n ~ 1.60. What is the focal length?

A) 36. em B) infinite C) 46. cm D) 18. em E) 30. em

Answer: E

Di/f: 2

16) What kind of lens is it that has a power of +10 Diopters and a first surface center of curvature

in front of the lens?

A) double convex

B) double concave

C) converging meniscus

D) plano concave

E) plano convex

Answer: C

Diff:2

411

B) a whole number of wavelengths.

0) a whole number of half-wavelengths.

Test Ite11l File

6) One beam of coherent light travels path PI in arriving at point Q and another coherent beam

travels path P2 in arriving at the same point. 11these two beams are to interfere destructively,

the path difference PI - P2 must be equal to

A) an odd number of half-wavelengths.

C) zero.

Answer: A

Di!f 2

7) For what slit separation will no 1st order double-slit-fringe appear for 550. nm light?

Answer: d less than 550. nm

Diff: 2

8) In a double-slit experiment, the slit separation is 2.0 mm, and two wavelengths, 750. nm and

900. nm, illuminate the slits. A screen is placed 2.0 m from the slits. At what distance from the

central maximum on the screen will a bright fringe from one pattern first coincide with a bright

fringe from the other?

Answer: 4.5 mm

Diff: 2

9) The 4th order bright fringe due to a double slit slit appears 4.0 mm above the central fringe for

a screen 3.5 meters away using 600.nm light. When 400. nm light used for 3rd order fringe

appears at what position?

A) 1.0mm B) 2.0 mm C) 4.0 mm 0) 3.0 mm E) 5.0 nun

Answer: B

Diff2

10) Constructive interference of two coherent waves wiJI occur if the path difference is

A) 3/4A.

Answer: B

Diffl

B) 6/n. C) 3/2 A. 0) 1/4A. E) 6/4A.

413

Chapter 24 Physical Optics: TlIe Wave Natllre of Lig/II

II ) Monochromatic light from a distant source is incident on two parallel narrow slits. After

passing through the slits the light strikes a screen, as shown in the sketch.

o

What will be the nature of the pattern of light observed on the screen?

A) The screen will be most brightly illuminated at point 0, with the intensity decreasing

slowly and uniformly as you move outward from point 0.

B) There will be a series of alternating light and dark bands.

C) A rainbow of colored lines will be seen spreading out on either side of point 0.

0) There will be two bright bands of light, one in line with each slit.

E) The screen will be uniformly illuminated except for two dark bands, one in line with each

slit.

Answer: B

Oiff: 1

12) Consider 550. nm light passing through 2 narrow slits 2.10 micro-meters apart. The 1st and

2nd order fringes are 1.00 mm apart on a distant screen. How far apart are the 2nd and 3rd

order fringes?

A) 1.35 mm B) 1.00 mm C) 0.750 mm 0) 0.500 mm E) 1.74 mm

Answer: E

Oiff: 2

13) Two beams of coherent light travel different paths arriving at point P. 11the maximum

constructive interference is to occur at point P, the two beams must

A) arrive 1800 out of phase.

B) arrive 900 out of phase.

C) travel paths that differ by a whole number of wavelengths.

0) travel paths that differ by an odd number of half-wavelengths.

Answer: C

Oiff: 2

14) The experiments of what person first clearly demonstrated the wave nature of light?

A) Maxwell B) Galileo C) Newton 0) Young E) Einstein

Answer: D

Oiffl

414

B)greatest for green light.

D) greatest for blue light.

Test Item File

15) At the first maxima on either side of the central bright spot in a double-slit experiment, light

from each opening arrives

A) in phase.

B)90' out of phase.

C) 180' out of phase.

D) 45' out of phase.

E) -45' out of phase.

Answer: A

Oiff: 1

16) Why would it be impossible to obtain interference fringes in a double-slit experiment if the

separation of the slits is less than the wavelength of the light used?

A) The two slits would not emit coherent light.

B)The very narrow slits required would generate many different wavelengths, thereby

washing out the interference pattern.

C) The fringes would be too close together.

D) In no direction could a path difference as large as one wavelength be obtained, and this is

needed if a bright fringe, in addition to the central fringe, is to be observed.

Answer: D

0i/f: 2

17) In a double-slit experiment, it is observed that the distance between adjacent maxima on a

remote screen is 1cm. What happens to the distance between adjacent maxima when the slit

separation is cut in half?

A) It increases to 2 cm. B) It increases to 4 cm.

C) It decreases to 0.5 cm. D) It decreases to 0.25 cm.

Answer: A

Oiff: 2

18) The separation between adjacent maxima in a double-slit interference pattern using

monochromatic light is

A) greatest for red light.

C) the same for all colors of light.

Answer: A

Oiff:2

415

Chapter 24 Physical Optics: The Wave Nature of Light

19) At the second maxima on either side of the central bright spot in a double-slit experiment, light

from

A) each opening travels the same distance.

B) one opening travels twice as far as light from the other opening.

C) one opening travels one wavelength of light farther than light from the other opening.

0) one opening travels two wavelengths of light farther than light from the other opening.

Answer: 0

Diff: 2

20) What do we mean when we say that two light rays striking a screen are in phase with each

other?

A) When the electric field due to one is a maximum, the electric field due to the other is also a

maximum, and this relation is maintained as time passes.

B) They alternately reinforce and cancel each other.

C) They have the same wavelength.

0) They are traveling at the same speed.

Answer: A

DifJ: 2

24.2 Thin-Film Interference

1) A soap film is being viewed in white light. As the film becomes very much thinner than the

wavelength of blue light, the film

A) appears black because it reflects no visible light.

B) appears blue since all other colors are transmitted.

C) appears white because it reflects all wavelengths of visible light.

0) appears red since all other colors are transmitted.

Answer: A

Diff: 2

2) Light in a frozen block of ice reflects off the ice-air interface and undergoes a phase shift of

A) 0'. B) 90'. C) 180'. 0) 270'.

Answer: A

Diff: 1

3) Consider an oil film (n = 1.50) on water (n = 1.33) and 600. nm incident light. The minimum

film thickness for constructive interference is

416

A) 100. nm.

Answer: A

Diff: 2

B) 200. nm. C) 113. nm. 0) 150. nm.

Test Item File

4) A lens with index of refraction 1.498 is to be coated with n ~ 1.455 material so that no light is

reflected at 4365. nm (wavelength in air).

(a) What minimum thickness is required?

(b) What next shorter wavelength (in air) will also be non-reflecting with the thickness

determined in part (a)?

Answer: (a) 1.500 Ilrn

(b) 4.500 ~lm

Diff: 3

5) The colors 'on an oil slick are caused by reflection and

A) diffraction. B) interference. C) refraction.

Answer: B

Diff 1

0) polarization.

6) For an oil film on water, constructive interference occurs with a minimum oil thickness of

A) AI 4.

Answer: A

Diff:2

B) 2A. C) A I 2. 0) A I 3. E) I..

7) When a beam of light, which is traveling in glass, strikes an air boundary, there is

A) a 90' phase change in the reflected beam.

B) no phase change in the reflected beam.

C) a 180' phase change in the reflected beam.

0) a 45' phase change in the reflected beam.

E) a _45' phase change in the reflected beam.

Answer: B

Diff: 2

8) Light of wavelength 0.50 Ilm illuminates a soap film (n ~ 1.33). What is the minimum thickness

of film that will give an interference when the light is incident normally on it?

Answer: 94. nm

Diff: 2

9) A lens is coated with material of index of refraction 1.38. What thickness of coating should be

used to give maximum transmission at a wavelength of 0.53 f!m?

Answer: 96. nm

Diff:2

10) Light which reflects off a pond of water undergoes a phase shift of

A) 90'. B) 180'. C) 0'. 0) 270'.

Answer: B

Diff: 1

E) 45'.

417

Chapter 24 Physical Optics: The Wave Natllre of Light

11 ) A convex lens is placed on a flat glass plate and illuminated from above with monochromatic

red light. When viewed from above, concentric bands of red and dark are observed. What does

one observe at the exact center of the lens where the lens and the glass plate are in direct

contact?

A) a bright red spot

B) a dark spot

C) a rainbow of color

0) a bright spot that is some color other than red

Answer: B

Diff:2

12) When a beam of light, which is traveling in air, is reflected by a glass surface, there is

A) no phase change in the reflected beam.

B) a 45' phase change in the reflected beam.

C) a 180" phase change in the reflected beam.

0) a 90' phase change in the reflected beam.

E) a _45' phase change in the reflected beam.

Answer: C

Diff: 1

13) The concentric fringes, formed when a curved lens is placed on an optical flat, are called

A) Galileo circles.

B) Newton's rings.

C) Young's rings.

0) Faraday's circles.

E) Maxwell circles.

Answer: H

Diff:l

14) A glass plate 2.5 em long is separated from another glass plate by a strand of someone's hair

(diameter 0.010 mm). How far apart are the adjacent interference bands when viewed with

light of wavelength 600 nm?

Answer: 0.75 mm

Dif!: 2

15) After a rain, one sometimes sees brightly colored oil slicks on the road. These are due to

A) interference effects.

H) polarization effects.

C) diffraction effects.

0) selective absorption of different wavelengths by oil.

E) birefringence.

Answer: A

Difj: 1

418 I

Test Item File

16) In terms of the wavelength of light in soapy water, what is the minimum thickness of soap film

that will reflect a given wavelength of light?

A) one-fourth wavelength

B)one-half wavelength

C) one wavelength

0) there is no minimum thickness

E) two wavelengths

Answer: A

Oifj: 2

17) A soap bubble has an index of refraction of 1.33.What minimum thickness of this bubble will

ensure maximum reflectance of normally incident 530. nm wavelength light?

Answer: 99.6nm

Oifj: 2

18) In terms of the wavelength of light in magnesium fluoride, what is the minimum thickness of

magnesium fluoride coating that must be applied to a glass lens to make it non-reflecting for

that wavelength? (The index of refraction of magnesium fluoride is intermediate to that of glass

and air.)

A) one-fourth wavelength B) two wavelengths

C) there is no minimum thickness 0) one-half wavelength

Answer: A

Oifj: 2

19) We have seen that two monochromatic light waves can interfere constructively or

destructively, depending on their phase difference. One consequence of this phenomena is

A) the colors you see when white light is reflected from a soap bubble.

B) a rainbow.

C) the appearance of a mirage in the desert.

0) the way in which polaroid sunglasses work.

E) the formation of an image by a converging lens, such as the lens in your eye.

Answer: A

Oi!!: 2

24.3 Diffraction

1 ) A diffraction grating has 6000. lines per centimeter ruled on it. What is the angular separation

between the second and the third orders on the same side of the central order when the grating

is illuminated with a beam of light of wavelength 550. nm?

Answer: 40S

Oiff:2

419

Chapter 24 Physical Optics: The Wave Nature of Light

2) Discuss what you see viewing a distant street light through a thin curtain (at night).

Answer: One expects to see a "cross" pattern of light which turns out to be the diffraction pattern

of the many crossed threads forming multiple two dimensional openings. Note that

where the curtain is folded at an angle the pattern enlarges because the projected

opening in the line of sight is less and the diffracted angle larger. Close attention will

show a colored pattern since large wavelengths are diffracted greater.

Oiff:3

3) A single-slit experiment uses light of wavelength 720. nm with a slit separation of 0.250 mm

and a screen placed 2.7m away.

(a) What is the angular width of the central fringe?

(b) What is the linear width of the central fringe on the screen?

(c) What is the linear distance on the screen between the central maximum and the 1st order

maximum?

Answer: (a) 5.76 x 10-3 radian

(b) 1.6 cm

(c) 1.2cm

Oiff: 3

4) The condition 2d sin(8) = nf. for X-ray diffraction maxima is attributed to

A) Young. B) Rayleigh. C) Bragg. D) Brewster.

Answer: C

Oiff: 2

E) Land.

5) How many orders are in the spectra formed by a grating with 3000. lines/ cm illuminated by

red light of wavelength 600. nm?

A)l B)5 qo m4 m3

Answer: B

Oiff:2

6) In a diffraction experiment, light of 600. nm wavelength produces a first-order maximum 0.350

mm from the central maximum on a distant screen. A second monochromatic source produces

a third-order maximum 0.870mm from the central maximum when it passes through the same

diffraction grating. What is the wavelength of the light from the second source?

Answer: 497. nm

Oiff: 2

420

•I

Test Item File

7) Consider two diffraction gratings; one has 4000 lines per cm and the other one has 6000 lines

per cm.

A) The 4000-line grating produces the greater dispersion.

B) Both gratings produce the same dispersion, but the orders are sharper for the 4000-line

grating.

C) Both gratings produce the same dispersion, but the orders are sharper for the 6000-line

grating.

0) The 6000-line grating produces the greater dispersion.

Answer: 0

Diff: 2

8) How do interference and diffraction differ? How are they similar?

Answer: Interference is the addition of a finite number (usually small number) of coherent waves

whereas diffraction involves an infinite (uncountably large) number of waves.

Diff: 3

9) A single slit, which is 0.0500 mm wide, is illuminated by light of 550. run wavelength. What is

the angular separation between the first two minima on either side of the central maximum?

Answer: 0.630"

Diff 2

10) Consider a diffraction grating with 7000. lines/ cm with a screen 2.50 m away and 440. run

wavelength light.

(a) How many side maxima would be observed on one side of the central maximum?

(b) What is the linear distance between the 1st and 2nd maxima?

Answer: '(a) 3

(b) 1.15 meters

Diff: 3

11 ) Consider two diffraction gratings with the same slit separation, the only difference being that

one grating has 3 slits and the other 4 slits. If both gratings are illuminated with a beam of the

same monochromatic light

A) the grating with 3 slits produces the greater separation between orders.

B) the grating with 4 slits produces the greater separation between orders.

C) both gratings produce the same separation between orders.

0) both gratings produce the same separation between orders, but the orders are better

defined with the 4-slit grating.

Answer: D

Diff 2

12) When red light illuminates a grating with 7000. lines per centimeter, its second maximum is at

62.4°. What is the wavelength of the light?

Answer: 633. nm

Diff: 2

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Chapter 24 Physical Optics: The Wave Natllre of Light

13) Single-slit diffraction is characterized by

A) a distance between fringes which is independent of wavelength.

B) decreasing angular separation of fringes as the order (m) increases.

C) narrowing of diffraction pattern as slit width is reduced.

D) rapid decrease in intensity of higher order fringes.

Answer: 0

Di/f: J

14) Why does light seem to go straight through an open doorway whereas sound seems to spread

out when it goes through the same doorway?

Answer: It has to do with the relative sizes of their wavelengths. The wavelength of light is«

opening size so very small diffraction; sound wavelengths are» opening so diffraction

is significant.

Diff: 2

15) The condition for interference maxima for a diffraction grating is identical to that for

A) a narrowing single slit. B) a double slit.

C) a thin film. D) a wide single slit.

Answer: B

Diff: J

24.4 Polarization

1 ) LCDs (Liquid Crystal Displays) such as those on most calculators (probably yours) are based

on the physical phenomena called

A) diffraction.

B) Rayleigh scattering.

C) birefringence.

D) dichroism.

E) polarization.

Answer: E

Diff:l

2) A ray of light traveling in water (n = 1.33) hits a glass surface (n = 1.50).At what angle, with the

surface, must the incident ray be in order that the polarization of the reflected ray is the

greatest?

422

A) 53.1"

Answer: D

Diff:2

B) 33.7" C) 36.9" D) 41.6" E) 48.4"

I

Test Item File

3) Light preceeds through three polarizing sheets. Unpolarized light enters the 1st sheet and the

resultant vertically polarized beam continues through the 2nd and 3rd. The 2nd sheet has its

transmission axis at 50.' with respect to the 1st, and the 3rd is at 70.' with respect to the 1st.

(a) What percent of the original intensity emerges from filter #1?

(b) What percent of the original intensity emerges from filter #2?

(c) What percent of the original intensity emerges from filter #3?

(d) If filter #2 has its transmission axis changed t030.', what % intensity now emerges from the

3rd filter?

Answer: (a) 50.%

(b) 21.%

(c) 18.%

(d) 22.%

Oiff: 3

4) A material which has the ability to rotate the direction of polarization of linearly polarized

light is said to be

A) circularly polarized.

B) birefringent.

C) optically active.

D) dichroic.

E) diffraction limited.

Answer: C

Oiff: 1

5) At what angle, with the surface, must light strike glass (refractive index 1.6) in order to

completely polarize the reflected ray?

A)4.0' B)86.' C)34.' D) 11.' E)56.'

Answer: A

Oiff 2

6) Another name for the POLARIZING ANGLE is the

A) Moles angle. B) refracted angle. C) Brewster angle.

Answer: C

Oiff: 1

D) Land angle.

•I

7) Liquid Crystal Displays (LCDs) depend upon which of the following for their operation?

A) coherence

B) polarization

C) diffraction

D) dichroism

E) thin film interference

Answer: B

Oiff:l

423

Chapter 24 Physical Optics: The Wave Naillre of Light

8) The polarization of sunlight is greatest at

A) sunrise.

C) both sunrise and sunset.

Answer: C

Diff 1

B) midday.

D) sunset.

9) Sunlight reflected from the surface of a lake

A) is unpolarized.

B) tends to be polarized with its electric field vector parallel to the surface of the lake.

C) has undergone refraction by the surface of the lake.

D) tends to be polarized with its electric field vector perpendicular to the surface of the lake.

E) is totally polarized.

Answer: B

Diff 2

10) An ideal polarizer is placed in a beam of unpolarized light and the intensity of the transmitted

light is 1.000. A second ideal polarizer is placed in the beam with its referred direction rotated

40" to that of the first polarizer. What is the intensity of the beam after it has passed through

both polarizers?

A) 0.7661 B) 0.4131 C) 0.5871 D) 0.6431 E) 0.5000

Answer: C

Diff: 2

11) For a beam of light, the direction of polarization is defined as

A) the beam's direction of travel.

B) the direction of the electric field's vibration.

C) the direction of the magnetic field's vibration.

D) the direction that is mutually perpendicular to the electric and magnetic field vectors.

Answer: B

Diff: 1

12) A polarizer (with its preferred direction rotated 30" to the vertical) is placed in a beam of

unpolarized light of intensity 1. After passing through the polarizer, the beam's intensity is

A) 0.2501. B) 0.7501. C) 0.5001. D) 0.8661. E) 0.5000.

Answer: C

Diff:2

13) What is the Brewster's angle for light traveling in vacuum and reflecting off a piece of glass of

index of refraction 1.52?

424

A) 48.9"

Answer: 0

Diff: 2

B) 33.3" D) 56.7" E) 41.1"

••• !

Test Item File

14) Two emerging beams of light produced by a birefringent crystal

A) are at different frequencies.

B) will produce an interference pattern when recombined.

C) are polarized in the same direction.

D) are polarized in mutually perpendicular directions.

E) are at 90' with respect to one another.

Answer: 0

Oif! 1

15) A beam of light passes through a polarizer and then an analyzer. In this process, the intensity

of the light transmitted is reduced to 10%of the intensity incident on the analyzer. What is the

angle between the axes of the polarizer and the analyzer?

Answer: 71.6'

Oi!!: 2

16) Suppose that you take the lenses out of a pair of polarized sunglasses and place one on top of

the other. Rotate one lens 9Cf with respect to the normal position of the other lens. Early in the

morning, look directly overhead at the sunlight coming down. What would you see?

A) The tenses would look completely dark, since they would transmit no light.

B) You would see some light, and the brightness would be a function of how the lenses were

oriented with respect to the incoming light.

C) You would see light with intensity reduced to about 50% of what it would be with one

lens.

D) You would see some light, and the intensity would be the same as if you had looked

through only one lens.

E) You would see some light, and the intensity would be greater than if you looked through

only one lens.

Answer: A

Oiff:l

24.5 Atmospheric Scattering of Light

1) If sunlight of color B is scattered through an angle 16 times greater than sunlight of color A,

then the wavelength of color Bis

A) twice that of color A.

B) 1/2 that of color A.

C) 16 times that of color A.

D) 1/16 that of color A.

E) 1/4 that of color A.

Answer: B

Oiff: 2

425

Chapter 24 Physical Optics: The Wave Na/llre of Ligh/

2) The sky appears "blue" because of

A) Bragg's Law.

B) Rayleigh scattering.

C) Brewster's polarization.

0) dichroism.

E) birefringence.

Answer: B

Oiff 1

3) On a clear day, the sky appears to be more blue toward the zenith (overhead) than it does

toward the horizon. This occurs because

A) the atmosphere is denser higher up than it is at the earth's surface.

B) the temperature of the upper atmosphere is higher than it is at the earth's surface.

C) the sunlight travels over a longer path at the horizon, resulting in more absorption.

0) the atmosphere is more reddish over the ocean.

Answer: C

Oiff:l

4) Rayleigh scattering would have 400. nm light be scattered how many times as much as 800. nm

light?

A) 32 B) 4 C) 8 0) 2 E) 16

Answer: E

Oiff:2

426 I

Chapter 25 Vision and Optical Instruments

25.1 The Human Eye

1 ) A nearsighted man wears -3.00 0 lenses. With these lenses, his corrected near point is 25.0 cm.

What is his uncorrected near point?

Answer: 14.3cm

Diff: 2

2) A farsighted person has a near point of 50. cm. In order to see objects as close as 25. cm what

power lens should be prescribed:

(a) for contact lenses?

(b) for eyeglasses worn 2.0 cm from the eye?

Answer: (a) 6.0 Oiopters

(b) 6.40iopters

Di/f: 3

3) Explain how the eye and a camera differ in adjusting for a change in focus.

Answer: The camera lens has a fixed focal length so it adjusts focus by varying the lens-film

distance. The eye has an essentially fixed lens-retina distance so the focal length of the

lens is varied by changing the lens curvature (by muscular action).

Diff:2

4) A hyperopic eye can focus on objects which are 75. cm and farther. What POWER and what

FOCAL LENGTH spectacles should be prescribed so it can see objects 25. cm and farther from

the eye? (Assume negligible distance between spectacles and eye.)

Answer: POWER = 2.7 Oiopters; f = 38. cm

Dif/: 3

5) A nearsighted person has a far point of 50. cm for one eye and 150.cm for the other. What

power contacllenses allow the person to see distant objects?

Answer: -2.00 and -0.667 0 respectively

Diff: 3

6) Astigmatism is usually due to

A) the cornea or lens being out of round.

B) accommodation.

C) myopia.

0) missing rods.

E) hyperopia.

Answer: A

Dif/: 1

427

Chapter 25 Vision and Opticaiinstruments

7) The near point of a farsighted person is 100 cm. She places reading glasses close to her eye, and

with them she can comfortably read a newspaper at a distance of 25 em. What lens power is

required?

A) +2.50 B) +3.00 C) -2.0 0 D) +3.20 E) -2.5 0

Answer: B

Diff: 2

8) When the cornea or lens is out of round, the eye suffers from

A) blindness.

B) myopia.

C) presbyteria.

D) astigmatism.

E) hyperopia.

Answer: 0

Diff: 1

9) Farsightedness can usually be corrected with

A) cylindrical lenses.

C) diverging lenses.

Answer: 0

Diff: 2

B) achromatic lenses.

D) converging lenses.

10) If a person's eyeball is too long from front to back, the person is likely to suffer from

A) spherical aberration. B) nearsightedness.

C) farsightedness. D) astigmatism.

Answer: 0

Diff: 1

11) If the human eyeball is too short from front to back, this gives rise to a vision defect that can be

corrected by using

A) convex-convex eyeglasses.

B) concave-convex eyeglasses.

C) cylindrical eyeglasses.

D) contact lenses, but no ordinary lenses.

E) shaded glasses (I.e., something that will cause the iris to dilate more).

Answer: A

Diff: 2

428 I

Test 1Iem File

12) If a person's eyeball is too short from front to back, the person is likely to suffer from

A) astigmatism.

B) spherical aberration.

C) farsightedness.

D) nearsightedness.

E) chromatic aberration.

Answer: C

Diff 1

13) Lisa Ann is nearsighted with a near point of 75. em.

(a) What FOCAL LENGTH is this?

(b) What POWER lens is needed to correct her nearsightedness (assuming distance from lens

to eye is negligible)?

Answer: (a) -75. em

(b) -1.33 Diopters

Diff: 3

14) In which of the following ways is a camera different from the human eye?

A) The camera always forms a real image, the eye does not.

B) The camera always forms an inverted image, the eye does not.

C) The camera utilizes a fixed focal length lens, the eye does not.

D) For the camera, the image magnification is greater than one, but for the eye the

magnification is less than one.

E) The camera cannot focus on objects at infinity but the eye can.

Answer: C

Diff: 1

15) The near point with age usually

A) steadily decreases.

C) steadily increases.

Answer: C

Diff:l

B) approaches 25. em.

D) increases and then decreases.

16) Rays that pass through a lens very close to the lens axis are more sharply focused than those

that are very far from the axis. The inability of a lens to sharply focus off-axis rays is called

spherical aberration. This effect helps us to understand why

A) we become more farsighted as we grow older.

B) we become more nearsighted as we grow older.

C) we can see only in black and white in dim light.

D) it is easier to read in bright light than in dim light.

E) a moving object is more readily detected than a stationary one.

Answer: D

Diff 2

429

Chapter 25 Visioll alld Optical/llstrumellts

17) A nearsighted person has a near point of 12. cm and a far point of 17. cm. If the lens is 2.0 cm

from the eye:

(a) what lens power will enable this person to see distant objects clearly?

(b) what then will be the new near point?

Answer: (a) -6.7 0

(b) 30. cm in front of the lens

Oiff: 3

18) A fish's eye is well-suited to seeing under water, but what can you say about his vision if he is

taken out of water?

A) His acuity (sharpness of vision) would be greater.

B) He would suffer from astigmatism.

C) He would be nearsighted.

0) He would be farsighted.

E) His vision would be limited to a cone of half-angle of about 49'.

Answer: C

Oiff: 2

19) What power lens is needed to correct for farsightedness where the uncorrected near point is 75

em?

A) -2.670

Answer: B

Oi!!: 2

B) +2.670 C) +5.33 0 0) -5.33 0 E) +1.00 0

20) Nearsightedness can usually be corrected with

A) achromatic lenses.

C) converging lenses.

Answer: B

Oiff:l

B) diverging lenses.

0) cylindrical lenses.

430

21 ) The principal refraction of light by the eye occurs at the

A) cornea. B) lens. C) sclera.

Answer: A

0iff: 1

22) "30/40 vision" is a measure of

A) eyeball size.

B) chromatic aberration.

C) visual acuity.

0) astigmatism.

E) the resolution of the eye.

Answer: C

Oiff: 1

0) iris. E) retina.

I

Test Item File

23) A person uses corrective glasses of power -8.5 D.

(a) Is this person nearsighted or farsighted?

(b) If the glasses are worn 2.0 cm from the eye, what is the person's far point without glasses?

Answer: (a) nearsighted

(b) 14. em

Diff: 2

24) What power lens is needed to correct for nearsightedness where the uncorrected far point is 75

em?

A) -1.33 D

Answer: A

Diff: 2

B) +1.33 D C) -0.75 D D) +0.75 D E) -1.00 D

25) The aperture in a camera plays the same role as what in the eye?

A) retina B) vitreous humor C) iris

Answer: C

Diff 1

D) cornea

26) Doubling the fCnumber of a camera lens (e.g., from 1/16 to f/32) will change the intensity of

light received by the film by what factor?

A)4 B)1/2 C)l D)2 E)1/4

Answer: E

Diff: 2

Choose from the followillg:

(a) composed of microscopic glassy fibers that slide over each other

(b) a jelly-like substance that fills most of the eye

(c) a circular diaphragm

(d) relays signals to the brain

(e) the central hole

(I) a curved transparent tissue where light first enters the eye

(g) photosensitive receptor cells of which the retina is composed

(h) a light-sensitive surface, upon which the image falls

27) Match the iris to the best description above.

Answer: (c) a circular diaphragm

Diff 1

28) Match vitreous humor to the best description above.

Answer: (b) a jelly-like substance that fills most of the eye

Diff: 1

29) Match retina to the best description above.

Answer: (h) a light-sensitive surface, upon which the image falls

Diff: 1

431

Chapter 25 Vision and Optical Instruments

30) Match optic nerve to the best description above.

Answer: (d) relays signals to the brain

Diff: 1

31 ) Match cornea to the best description above.

Answer: (f) a curved transparent tissue where light first enters the eye

Diff:l

32) Match pupil to the best description above.

Answer: (e) the central hole

Diff: 1

33) Match rods and cones to the best description above.

Answer: (g) photosensitive receptor cells of which the retina is composed

Diff: 1

34) Match lens to the best description above.

Answer: (a) composed of microscopic glassy fibers that slide over each other

Dif/: 1

25.2 Microscopes

1) Angular magnification of a magnifying glass is largest when the image is at

A) the near point.

B) the focal point.

C) the pupil of the eye.

D) infinity.

E) the far point.

Answer: A

Diff:l

2) Pat is viewing the moon with her new telescope. She is using a 10.mm eyepiece. Which of the

following eyepieces will double the magnification?

A) 40. Diopter

B) 8.mm

C) 200. Diopter

D) 12.mm

E) 5. Diopter

Answer: C

Diff: 2

432 I

Test Item File

3) What is the maximum angular magnification of a magnifying glass of focal length 10 em?

(Assume the near point is at 25 em.)

Answer: 2.5

Diff:2

4) Kelli examines her new ruby ring with the jeweler's "loop". The ruby appears 7.0 times larger.

If her near point is 35. em, what is the focal length of the lens?

A) 36.mm B) 70. mm C) 67. mm 0) 42. mm E) 50. mm

Answer: E

Diff: 2

5) A magnifying glass of focal length 150.mm is used to examine an old manuscript.

(a) What is the maximum magnification given by the lens?

(b) What is the magnification for relaxed eye-viewing (image at infinity)?

Answer: (a) 2.67

(b) 1.67

DifJ: 3

6) Consider a magnifying glass with a power of 3.0 O.

(a) What is the maximum magnification for a person with a near point of25. em?

(b) What is the magnification when viewing with a relaxed eye?

Answer: (a) 1.75

(b) 0.75

DifJ: 3

25.3 Telescopes

1 ) Jennifer bought a 7 x 25 pair of binoculars for observing baseball. The 25 describes the

A) aperture in em.

B) aperture in mm.

C) fI number.

0) magnification.

E) (f(number)-l.

Answer: B

Diff: J

2) Which of the following binoculars would be best for observing very faint comets among the

stars?

-\I

A) 7 x 60

Answer: A

Diff: J

B) 12 x 50 C) 5 x 20 0) 10 x 35 E) 8 x 50

433

Chapter 25 Vision mid Optiea/Instruments

3) Mary builds a simple magnifying telescope using two lenses of focal length 80. cm and 5.0 cm.

The respective diameters are 60. mm and 10.mm. How many degrees wide does the moon

appear through the telescope if it appears only 1/2 degree wide with the "naked eye"?

Answer: 8 degrees wide (16 times larger)

Oilf 2

4) Which cones on the eye are most sensitive to light?

A) red B) infrared C) green

Answer: C

Oiff 1

D)UV E) blue

5) Consider the image formed by a refracting telescope. Suppose an opaque screen is placed in

front of the lower half of the objective lens. What effect will this have?

A) The top half of the image will be blacked out.

B) The lower half of the image will be blacked out.

C) The entire image will be blacked out, since the entire lens is needed to form an image.

D) The image will appear as it would if the objective were not blocked, but it will be dimmer.

E) There will be no noticeable difference in the appearance of the image with the objective

partially blocked or not.

Answer: D

0if/: 3

6) A student wishes to build a telescope. She has available an eyepiece of focal length -5.0 cm.

What focal length objective is needed to obtain a magnification of lOx?

Answer: 50. cm

0iff:2

7) An astronomical telescope has 150. cm between eyepiece and objective lenses and an angular

magnification of 75.

(a) What is the focal length of the objective lens?

(b) What is the power of the eyepiece?

Answer: (a) 148.cm

(b) 50. Diopters

Oiff3

8) The objective of a telescope has a focal length of 100.cm and its eyepiece has a focal length of

50.0 mm. What is the magnification of this telescope when viewing an object at infinity?

A) 20. B) 500. C) 0.05 D) 40. E) 2.00

Answer: A

Oi!!: 2

434

•i

Test Item File

9) How is it possible for the angular magnification to be large and, at the same time, for the lateral

magnification to be small? Give an example.

Answer: The angular mag. is the ratio of ANGULAR size looking through the instrument

compared to the angular size without. The lateral magnification is the ratio of the actual

size of image compared to that of the object. The two magnifications are comparing

different things. As an example: the moon may appear larger (in angle) through a

telescope but the image is certainly smaller than the moon itself.

Oiff:3

10) Many Earth-based telescopes are larger than the Hubble Space Telescope, so what justifies the

great expense of a "space-based" instrument?

Answer: The atmosphere distorts images and usually limits resolution. A telescope in the vacuum

of space can achieve its intrinsic resolution and yield pictures with relatively high detail.

It also can use parts of the spectrum which get absorbed by the atmosphere.

Oilf 2

11) All of the following are reflecting telescopes, except

A) Newtonian.

B) Yerkes.

C) Cassegrain.

D) Hale.

E) the 10.m Keck.

Answer: B

Oiff: 1

12) An objective lens of a telescope has a 1.90m focal length. When viewed through this telescope,

the moon appears 5.25 times larger than normal. How far apart are the objective lens and the

eyepiece when this instrument is focused on the moon?

Answer: 2.26m

Oiff: 2

13) For relaxed viewing (microscope or telescope) the eyepiece is adjusted to place the image at

A) the near point.

B) the focal point.

C) the pupil of the eye.

D) infinity.

E) the radius of curvature.

Answer: 0

Oiff:l

435

Chapter 25 Vision and Optical Instruments

14) A telescope has an angular magnification of 250. when operated with a 20. mm eyepiece. What

is the focal length of the objective?

A) 5.0 cm B) 25. meters C) 5000. cm 0) 5.0 meters E) 2.5 m

Answer: 0

DifJ: 2

15) An astronomical telescope operates at f/12 and has an aperture of 36. cm. What is its angular

magnification when used with a 2.0 em eyepiece?

A) 2.1 x 102 B) 1.4 x 102 C) 6.0 0) 72 E) 18

Answer: A

DifJ: 2

16) A refracting telescope has an eyepiece of focal length -80. mm and an objective of focal length

36. cm. What is the magnification?

Answer: 4.5 x

Diff: 2

17) A terrestrial telescope has focal lengths of 15.mm, 7.5 em, and 120. cm for eyepiece, erecting

lens, and objective respectively.

(a) What is the magnification of the telescope?

(b) Is this an angular magnification or a lateral size magnification?

(c) What is its length (objective to eyepiece distance)?

Answer: (a) 80.

(b) angular mag.

(c) 152. em

Diff: 3

18) Christie bought a 9 x 50 pair of binoculars for stellar observing. The 9 is the

A) f/ number.

B) aperture in em.

C) angular magnification.

D) aperture in mm.

E) f/ number-1

Answer: C

Diff: 1

19) The first important discoveries made with a telescope (in 1609)were done by

A) Cassegrain.

B) Newton.

C) Hale.

D) Galileo.

E) Stonehenge observers.

Answer: 0

Diff: 1

436 I

I

Test lIem File

20) Both the microscope and the telescope make the object appear much larger. Why are these two

instruments designed differently (e.g., why are the equations for magnification quite

different)?

Answer: The object for a telescope is at infinity whereas the object of a microscope is very close to

the objective. The ray diagrams and the designs are thus quite different.

0iff:3

25.4 Diffraction and Resolution

1 ) If the pupil diameter of the dark-adapted eye is 5.0 mm, what is the maximum distance at

which two point sources of light that are 3.0 mm apart can still be resolved?

Answer: 25. m

Oiff: 2

2) What is the resolution limit at 400. nm, due to diffraction, of the Hubble Space Telescope which

has an aperture of 2.4 meters?

Answer: 2.0 x 10-7 radians ~ 42. milli-arc-second

Oiff: 2

3) The resolution limit of a circular aperture telescope is

A) inversely proportional to wavelength.

B) proportional to frequency of light.

C) less than that of a square aperture whose diagonal equals the diameter.

0) inversely proportional to aperture size.

Answer: 0

Oiff: 1

4) A person gazes at a very distant light source. If she now holds up two fingers, with a very

small gap between them, and looks at the light source, she will see

A) a series of bright spots.

B) the same thing as without the fingers, but dimmer.

C) a hazy band of light varying from red at one side to blue or violet at the other.

0) a sequence of closely spaced bright lines.

Answer: 0

Oiff: 2

5) The world's largest refracting telescope is operated at the Yerkes Observatory in Wisconsin. It

has an objective of diameter of 1.02 m. Suppose such an instrument could be mounted on a spy

satellite at an elevation of 300. km above the surface of the Earth. What is the minimum

separation of two objects on the ground if their images are to be clearly resolved by this lens?

(Assume an average wavelength of 0.55 ~m for white light.)

Answer: 0.20 m

Oiff: 2

437

Chapter 25 Visioll alld Optical hlstrllmellts

6) What is the minimum distance of two points on the moon that can be just resolved by the Keck

10. meter telescope in Hawaii (use a wavelength of 600. nm, lunar distance of 380. thousand

Km):

(a) if there were no atmosphere?

(b) if the atmosphere limits resolution to 0.2 arc-sec?

Answer: (a) 28. meters

(b) 0.4 Km

Diff 3

7) In single-slit diffraction

A) the central maximum is about as wide as the other maxima.

B) the central maximum is much narrower than the other maxima.

C) the central maximum is about twice as wide as the other maxima.

D) the intensities of successive maxima are roughly the same, falling off only gradually as one

goes away from the central maximum.

E) the slit width must be less than one wavelength for a diffraction pattern to be apparent.

Answer: C

Diff 2

8) Assuming a pupil diameter of 3. mm, what is the angular resolution of the human eye at the

middle of the visible spectrum (550. nm)?

A) 0.8 degree

B) 0.8 arc-minute

C) 0.2 degree

D) 0.2 arc-minute

E) 2. milliradian

Answer: B

Diff:2

9) In which of the following is diffraction NOT exhibited?

A) viewing a light source through a small pinhole

B) examining a crystal by X-rays

C) resolving two nearby stars with a telescope

D) using a microscope under maximum magnification

E) determining the direction of polarization with a birefringent crystal

Answer: E

Diff:l

10) Discuss a similarity and a difference between the spectrum formed by a diffraction grating (a

large number of slits) and that formed by just a double slit.

Answer: The maxima of both satisfy d sin(8) = nA, but the fringes formed by the grating are much

sharper (narrow).

Diff:3

438

Il=

I,-

I

I

Test Item File

11 ) What is the smallest angular separation (in minutes of arc) for which two point sources can be

resolved using 30.0 mm microwaves and a 3.00 m diameter radar dish?

Answer: 41.9'

Oiff:2

12) Using the Rayleigh Criterion for 400. nm light, what sized space telescope could have 1.0 krn

resolution of objects on Mars when viewed from above the Earth? (assume an Earth-Mars close

distance of 80. million krn)

A) 3.9 m B) 39. m C) 3.9 km D) 0.39 km E) 39. krn

Answer: B

Oif!: 2

13) An important reason for using a very large diameter objective in an astronomical telescope in

space is

A) to increase the magnification.

B) to increase the resolution.

C) to increase the width of the field of view.

D) to form a virtual image, which is easier to look at.

E) to increase the depth of the field of view.

Answer: B

Oiff 1

14) Railroad tracks are spaced about 1.7m apart. On a clear day, how high could a plane fly before

the pilot is no longer able to resolve the two separate rails? (Assume that the diameter of the

pupil is about 3. mm and take as the wavelength that to which the eye is most sensitive, namely

530. nm.)

Answer: about 8. krn

Oiff: 2

15) The resolving power of a microscope refers to the ability to

A) distinguish objects of different colors.

B) form clear images of two points that are very close together.

C) form a very large image.

D) form a very bright image.

E) form a very microscopic image.

Answer: B

Oiff: 1

439

Chapter 25 Visioll alld Optical Illstrumellts

16) Radio waves are diffracted by large objects such as buildings, whereas light is not. Why is this?

A) The wavelength of light is much smaller than the wavelength of radio waves.

B) Radio waves are unpolarized, whereas light is plane polarized.

C) Radio waves are coherent, and light is usually not coherent.

0) The wavelength of light is much greater than the wavelength of radio waves.

Answer: A

Diff 2

17) If the diameter of a radar dish is doubled, what happens to its resolving power assuming that

all other factors remain unchanged?

A) It quadruples.

B) It doubles.

C) It halves.

0) It is reduced to one-quarter its original value.

E) It is reduced to one-eighth its original value.

Answer: B

Diff 1

18) A single slit, which is 0.050 mm wide, is illuminated by light of 550. nm wavelength. What is

the angular separation between the first two minima on either side of the central maximum?

Answer: 0.63°

Diff:2

19) With what color light would you expect to be able to see the greatest detail when using a

microscope?

A) blue, because it is brighter

B) red, because of its long wavelength

C) blue, because of its shorter wavelength

0) red, because it is refracted less than other colors by glass

E) The color makes no difference in the resolving power, since this is determined only by the

diameter of the lenses.

Answer: C

Diff: 2

20) Assuming the film used has uniform sensitivity throughout the visible spectrum, in which of

the following cases would you be able to best distinguish between two closely spaced stars?

(The lens referred to is the objective lens of the telescope used.)

A) Use a large lens and blue light. B) Use a small lens and red light.

C) Use a large lens and red light. 0) Use a small lens and blue light.

Answer: A

Diff: 1

440

l=

l-

I

'..

Test Item File

21 ) Consider a camera with a 20. em diameter lens recording images at 600. nm wavelength.

(a) What is the angular resolution limit?

(b) What is the minimum sized features which can be resolved on Mars (at a distance of 9.0<

107 km) with this lens?

Answer: (a) 3.7 x 10-6 radian = 0.75 arc sec

(b) 3.3 x 102 km

Diff: 3

25.5 Color

1) If you wear green sunglasses and look at equations written in white chalk on a chalkboard, you

would see the chalk as

A) green. B) white. C) red. D) black. E) yellow.

Answer: A

Diff:l

2) When a hologram is illuminated with a beam of coherent light, it produces

A) both a real and a virtual image.

B) only a real image of the object.

C) only a virtual image of the object.

Answer: A

Diff: 2

3) Color blindness is caused by

A) damage to the retina.

B) cataracts.

C) a missing cone-type.

D) a missing rod-type.

E) lack of melanin.

Answer: C

Diff: 1

4) Black light

A) has a frequency higher than violet light.

B) has a frequency between red light and violet light.

C) has a frequency lower than red light.

Answer: A

Diff:l

441

Chapter 25 Vision and Optical Instruments

5) Color TV is produced by

A) cyan, magenta, and yellow beams of electrons merging at the screen.

B) red, green, and blue beams of electrons merging at the screen.

C) A single beam of electrons striking a triad of phosphors of red, green, and blue.

D) A single beam of electrons striking a triad of phosphors of cyan, magenta, and yellow.

Answer: C

Diff: 1

442

6) If a red filter were placed in front of blue dungarees, you would see

A) white. B) green. C) blue. D) red.

Answer: E

Diff: 1

7) Mixing pigments is anexample of the _ method of color production.

A) complementary

B) subtractive

C) additive

D) composite

E) "tri-color"

Answer: B

Diff: 1

E) black.

I

Chapter 22 Reflection and Refraction of Light

22.1 Wave Fronts and Rays

1 ) Which of the following is a false statement?

A) All points on a given wave front have the same phase.

B) Rays are always perpendicular to wave fronts.

C) All wave fronts have the same amplitude.

0) The spacing between adjacent wave fronts is one-half wavelength.

Answer: C

Oiff: 1

2) The use of wave fronts and rays to describe optical phenomena is called

A) wave optics. B) geometrical optics.

C) dispersive optics. 0) quantum optics.

Answer: B

Oiff:l

22.2 Reflection

1) A laser beam strikes a plane reflecting surface with an angle of incidence of 37'. What is the

angle between the incident ray and the reflected ray?

Answer: 74.0

Oiff: 2

2) The Apollo missions left mirrors on the moon so laser beams could be reflected off the moon

from the Earth. The moon wobbles so a regular mirror would seldom be lined up correctly, yet

the mirrors are always correctly aligned. How do you suppose NASA accomplished this?

Answer: They used "comer reflectors" shaped like the vertex of a cube. A ray of light hitting such

a mirror will return along the incident direction.

Oiff:3

3) The angle of incidence can vary between zero and

A) 1 radian.

B) ,,/2 radians.

C) " radians.

0) 2" radians.

E) 3,,/2 radians.

Answer: B

Oiff: 1

374

3) Resonance in a series RLC circuit occurs when

A) (XL - Xc) 2 is equal to R2.

C) Xc is greater than XL.

Answer: 0

Dif!: 2

B)XL is greater than XC.

D) XL equals XC.

Test Item File

r

4) A 120. mH inductor is in series with a 20. Q resistor and a variable capacitor (0.110 I'F to 0.400 I'

F).

(a) What is the range of resonant frequencies possible?

(b) Connected to a 24. volt rms source, what current flows at resonance?

Answer: (a) 0.726 KHz to 1.39 KHz

(b) 1.20 A

Diff: 3

373

4) Law of reflection is which of the following?

A) 8i = 8r

B) (I'2/AI) (sin81/sin82) = I

C) = (d/n)

0) A/'m

E) arc sin(n2/nl)

Answer: A

Diff: 1

Test Item File

5) When light shines on the surface of this page, the reflection is

A) dilluse. B) total.

Answer: A

Diff: 1

C) specular.

6) Reflection all a shiny mirror is called

A) specular reflection.

C) irregular reflection.

Answer: A

Diff: 1

B) diffuse reflection.

0) internal reflection.

I

7) The angle of incidence

A) must equal the angle of reflection.

B) is always less than the angle of reflection.

C) may be greater than, less than, or equal to the angle of reflection.

0) is always greater than the angle of reflection.

Answer: A

Diff:l

22.3 Refraction

1) A ray of light, which is traveling in a vacuum, is incident on a glass plate (n = ng). For

increasing angles of incidence, the angle of refraction

A) increases, approaching the limiting value of 9(1'.

B) decreases, approaching the limiting value of zero degrees.

C) increases, approaching the limiting value of sin-l(l / ng) degrees.

0) increases, approaching the limiting value ofsin-1(ng) degrees.

Answer: C

Dif!' 2

375

Chapter 22 Reflection and Refraction of Light

2) Which of the following is equivalent to Snell's Law? (v is light velocity)

A) vI / V2= sin(81) sin(82)

B) vI tan(81) = v2 tan(82)

C) VI / v2 = sin(82) / sin(81)

0) vI / V2= sin(81) / sin(82)

E) n1 sin(82) = n2 sin(81)

Answer: 0

0iff:2

3) A light beam having a wavelength of 470. nm in air is directed into glycerine (n = 1.47).

(a) What is the frequency of the light in the glycerine?

(b) What is its wavelength in the glycerine?

(c) If the incident angle is 75.0°,what is the refracted angle?

Answer: (a) 6.38 x 1014 Hz

(b) 320. nm

(c) 41.1°

Oi!!: 3

4) As light refracts going from one medium to another, which of the following remains constant?

A) wavelength B) refractive index C) wave velocity 0) frequency

Answer: 0

Oiff: 2

5) A person looks straight down into a large cube of glass. Three cm below the surface is a bubble.

How far below the surface does the bubble appear to the person?

Answer: 2.0 cm below

Oif[3

6) How long does it take a light beam to cross a 6. m wide room? If the air were replaced with a

transparent medium of index n, how much longer would it take?

Answer: 2 x 10-8 s; n times longer

0iff:3

7) When looking into a pond or lake of clear water, the apparent depth is what fraction of the

actual depth?

A) 1/4 B) 1/3 C) 1/2 0) 9/10 E) 3/4

Answer: E

Oiff:3

376

Test Item File

8) Snell's law can be written as: sin(el) / sin(e2) = _

A) v2 / VI

Answer: B

DiJf: 2

9) If a transparent material has an index of refraction of 1.67, what is the speed of light in the

material?

Answer: 0.599c = 1.80 x 108 m/ s

Diff: 2

10) Red light with a wavelength of 650. nm travels from air into a liquid with an index of 1.33.

What is the frequency and wavelength in the liquid?

Answer: 4.61 x 1014Hz and 489. nm

Diff: 3

11 ) My flashlight beam makes an angle of 60. degrees with the surface of the water before it enters

the water. In the water what angle does the beam make with the surface?

Answer: E

Diff: 2

B) 3D' C) 60' D) 22'

12) A ray of light consisting of blue light (wavelength 480 nm) and red light (wavelength 670 nm)

is incident on a thick piece of glass at 80'. What is the angular separation between the refracted

red and refracted blue beams whiie they are in the glass? (The respective indices of refraction

for the blue light and the red light are 1.4636and 1.4561.)

A) 0.277' B) 0.455' C) 0.330' D) 0.155' E) 0.341'

Answer: A

Diff: 3

13) Which of the following materials has the slowest speed of light?

A) water B) oii C) air D) flint glass

Answer: E

Diff:l

E) diamond

14) Light of wavelength 550. nm in air is found to travel at 1.96x 108 m/ s in a certain liquid.

(a) Determine the index of refraction of the liquid,

(b) Determine the frequency of the light in air.

Answer: (a) 1.53

(b) 5.45 x 1014 Hz

Diff:3

377

Chapter 22 Reflectioll alld Refractioll of Light

15) A beam of light (f = 5 x 1014 Hz) enters a piece of glass (n = 1.5). What is the frequency of the

light while it is in the glass?

A) 5 x 1014 Hz

B) 7.5 x 1014 Hz

C) 3.33 x 1014 Hz

D) 5 x 1013 Hz

E) 7.5 x 1013 Hz

Answer: A

Diff: 1

16) A parallel light beam containing two wavelengths. 480. nm and 700. nm, strikes a plain piece of

glass at an angle of incidence of 60". The index of refraction of the glass is 1.4830 at 480. nm and

1.4760 at 700. nm. Determine the angle between the two beams in the glass.

Answer: 0.196'

Diff 3

17) An oil layer that is 5.0 em thick is spread smoothly and evenly over the surface of water on a

windless day. What is the angle of refraction in the water for a ray of light that has an angle of

incidence of 45" as it enters the oil from the air above? (The index of refraction for oil is 1.15,

and for water it is 1.33.)

A) 32.1'

Answer: A

Diff: 2

B) 27.2" C) 35.5' D) 25.6' E) 38.6'

18) A light beam composed of red and blue light is incident upon a rectangular glass plate, as

shown.

p

The light emerges into the air from point P as two separate beams

A) that are parallel, with the red beam displaced below the blue beam.

B) that are parallel, with the blue beam displaced below the red beam.

C) that are not parallel, with the blue beam displaced below the red beam.

D) that are not parallel, with the red beam displaced below the blue beam.

Answer: B

Diff:3

378

Test Item File

19) A ray of light, which is traveling in air, is incident on a glass plate at a 45' angle. The angle of

refraction in the glass

A) is greater than 45'.

B) is less than 45'.

C) is equal to 45'.

D) is unknown because it all depends on the index of refraction of glass.

Answer: B

Diff: 1

20) When a ray of light passes obliquely from one medium to another, which of the following

changes?

A) direction of travel

B) speed, direction of travel, but not wavelength

C) wavelength

D) wavelength, speed, & direction of travel

E) speed

Answer: D

Diff: 2

21) A point source of light is positioned 20.0m below the surface of a lake. What is the diameter of

the largest circle on the surface of the water through which light can emerge?

Answer: 45.6m

Diff:2

22) A beam of light, traveling in air, strikes a plate of transparent material at an angle of incidence

of 56'. It is observed that the reflected and refracted beams form an angle of 90'. What is the

index of refraction of this material?

A) n = 1.43

Answer: 0

Diff:2

B) n = 1.53 C) n = 1.40 D) n = 1.48 E) n = 1.44

379

Chapter 22 Reflection and Refraction of Light

23) Shown here are some possible paths that a light ray can follow in going either from glass to air

or from air into glass.

F

In the drawing you are not told whether the light is going from left to right or from right to left.

Which path did the light follow?

A) path C B) path G C) path F 0) path E E) path 0

Answer: 0

Diff:2

24) When a beam of light (wavelength = 590 nrn), originally traveling in air, enters a piece of glass

(index of refraction 1.50), its frequency

A) increases by a factor of 1.50.

B) is reduced to 2/3 its original value.

C) is unaffected.

0) increases by a factor of-J2,.

E) increases by a factor of...[r..

Answer: C

Diff: 1

25) When a beam of light (wavelength = 590 nrn), originally traveling in air, enters a piece of glass

(index of refraction 1.50), its wavelength

A) increases by a factor of 1.50.

B) is reduced to 2/3 its original value.

C) is unaffected.

0) increases by a factor of...[r..

E) is reduced by a factor of...[r..

Answer: B

Diff: 2

380 I

Test Item File

26) For all transparent material substances, the index of refraction

A) is less than 1.

B) is greater than 1.

C) is equal to 1.

0) could be greater than 1 or less than 1; it all depends on optical density.

Answer: B

Diff: 1

27) The angle of incidence

A) is always greater than the angle of refraction.

B) must equal the angle of refraction.

C) is always less than the angle of refraction.

0) may be greater than, less than, or equal to the angle of refraction.

Answer: 0

Diff 2

28) Light travels fastest

A) in a vacuum.

C) through glass.

Answer: A

Diff: 1

B) through water.

0) through diamond.

29) A light ray strikes a glass plate of thickness 0.80 em at an angle of incidence of 60'. The index of

refraction of the glass is 1.55. By how much is the beam displaced from its original line of travel

after it has passed through the glass?

Answer: 0.42 em

Diff3

30) A buoy, used to mark a harbor channel, consists of a weighted rod 2.00 m in length. 1.50 m of

the rod is immersed in water and 0.500 m extends above the surface. If sunlight is incident on

the water with an angle of incidence of 40.0', what is the length of the shadow of the buoy on

the level bottom of the harbor?

Answer: 1.25 m

Diff: 2

31) The index of refraction of diamond is 2.42. This means that a given wavelength of light travels

A) 2.42 times faster in air than it does in diamond.

B) 2.42 times faster in diamond than it does in vacuum.

C) 2.42 times faster in vacuum than it does in diamond.

0) 2.42 times faster in diamond than it does in air.

Answer: C

Diff: 2

381

Chapter 22 Reflection and Refraction of Ligilt

32) When a light wave enters into a medium of different optical density

A) its speed and frequency change.

B) its speed and wavelength change.

C) its frequency and wavelength change.

D) its speed, frequency, and wavelength change.

Answer: B

Diff: 2

33) Light of wavelength 550 nm in air is found to travel at 1.96x 108 ml s in a certain liquid.

Determine

(a) the frequency of the light in the liquid.

(b) the wavelength of the light in the liquid.

Answer: (a) 5.45 x 1014Hz

(b) 359. nm

Diff:3

34) Index of refraction is which of the following?

A) 8i ; 8r

B) (A2/AI) (sin81/sin82); 1

C) ; (din)

D) A/Am

E) arcsin(n2/nl)

Answer: D

Diff:2

35) Apparent depth is which of the following?

A) 8i ; 8r

B) (A2/AI) (sin81/sin82); 1

C); (din)

D) A/Am

E) arc sin(n2/nl)

Answer: C

Diff: 2

382

36) Optical density is directly proportional to

A) mass density.

C) index of refraction.

Answer: C

Diff:2

B) light speed.

D) index of reflection.

I

Test Item File

37) Snell's law is equivalent to which of the following?

A) 6i = 6r

B) (AZ!AI) (sin6I!sin6Z) = I

C) = (d!n)

D) A!1m

E) arc sin(nz!nI)

Answer: B

Diff:2

38) An index of refraction less than one for a medium would imply that

A) refraction is not possible.

B) the speed of light in the medium is greater than the speed of light in vacuum.

C) the speed of light in the medium is the same as the speed of light in vacuum.

D) reflection is not possible.

Answer: B

Diff: 1

39) A light beam enters water at an angle of incidence of 37'. Determine the angle of refraction.

Answer: Z6.9 °

Diff:2

22.4 Total Internal Reflection and Fiber Optics

1) Critical angle is which of the following?

A) 6i =6r

B) (AZ! 1.1)(sin6I! sin6Z) = 1

C) = (d!n)

D)A!1m

E) arc sin(nz!nI)

Answer: E

Diff: 1

Z) The critical angle in ordinary glass is

A) greater than 45°.

C) less than 45"'.

Answer: C

Diff: 1

B) sin(I!n).

D) 45°.

383

Chapter 22 Reflection and Refraction of Light

3) A light beam with wavelength 440. nm in a material then enters air and its wavelength

becomes 577. nm.

<a) What is the index of refraction for the material?

(b) At what angle with the surface will the beam be totally reflected back in the material?

Answer: (a) 1.31

(b) 40.30

Diff: 3

4) The critical angle is given by sindl/nl) for what condition?

Answer: The second index n2 =1.00

Diff: 1

5) Fiber optics depends upon the phenomenon of

A) total internal reflection.

C) polarization.

Answer: A

Diff: 1

B) diffuse reflection.

0) dispersion.

6) When TOTAL REFLECTION occurs at a surface, the incident angle must be in the substance

with the higher

A) speed of light. B) index of refraction.

C) incident angle. 0) c/n.

Answer: A

Diff: 1

7) An optical fiber is 1.00 meter long and has a diameter of 20.0 flm. Its ends are perpendicular to

its axis. Its index of refraction is 1.30.What is the minimum number of reflections a light ray

entering one end will make before it emerges from the other end?

A) 2.42 x 105 B) 2.56 x 105 C) 2.02 x 105 0) 1.85 x 105 E) 2.85 x 105

Answer: 0

Diff: 3

8) Light in a transparent material (index of refraction 1.333)strikes the boundary with another

transparent material (n = 1.010).

(a) What is the critical angle for total internal reflection?

(b) By what percent does the wavelength change going from the 1st to the 2nd material?

Answer: (al 49.260

(b) 32.0%

Diff: 3

384

Test Item File

9) For certain angles, TOTAL INTERNAL REFLECTION can occur when light tries to pass from

one medium to another which has

A) a larger index of refraction.

B) a smaller index of refraction.

C) the same index of refraction.

D) an index of refraction which issin-1(45').

E) an index of refraction which is sin-1(n).

Answer: B

Diff:l

10) The critical angle for a beam of light passing from water into air is 48.8'. This means that all

light rays with an angle of incidence greater than this angle will be

A) absorbed.

B) totally transmitted.

C) partially reflected and partially transmitted.

D) totally reflected.

Answer: D

Diff:l

11 ) A ray of light (inc) enters a 45' - 90" glass prism from air (bottom left), as shown.

B c

A D

inc E

In what direction does the light re-emerge back into the air?

A)D

Answer: E

Diff: 2

B) B C)A D)C E) E

12) The end of a cylindrical plastic rod is polished and cut perpendicular to the axis of the cylinder.

Determine the minimum index of refraction so that a light ray entering the end of the rod will

always be totally internally reflected within the rod, i.e., it will never escap" the rod until it

comes to the other end.

Answer: 1.414

Diff:2

385

Chapter 22 Reflection and RefractiOll of Light

13) Mirages are due to

A) reflection.

B) polarization.

C) refraction.

0) dispersion.

E) total internal reflection.

Answer: C

Diff: 1

14) A light ray enters a glass enclosed fishtank. From air it enters the glass at20.0 with respect to

the surface, then emerges into the water. The index for glass is 1.50 and for water 1.33.

(a) What is the angle of refraction in the glass?

(b) What is the angle of refraction in the water?

(c) Is there any incident angle in air for which the ray will not enter the water due to total

internal reflection?

Answer: (a) 39.0

(b) 45.0

(c) no

Diff: 3

15) Fiberscopes are based on the physical phenomena called

A) diffusion.

B) dispersion.

C) total internal reflection.

0) absorption.

E) polarization.

Answer: C

Diff: 1

386

Test Item File

16) A light ray emerges from the bottom of a 45' glass prism into air, as shown in the sketch.

A o

From which direction was the ray incident on the prism?

A)C

Answer: C

Diff: 2

B)A C)D D)B

17) What is the critical angle for light traveling from crown glass (n; 1.52) into water (n; 1.33)?

NW ~~ q~ ~W 86r

Answer: E

Diff: 2

22.5 Dispersion

1 ) The person who proved that white light is composed of light of different colors is

A) Willebrod Snell.

B) Christen Huygens.

q Isaac Newton.

D) General Electric.

E) Thomas Edison.

Answer: C

Diff: J

2) In common transparent media, as the frequency of light increases, the index of refraction

A) increases. B) stays constant.

C) decreases. D) varies as the sine of the incident angle.

Answer: A

Diff: J

3) Arrange in order of increasing wavelength: blue, green, indigo, orange, red, violet, yellow.

Answer: violet, indigo, blue, green, yellow, orange, red.

Diff: 2

387

Chapter 22 Reflection and Refraction of Light

4) You can only see a rainbow if

A) the sun is behind you.

C) the sun is 900 to the side.

Answer: A

Diff: 1

5) White light is

A) dichromatic.

C) achroma tic.

Answer: 0

Diff: 1

6) Rainbows are caused by sunlight being

A) dispersed.

B) dispersed, refracted, & reflected.

C) refracted.

0) reflected.

E) refracted & reflected but not dispersed.

Answer: B

Diff: 1

B) the sun is in front of you.

0) the sun is 18U' to the side.

B) monochromatic.

0) polychromatic.

7) The color on the outer edge of the primary rainbow is

A) white B) red C) violet

Answer: C

Diff: 1

0) yellow E) green

8) White light, coming from medium 1 (index of refractionn1), will disperse upon entering

medium 2 (index of refraction n2) when

A) (n2 > n1).

C)(n2 = n1).

Answer: 0

Diff: 2

B) (n2 < n1).

0) (n2 > n1) or (n2 < n1).

9) When the index of refraction of a transparent material varies with wavelength, the material

exhibits

A) density variation.

B) polarization.

C) dispersion.

0) reflection.

E) total internal reflection.

Answer: C

Diff: 1

388

Test Item File

10) Which of the following colors undergoes the greatest REFRACTION when passing from air

into glass?

A) yellow B) red C) blue 0) orange E) green

Answer: C

Oiff: 1

11 ) White light is

A) light of wavelength 550 nm, in the middle of the visible spectrum.

B) the term used to describe very bright light.

C) a mixture of red, green, and blue light.

0) a mixture of all frequencies.

E) the opposite (or complementary color) of black light.

Answer: 0

Oiff 1

12) Laser light is

A) invisible in air.

C) dispersive.

Answer: B

Oiff: 1

B) monochromatic.

0) created by total reflection.

13) When white light enters a more optically dense medium than that from which it came, the

green color component refracts the red color component.

A) more than B) the same as C) less than

Answer: A

Oiff: 1

14) White light is

A) the absence of color.

Answer: B

Oiff 1

B) polychromatic. C) monochromatic.

15) Which color of light undergoes the greatest refraction when passing from air to glass?

A) yellow B) red C) green 0) blue E) cyan

Answer: 0

Oiff:l

16) More of the rainbow can be seen from the ground when

A) the sun is higher. B) there is an eclipse.

C) the sun is lower. 0) the sun is in front of you.

Answer: C

Oiff: 1

389

Chapter 22 Reflection and Refraction of Light

17) A beam of white light is incident on a thick glass plate with parallel sides, at an angle between

00 and 900 with the normal. Which color emerges from the other side first?

A) red

B) green

C) violet

D) none of the other choices; all colors emerge at the same time

Answer: A

Diff: 2

18) The color on the outer edge of a rainbow is for the primary rainbows and

for the secondary.

A) violet, red

B) violet, violet

C) red, violet

D) green, yellow

E) red, red

Answer: C

Diff: 1

19) The index of refraction for a certain material is 1.399 for red light and 1.432 for blue light. Find

the angle separating the two refracted colors if the:

(a) angle of incidence is 3lY'.

(b) angle of incidence is 600.

Answer: (a) 0.500

(b) 1.040

Diff:3

390

Chapter 23 Mirrors and Lenses

23.1 Plane Mirrors

I) A plane mirror forms an image that is

A) real and upright.

C) virtual and upright.

Answer: 0

Diff: 2

B) real and upside down.

D) virtual and upside down.

2) The IMAGE of a plane mirror (of a real object) has the following characteristics:

A) virtual, inverted, and magnification> I B) virtual, erect, and magnification = I

C) real, erect, and magnification = I D) real, inverted, and magnification < I

Answer: B

Diff: 2

3) David stands 2.5 meters in front of a plane mirror.

(a) How far from David is David's image in the mirror?

(b) If David moves away from the mirror at 1.5 ml s, how fast are David and his image moving

apart from each other?

(c) If David is 180. em tall, how tall is his image in the mirror?

Answer: (a) 5.0 cm

(b) 3.0 mls

(c) 180. cm

Diff:3

4) An object is placed a distance d in front of a plane mirror. The size of the image will be

A) dependent on the distance d.

B) half as big as the size of the object.

C) twice the size of the object.

D) dependent on where you are positioned when you look at the image.

E) the same size as the object, independent of the distance d or the position of the observer.

Answer: E

Diff:2

391

Chapter 23 Mirrors and Lenses

5) Suppose a lighted candle is placed a short distance from a plane mirror, as shown here.

M

c.

Where will the image of the flame be located?

A) at A

C) at C

Answer: C

Diff:2

B) at B

D) at M (at the mirror)

6) At which, if any, of the points indicated here should you place your eye if you wish to see an

image of the arrow in the mirror?

392

A)A

Answer: 0

Diff:2

t

o.

B) B

IMirror

C)C 0)0

I

Test Item File

7) Two plane mirrors intersect at an angle of 120'. Draw ray diagrams to determine the locations

of all the images formed by an object placed at a point P between the mirrors, closer to one

mirror than the other.

Answer:

Oifj: 3

8) At an amusement park you stand between two plane mirrors, which intersect at an angle of 60'

. You are positioned at point P in the drawing here. You are 1.0 m from the nearest mirror, and

15' above it.

o

P

I 1M

What is the distance from you to the nearest image and to the second nearest image?

Answer: 2.0 m ; 5.5 m

Oiff:2

9) II you place a plane mirror vertically into water, and a dolphin moves toward it with a speed of

4 ml s, she will see her image move toward her at a relalive speed of

A) 6. m/s. B) 10. m/s. C) 2. m/s. D) 4. m/s. E) 8. m/s.

Answer: E

Oifj: 2

10) The radius of curvature for a plane (flat) mirror is

A) negative. B) infinite. C) zero.

Answer: C

Oiff:l

D) imaginary.

11) I recently had to replace the side view mirror on my truck. How tall should the mirror have

been if I am to see all of a car 2.0 m high when it is following 20. m back (measured from the

mirror). The mirror is 0.50 m from my eyes.

N~= ~~9= 05.2= ~~O= m~=

Answer: B

Oiff: 2

393

Chapter 23 Mirrors alld Lellses

12) A friend who is 180. cm tall stands 2.0 m from a plane wall mirror. You stand slightly behind

him, 3.0 m from the wall mirror. How tall must the mirror be if you are to see all of your friend

in the mirror?

Answer: 1.08 meter

Diff: 2

13) You may have seen ambulances on the street with the Jetters of the word AMBULANCE

written on the front of them, in such a way as to appear correctly when viewed in your car's

rear-view mirror.

a) '1~13nTvN:)E

c) ECNALUBMA

e) 3:)VlAJUBMA

b) AMBUJAVl:)3

d) 3:)N'v'ln13 ~'v'

How do the letters appear when you look directly at the ambulance?

A) figure a B) figure b C) figure c 0) figure d

Answer: E

DifJ: 2

E) figure e

14) A man 190. cm tall stands 25. m from a plane wall mirror. One meter in front of him sits his

dog, 30. cm tall. What minimum mirror size is needed for the man to see all of his dog's

reflection?

Answer: 18.8 cm tall

DifJ: 2

23.2 Spherical Mirrors

1) If you stand in front of a convex mirror, at the same distance from it as its focal length,

A) you will see your image and you will appear smaller.

B) you won't see your image because there is none.

C) you will see your image and you will appear larger.

0) you will see your image at your same height.

E) you won't see your image because it's focused at a different distance.

Answer: B

Diff: 2

394

Test Item File

2) A 2.3 cm tall statue is 15. em in front of a convex mirror. The mirror radius of curvature is 18.

em.

(a) Is the image real or virtual?

(b) How far is the image from the mirror?

(c) Is the image upright or inverted?

(d) How high is the image?

Answer: (a) virtual

(b) 5.6cm

(c) upright

(d) 0.86 cm

Di/f3

3) In air a concave mirror has a focal length of 30. em. Under water that same mirror would have

____ focal length.

A) a larger B) the same C) a smaller

Answer: B

Diff:2

4) A "parallel ray" is a ray parallel to the

A) mirror radius B) object axis

Answer: 0

Diff: 1

C) chief ray 0) optic axis

5) Given a concave mirror, rays of light originating from the center of curvature reflect off the

mirror and focus at

A) 2 R from the mirror.

C) the center of curvature.

Answer: C

Diff: 2

B) the focal point.

0) infinity.

6) The magnification M = -di/ do is the ratio of image to object

A) angular size. B) distance. C) focal distances.

Answer: 0

Diff: 1

0) heights.

395

Chapter 23 Mirrors and Lenses

7) A 3.0 cm tall statue is 24. cm in front of a concave mirror. The mirror radius of curvature is 20.

cm.

(a) Is the image real or virtual?

(b) How far is the image from the mirror?

(c) Is the image upright or inverted?

(d) How high is the image?

Answer: (a) real

(b) 17. cm

(c) inverted

(d) 2.1 cm

Diff: 3

8) Consider a converging lens. If the object is inside the focal point, then the image will always be

A) real. B) virtual.

C) at the focal point. 0) at infinity.

Answer: B

Diff: 2

9) Is it possible for a convex mirror to form a real image?

Answer: yes, if the object was virtual (formed by another lens or mirror)

Diff: 2

IO) Describe a mirror which takes an object at a distance of 47. em and forms a real image at 23. em.

Answer: concave mirror with focal length 31. em (radius 62. cm)

Diff: 2

11) A negative magnification for a mirror means

A) the image is inverted, and the mirror is concave.

B) the image is inverted, and the mirror is convex.

C) the image is inverted, and the mirror may be concave or convex.

D) the image is upright, and the mirror may be concave or convex.

E) the image is upright, and the mirror is convex.

Answer: C

Diff 2

12) Which of the following is an accurate statement?

A) A mirror always forms a virtual image.

B) A mirror always forms a real image.

e) A mirror always forms an image larger than the object.

0) A mirror always forms an image smaller than the object.

E) None of the other choices are true.

Answer: E

Diff:2

396

Test Item File

13) Two parallel rays (also parallel to the optic axis) reflect from a concave mirror. They intersect at

A) the center of curvature. B) the focal point.

C) a point behind the mirror. 0) infinity.

Answer: B

Diff: 2

14) What is the index of refraction inside a certain transparent materia! if the critical angle is found

to be 48.°(air is outside)?

A) 1.49

Answer: C

Diff:2

B) 1.48 C) 1.35 OJ 0.743 E) 1.22

15) Sometimes when you look into a curved mirror you see a magnified image (a great big you!)

and sometimes you see a diminished image (a little you). If you look at the bottom (convex)

side of a shiny spoon, what will you see?

A) You will either see a little you or a great big you, depending on how near you are to the

spoon.

B) You will see a little you, upside down.

C) You will see a little you, right side up.

0) You won't see an image of yourself because no image will be formed.

E) You will see a little you, but whether you are right side up or upside down depends on

how near you are to the spoon.

Answer: C

Diff: 2

397

Chapter 23 Mirrors alld Lellses

16) An object is placed 3 cm from a convex mirror of radius 4 em.

(a) Graphically determine the size and position of the image.

(b) Is the image real or virtual?

Answer: (a) (see sketch)

Dilf: 3

(b) virtual

o F c

17) In using ray tracing to graphically locate the image of an object that is placed in front of a

mirror, describe three simple rays that you could draw that pass by the head of the object.

Answer: Ray I: the radial ray; i.e., the ray drawn toward the center of curvature, which is then

reflected back along the same path.

Ray 2: the parallel ray; i.e., the incoming ray parallel to the main axis, which is then

reflected along a path that extends to the focal point.

Ray 3: the focal ray; i.e., the ray drawn toward the focal point, which is then reflected

back parallel to the main axis.

Diff:3

398

18) Which of the following aberrations does not apply to mirrors?

A) astigmatism B) chromatic C) spherical

Answer: B

Diff: 1

0) coma

Test Ite", File

19) An object is placed 6 cm from a concave mirror of radius 4 cm. Graphically determine:

(a) the image position.

(b) if the image is larger, smaller, or the same size as the object.

(c) if the image is real or virtual.

Answer: (a) (shown)

(b) smaller

(c) real

Diff:3

20) The power of the human eye is approximately how many Diopters? (hint: estimate the size of

the eyeball)

A) 1 B)4 C) -25 0) -4 E) 25

Answer: E

Diff:2

21) The rear-view mirrors on the passenger side of many new cars have a warning written on

them: "OBJECTSIN MIRROR ARE CLOSERTHAN THEY APPEAR." This implies that the

mirror must be

A) concave.

Answer: A

Diff: 1

B) plane. C) convex. 0) transparent.

22) If you stand in front of a concave mirror, exactly at its focal point,

A) you won't see your image because there is none.

B) you will see your image, and you will appear smaller.

C) you will see your image at your same height.

0) you will see your image and you will appear larger.

E) you won't see your image because it's focused at a different distance.

Answer: A

DiJf: 2

399

Chapter 23 Mirrors and Lenses

23) If you stand in front of a concave mirror, exactly at its center of curvature,

A) you will see your image and you will appear smaller.

B) you will see your image and you will appear larger.

C) you won't see your image because there is none.

D) you won't see your image because it's focused at a different distance.

EJ you will see your image at your same height.

Answer: E

Diff: 2

24) If you stand in front of a convex mirror, at the same distance from it as its radius of curvature,

A) you won't see your image because there is none.

BJyou will see your image and you will appear larger.

C) you will see your image and you will appear smaller.

D) you will see your image at your same height.

E) you won't see your image because it's focused at a different distance.

Answer: C

Diff: 2

25 J An object 2.0 cm tall is placed 24. cm in front of a convex mirror whose focal length is 30. cm.

(aJ Where is the image formed?

(b) How tall is it?

Answer: (a) 14. cm behind the mirror

(bJ 1.2 cm tall

Di!!: 3

26 J An object is placed 15. cm from a concave mirror of focal length 20. cm. If the object is 4.0 em

tall,

(aJ where is the image formed?

(b) how tall is it?

Answer: (aJ 60. cm behind the mirror

(b) 16. cm tall

Di!!: 3

400

Test Item File

23.3 Lenses

1 ) A lens projects an image of a man as seen in the figure. Rays marked A, B, and C travel to the

lens from the man's ear.

f --*-------

Draw the three refracted rays as they proceed to the right of the lens; noting that A is parallel to

the axis, Bgoes through the center of the lens, C proceeds to the bottom of the lens, and the

point marked f is the focal point of the lens.

Answer:

Diff: 3

2) In a single-lens reflex camera the lens-film distance may be varied by sliding the lens forward

or backward with respect to the camera housing. If, with such a camera, a fuzzy picture is

obtained, this means that

A) the lens was too far from the film.

B) too little light was incident on the film.

C) the lens was too close to the film.

D) one cannot say which of the other reasons is valid.

E) too much light was incident on the film.

Answer: D

DifJ: 2

401

Chapter 23 Mirrors a1ld Le1lses

3) A 3.0 cm tall statue is 48. cm in front of a biconvex lens (focal length 20. cm).

(a) Is the image real or virtual?

(b) How far is the image from the lens?

(c) Is the image upright or inverted?

(d) How high is the image?

Answer: (a) real

(b) 34.cm

(c) inverted

(d) 2.1cm

Oiff:3

4) Light from an object proceeds through 3 lenses, each with magnification 2, -4, 0.2 respectively.

The overall magnification is

A) 2 - 4 + 0.2 = -1.8.

B) 2 x (-4) x 0.2 = -1.6.

C) 2/(-4)/0.2 = -2.5.

D) +8/5.

E) +5/8.

Answer: B

Oiff: 2

5) A slide projector is designed with its lens 6.0 m from the screen. The projected image is 1.5m

square of a slide object 2.5 cm square.

(a) What is the object distance from the lens?

(b) What should be the lens focal length?

(c) What is the lens POWER?

Answer: (a) 10. cm

(b) f = 9.8 cm

(c) 10.2 Diopters

Oiff:3

6) The image of the rare stamp you see through a magnifying glass is

A) always the same orientation as the stamp.

B) always upside-down compared to the stamp.

C) either the same orientation or upside-down, depending on how dose the stamp is to the

glass.

D) either the same orientation or upside-down, depending on the thickness of the glass used.

Answer: C

Oiff 2

402

B) at the center

D) half way to the center

Test Item File

7) A fish appears to be at the center of a spherical fish bowl. We know light rays leaving the bowl

refract at the glass surface so where actually is the fish? (assume the water and glass have n =

1.33)

A) 1.33Rbehind the glass

C) R/ 1.33 behind the glass

Answer: B

Diff: 2

8) Describe a double convex lens made with n = 1.45 glass having radii of 27. cm.

Answer: converging lens of power 3.3 Diopters (30.cm focal length)

Diff: 2

9) Consider a converging lens forming an image on a screen. What property of the image would

be affeeled by covering the top half of the lens?

Answer: It would be half as bright since half of the light gets through the lens.

Diff: 2

10) A lamp is placed 1m from a screen. Between the lamp and the screen is placed a converging

lens of focal length 24 cm. The filament of the lamp can be imaged on the screen. As the lens

position is varied with respect to the lamp,

A) a sharp image will be seen when the lens is 60 cm from the lamp.

B) a sharp image will be seen when the lens is 40 cm from the lamp.

e) no sharp image will be seen for any lens position.

D) a sharp image will be seen when the lens is halfway between the lamp and the screen.

E) a sharp image will be seen when the lens is either 40 cm from the lamp or 60 cm from the

lamp, but not otherwise.

Answer: E

Diff: 2

11 ) An object is placed at the origin. A converging lens of focal length 10mm is placed at x = 40

mm on the x axis. A second converging lens of focal length 20 mm is placed at x = 90 mm.

Graphically determine the size and location of the final image.

Answer:

Diff:2

403

Chapter 23 Mirrors and Lellses

12) When an object is placed 60. cm from a converging lens, it forms a real image. When the object

is moved to 40. cm from the lens, the image moves 10. cm farther from the lens. What is the

focal length of the lens?

AI~= ~~= C)~= mn= 8~=

Answer: A

Oiff: 2

13) A diver looks in a mirror under water. If the diver's face is 30. cm from the mirror and the

water index is 1.333, what is the lateral magnification?

Answer: ONE; the index has no effect upon REFLECTION

Oiff: 1

14) If you stand in front of a double-concave lens, exactly at its center of curvature, your image

will appear where you are, but

AI larger and upside down. B) the same size and upside down.

C) larger and upright. D) the same size and upright.

Answer: B

Oifj: 2

15) [s it possible to see a virtual image?

AI no, since virtual images do not really exist

B) no, since the rays that seem to emanate from a virtual image do not in fact emanate from

the image

C) yes, since the rays that appear to emanate from a virtual image can be focused on the

retina just like those from an illuminated object

D) yes, since almost everything we see is virtual because most things do not themselves give

off light, but only reflect light coming from some other source

E) yes, but only indirectly in the sense that if the virtual image is formed on a sheet of

photographic film, one could later look at the picture formed

Answer: D

Oifj: 2

16 I How far from a lens of focal length 50.0 mm must the object be placed if it is to form a virtual

image magnified in size by a factor of three?

AI 33.3 mm BI 48.0 mm CI 38.3 mm DI 42.2 mm E) 54.4 mm

Answer: A

Oif/: 2

17) A slide projector has a lens of focal length 150. mm. An image 100. cm x 100. cm is formed of a

slide whose dimensions are 50.0 mm x 50.0 mm. How far from the lens must the screen be

placed?

Answer: 3.15 m

Oiff:2

404

Test Item File

18) Two thin lenses, of focal lengths f1 and f2, placed in contact with each other are equivalent to a

single lens of focal length

A) f1 + f2.

B) 1/ ( f1 + f2).

C) f1f2/ (f1 + f2).

0) ( f1 +f2)/ f1f2.

E) (l/f1) + 0/f2).

Answer: C

Diff: 2

19) Two thin double-convex (convex-convex) lenses are placed in contact. If each has a focal

length of 20. cm, how would you expect the combination to function?

A) about like a single lens of focal length 40. cm

B) about like a single lens of focal length 20. cm

C) about like a single lens of focal length slightly greater than 20. cm

0) about like a single lens of focal length less than 20. cm

Answer: 0

Diff:2

20) A diverging lens (f = -4 cm) is positioned 2 cm to the left of a converging lens (f = +6 cm). A

1-mm diameter beam of parallel light rays is incident on the diverging lens from the left. After

leaving the converging lens, the outgoing rays

A) diverge.

B) converge.

C) form a parallel beam of diameter 0 > 1 mm.

0) form a parallel beam of diameter 0 < 1 mm.

E) will travel back toward the light source.

Answer: C

Difj: 2

21 ) How does the thickness of a lens relate to it being converging or diverging?

Answer: A converging lens is thicker at its center than it is at its edges and a diverging lens is

thinner at its center than it is at its edges.

Diff: J

22) A camera with a telephoto lens of focal length 125.mm is used to take a photograph of a plant

1.8m tall. The plant is 5.0 m from the lens.

(a) What must be the distance between the lens and the camera film if the image is sharply

focused?

(b) How tall is the image?

Answer: (a) 128.mm from lens to film

(b) 45. mm tall

Diff: 3

405

Chapter 23 Mirrors and Lenses

23) Where must an object be placed with respect to a converging lens of focal length 30 em if the

image is to be virtual, and three times as large as the object?

Answer: 20 em from the lens

Oiff: 2

24) The simplest type of camera is a pin-hole camera; you might have even made one. It consists

of a box with a single pinhole in it, and a piece of film on the inner side opposite the hole.

Suppose you photograph your friend with it. Your friend's image on the film will appear

A) upside down because light travels in a straight line.

B) right side up because light travels in a straight line.

C) upside down because light refracts at the pinhole.

D) right side up because light refracts at the pinhole.

Answer: A

Oiff: 1

25) In using ray tracing to graphically locate the image of an object that is placed in front of a lens,

describe three simple rays that you could draw that pass by the head of the object.

Answer: Ray 1: the vertex ray; i.e., the ray passing through the center of the lens, which emerges

undeflected.

Ray 2: the parallel ray; i.e., the incoming ray parallel to the main axis, which is then

refracted along a path that extends to the focal point.

Ray 3: the focal ray; i.e., the ray drawn toward the focal point, which is then refracted

parallel to the main axis.

Oiff: 3

26) How far from a 50. mm focal length lens, such as is used in many 35. mm cameras, must an

object be positioned if it is to form a real image magnified in size by a factor of three?

A) 58. mm B) 76. mm C) 46.mm D) 67. mm E) 52. mm

Answer: 0

0iff:2

27) Two very thin lenses, each with focal length 20. em, are placed in contact. What is the focal

length of this compound lens?

N~= ~ill= C)n= ~m= mn=

Answer: B

Oiff: 2

28) An object is placed 9.5=from a lens of focal length 24 em.

(a) Where is the image formed?

(b) What is the magnification?

Answer: (a) 16=from the lens on the same side as the object

(b) m = 1.7

OifI: 3

406

Test Item Fite

29) The images formed by concave lenses

A) are always virtual.

B) could be real or virtual, but always real when the object is placed at the focal point.

C) could be real or virtual; it depends on whether the object distance is smaller or greater

than the focal length.

0) are always real.

Answer: C

Diff: 2

23.4 Lens Aberrations

1 ) Spherical mirrors suffer from

A) both spherical and chromatic aberration.

B) neither spherical nor chromatic aberration.

C) chromatic aberration, but not spherical aberration.

0) spherical aberration, but not chromatic aberration.

Answer: 0

Diff: 1

2) Spherical lenses suffer from

A) both spherical and chromatic aberration.

B) spherical aberration, but not chromatic aberration.

C) neither spherical nor chromatic aberration.

0) chromatic aberration, but not spherical aberration.

Answer: A

Diff: 1

3) If the refractive index of the glass in a lens varies with wavelength, then which of the following

results?

A) spherical aberration

B) light scattering

C) total reflection

0) astigmatism

E) chromatic aberration

Answer: E

Diff: 1

I

4) Spherical aberration can occur in

A) mirrors and lenses. B) mirrors but not lenses.

Answer: A

Diff:l

C) lenses but not mirrors.

407

Chapter 23 Mirrors and Lenses

5) Chromatic aberration occurs because of

A) polarization.

B) spherical surfaces.

C) dispersion.

D) internal reflection.

E) astigma tism.

Answer: C

Diff:l

6) When two parallel white rays pass through the outer edges of a converging glass lens,

chromatic aberration will cause colors to appear on the screen in what order, from the top

down?

A) red, blue, red, blue

B) blue, red, blue, red

C) red, blue, blue, red

D) blue, red, red, blue

E) blue, blue, red, red

Answer: D

Diff:2

23.5 The Lens Maker's Equation

1 ) A +20 Diopter lens has what power in water?

A) greater than 20. D B) the same 20. D

Answer: C

Diff: 2

C) less than 20. D

2) A plano-convex lens is to have a focal length of 40 em. It is made of glass of index of refraction

1.65. What radius of curvature is required?

M~rm m~rm 011rm ~nrm m~rm

Answer: B

Diff: 2

408

Test Item File

3) A camera uses a biconvex lens made of glass with an index of refraction of 1.60 and has a

radius of curvature of 12. cm for the 1st surface and 24. cm for the 2nd.

(a) What is the focal length of this lens when used in air?

(b) If used under water (n = 1.33), what is the focal length?

Answer: (a) 13. cm

(b) 39. cm

Diff: 3

4) What is the FOCAL LENGTH of a lens whose two radii of curvatures are equal

(RI =R2)?

A) zero

Answer: C

Diff: 2

B) 2R2 / (n-I) C) infinite E) 1/ (2R2)

5) The curved surface of a 50. cm focal length "plano-convex" lens has a radius of curvature of 30.

cm. What is the refractive index of the glass?

Answer: n = 1.6

Diff: 2

6) What Diopter takes an object at 47. cm and forms an upright image 23. cm from the lens?

A) +2.20

B) -0.022 0

C) -2.2 0

D) 2.2 x 102 0

E) +0.0220

Answer: C

Diff: 2

7) Compare two diverging lenses similar except that lens Bis rated at 20 Diopters, whereas lens A

is rated at 10 Diopters. The focal length of lens Bis

A) twice the focal length of lens A.

B) one-fourth of the focal length of lens A.

C) one-half of the focal length of lens A.

D) 1/..j2 of the focal length of lens A.

E) four times the focal length of lens A.

Answer: C

Diff: 1

8) Why do large aperture telescopes use a mirror instead of a lens to focus light?

Answer: Large mirrors are much cheaper than lenses (the largest lens has a I m diameter) and

mirrors have an added advantage of no chromatic aberration.

Diff: 2

409

Chapter 23 Mirrors and Leuses

9) What POWER lens placed next to a lens of 25. cm focal length would produce a combination

with an effective INFINITE focal length?

Answer: -4.0 Diopters

Diff: 2

10) A converging lens with the same curvature on both sides and focal length 25. cm is to be made

from crown glass (n = 1.52).What radius of curvature is required for each face?

Answer: 26. cm

Diff: 2

1I) A 4.0 cm high object is 20. cm in front of a 1.333 Diopter plano-convex lens.

(a) Find the image position. Real or Virtual?

(b) Find the image size. Erect or Inverted?

Answer: (a) 60. cm in front of lens; virtual image

(b) 12. cm high; erect

Diff: 3

12) Take the lens maker equation and show that a lens which has been turned around (surface 1

becomes 2 and 2 becomes 1) has the same focal length.

Answer: 1/ f=(n-l)(l! Rl - I/R2) A sign change occurs when 1 and 2 are exchanged, and the

radii themselves change sign because the center of curvature moves to other side of

surface. These sign changes cancel each other out and yield the same f.

Diff:3

13) A concave meniscus lens with an index of refraction of 1.48 has radii of 6.0 cm and 4.0 cm (see

figure).

410

What is the power of the lens in DIOPTERS?

A) -0.040 B) -20. C) -0.25

Answer: E

Diff: 2

D) -0.20 E) -4.0

Test Item File

14) A double convex lens has faces of radii 18.0 em and 20.0 em. When an object is placed 24.0 cm

from the lens, a real image is formed 32.0 em from the lens. Determine:

(a) the focal length of the lens.

(b) the index of refraction of the lens material.

Answer: (a) 13.7 em

(b) n = 1.69

Diff:3

15) A double convex (convex-convex) thin lens has radii of curvature 46. em, and is made of glass

of index of refraction n = 1.60. What is the focal length?

A) 36. cm B) infinite C) 46. em D) 18. em E) 30. em

Answer: E

Diff: 2

16) What kind of lens is it that has a power of +10 Diopters and a first surface center of curvature

in front of the lens?

A) double convex

B) double concave

C) converging meniscus

D) plano concave

E) plano convex

Answer: C

Diff: 2

411

Chapter 24 Physical Optics: The Wave Nature of Light

24.1 Young's Double-Slit Experiment

1 ) Two light sources are said to be coherent if they

A) are of the same frequency.

B) are of the same frequency, and maintain a constant phase difference.

C) are of the same frequency and amplitude.

D) are of the same amplitude, and maintain a constant phase difference.

Answer: B

Diff: 2

2) The path difference for destructive interference is rriA/2 where

A) m = 1, 2, 3, 4, .

B) m = 0, 2, 4, 6, .

C) m= 2, 4, 6, 8, .

D) m= 0, 1, 2, 3, .

E) m = 1, 3, 5, 7, .

Answer: E

Diff: 2

3) A double-slit experiment uses light of wavelength 633. nm with a slit separation of 0.100 mm

and a screen placed 2.0 m away.

(a) What is the linear width of the central fringe?

(b) What is the lateral distance between 1st and 2nd order fringes?

(c) What is the angular separation between the central maximum andthe 1st order maximum?

Answer: (a) 1.3 em

(b) 1.3 em

(c) 6.33 milliradian

Diff: 3

4) What is the "small angle approximation" and for what angles is it appropriate?

Answer: sin(e) = e when e « 1 radian (i.e., 57. degrees)

Diff: 2

5) If two light waves are coherent, which of the following is NOT necessary?

A) They must have the same frequency.

B) They must have the same wavelength.

C) They must have the same amplitude.

D) They must have the same velocity.

E) They must have a constant phase difference at every point in space.

Answer: C

Diff: 2

412

Ch 17 Review Questions – Reflection and Mirrors

809: I can apply the law of reflection.

1. Draw a picture illustrating the law of reflection, labeling relevant angles. Also, label the incident ray and reflected ray.

17.1: I can apply the law of reflection to a flat mirror.

17.12: I can distinguish between diffuse and specular reflection.

2. What is an example of a surface that has diffuse reflection? Specular? You may want to

draw diagram for yourself.

17.2: I can distinguish between convex and concave mirrors.

3. Which mirror do you think is often called a “diverging mirror”, the convex or the concave?

Why?

4. T or F : All incoming rays parallel to the principal axis for a concave mirror get reflected and

then pass through the focal point.

17.3: I can identify which type of mirror corresponds to a negative or positive focal length.

5a. Explain why you could say that a convex mirror has a “virtual” focal point. This is one way

of interpreting the negative sign of its focal length.

5b. What is another way of remembering/explaining why a convex mirror has a negative focal

length? Think about a number line…

17.4: I can identify whether an image for a given mirror is considered to have a positive or

negative image distance.

6. What does a negative image distance imply for a mirror? Conversely, what does a positive

image distance imply?

17.5: I can identify when an object has a positive or negative magnification for a given mirror.

7. What does a negative magnification imply for a mirror? Conversely, what does a positive

magnification imply? Be careful not to make assumptions and to consider all cases. Look at

your notes or draw diagrams if it helps you.

17.6: I can identify when an object has an absolute value of magnification less than unity or

greater than unity for a mirror. (Note: “unity” is the fancy science/math word for the number 1)

8. If an image has a magnification of -4.2, what does that mean? How would that change if it

were +4.2?

9. If an image has a magnification of -0.7, what does that mean? How would that change if it

were +0.7?

17.7: I can draw ray diagrams for both convex and concave mirrors.

10. Can you jot down, in your own words, 2-3 steps explaining how to do a ray diagram for

concave mirrors? Convex? Don’t look at the list of steps given on the worksheet. The only

thing you may use is an actual ray diagram to jog your memory.

17.8: I can label all relevant variables on a ray diagram.

17.9: I can calculate the object distance, image distance or focal length of a mirror when given sufficient information in a problem.

17.10: I can calculate the object height or image height when given sufficient information in a problem.

17.11: I can calculate the magnification of a mirror when given sufficient information in a problem.

I have a 65 mm focal length CONVEX mirror. I place an upright meter-stick 25 mm from

the mirror.

11a. Draw a sketch of the situation using a straight-edge.

11b. Find the image distance. Comment on its sign.

11c. Find the magnification. Comment on its magnitude and sign.

11d. Find the image height.

2) The use of wave fronts and rays to describe optical phenomena is called A) wave optics. B) geometrical optics. C) dispersive optics. D) quantum optics.

Answer: B Diff: 1

1) A laser beam strikes a plane reflecting surface with an angle of incidence of 37°. What is the angle between the incident ray and the reflected ray? Answer: 74.0° Diff:2 2) The Apollo missions left mirrors on the moon so laser beams could be reflected off the moon from the Earth. The moon wobbles so a regular mirror would seldom be lined up correctly, yet the mirrors are always correctly aligned. How do you suppose NASA accomplished this? Answer: They used "corner reflectors" shaped like the vertex of a cube. A ray of light hitting such a mirror will return along the incident direction. Diff:3 3) The angle of incidence can vary between zero and

A) 1 radian.

B) /2 radians. C) π radians. D) 2π radians. E) 3π/2 radians.

Answer: B Diff:1 4) Law of reflection is which of the following?

Answer: A Diff: 1 5) When light shines on the surface of this page, the reflection is

A) diffuse. B) total.

C) specular. Answer: A Diff: 1

6) Reflection all a shiny mirror is called A) specular reflection. B) diffuse reflection. C) irregular reflection. D) internal reflection.

Answer: A Diff: 1 7) The angle of incidence

A) must equal the angle of reflection. B) is always less than the angle of reflection. C) may be greater than, less than, or equal to the angle of reflection. D) is always greater than the angle of reflection.

Answer: A Diff:l 23.1 Plane Mirrors 1) A plane mirror forms an image that is

A) real and upright. B) real and upside down. C) virtual and upright. D) virtual and upside down.

Answer: C Diff: 2 2) The IMAGE of a plane mirror (of a real object) has the following characteristics:

A) virtual, inverted, and magnification> 1 B) virtual, erect, and magnification = 1 C) real, erect, and magnification = 1 D) real, inverted, and magnification < 1

Answer: B Diff: 2 3) David stands 2.5 meters in front of a plane mirror.

(a) How far from David is David's image in the mirror? (b) If David moves away from the mirror at 1.5 ml s, how fast are David and his image moving

apart from each other? (c) If David is 180. cm tall, how tall is his image in the mirror?

Answer: (a) 5.0 m

(b) 3.0 m/s (c) 180. cm

Diff:3

4) An object is placed a distance d in front of a plane mirror. The size of the image will be

A) dependent on the distance d. B) half as big as the size of the object. C) twice the size of the object. D) dependent on where you are positioned when you look at the image. E) the same size as the object, independent of the distance d or the position of the observer.

Answer: E Diff:2 5) Suppose a lighted candle is placed a short distance from a plane mirror, as shown here. Where will the image of the flame be located?

A) at A B) at B C) at C D) at M (at the mirror)

Answer: C Diff:2 6) At which, if any, of the points indicated here should you place your eye if you wish to see an image of the arrow in the mirror?

A) A B) B C) C D) D

Answer: D Diff:2 9) II you place a plane mirror vertically into water, and a dolphin moves toward it with a speed of 4 m/s, she will see her image move toward her at a relative speed of

A) 6. m/s. B) 10. m/s. C) 2. m/s. D) 4. m/s. E) 8. m/s.

Answer: E Diff: 2 13) You may have seen ambulances on the street with the Jetters of the word AMBULANCE written on the front of them, in such a way as to appear correctly when viewed in your car's rear-view mirror.

How do the letters appear when you look directly at the ambulance?

A) figure a B) figure b C) figure c D) figure d E) figure e

Answer: E Diff: 2 23.2 Spherical Mirrors 1) If you stand in front of a convex mirror, at the same distance from it as its focal length,

A) you will see your image and you will appear smaller. B) you won't see your image because there is none. C) you will see your image and you will appear larger. D) you will see your image at your same height. E) you won't see your image because it's focused at a different distance.

Answer: A Diff: 2 2) A 2.3 cm tall statue is 15. cm in front of a convex mirror. The mirror radius of curvature is 18. cm.

(a) Is the image real or virtual? (b) How far is the image from the mirror? (c) Is the image upright or inverted? (d) How high is the image?

Answer: (a) virtual (b) 5.6cm (c) upright (d) 0.86 cm

Diff:3 4) A "parallel ray" is a ray parallel to the

A) mirror radius B) object axis C) chief ray D) principal axis

Answer: D Diff: 1 5) Given a concave mirror, rays of light originating from the center of curvature reflect off the mirror and focus at

A) 2r from the mirror. B) the focal point. C) the center of curvature. D) infinity.

Answer: C Diff: 2 6) The magnification M = -di/ do is the ratio of image to object

A) angular size. B) distance. C) focal distances. D) heights.

Answer: B Diff: 1 7) A 3.0 cm tall statue is 24. cm in front of a concave mirror. The mirror radius of curvature is 20. cm.

(a) Is the image real or virtual? (b) How far is the image from the mirror? (c) Is the image upright or inverted? (d) How high is the image? Answer: (a) real (b) 17. cm (c) inverted (d) 2.1 cm Diff: 3

10) Describe a mirror which takes an object at a distance of 47. cm and forms a real image at 23. cm. Answer: concave mirror with focal length 15.4. cm (radius 31. cm) Diff: 2 11) A negative magnification for a mirror means

A) the image is inverted, and the mirror is concave. B) the image is inverted, and the mirror is convex. C) the image is inverted, and the mirror may be concave or convex. D) the image is upright, and the mirror may be concave or convex. E) the image is upright, and the mirror is convex.

Answer: C Diff 2 12) Which of the following is an accurate statement?

A) A mirror always forms a virtual image. B) A mirror always forms a real image. e) A mirror always forms an image larger than the object. D) A mirror always forms an image smaller than the object. E) None of the other choices are true.

Answer: E Diff:2 13) Two parallel rays (also parallel to the principal axis) reflect from a concave mirror. They intersect at

A) the center of curvature. B) the focal point. C) a point behind the mirror. D) infinity.

Answer: B Diff: 2 15) Sometimes when you look into a curved mirror you see a magnified image (a great big you!) and sometimes you see a diminished image (a little you). If you look at the bottom (convex) side of a shiny spoon, what will you see?

A) You will either see a little you or a great big you, depending on how near you are to the spoon.

B) You will see a little you, upside down. C) You will see a little you, right side up. D) You won't see an image of yourself because no image will be formed. E) You will see a little you, but whether you are right side up or upside down depends on how

near you are to the spoon.

Answer: C Diff: 2 16) An object is placed 3 cm from a convex mirror of radius 4 cm. (a) Graphically determine the size and position of the image. (b) Is the image real or virtual? Answer: (a) (see sketch) (b) virtual Dilf: 3 17) In using ray tracing to graphically locate the image of an object that is placed in front of a mirror, describe three simple rays that you could draw that pass by the head of the object.

Answer: Ray 1: the radial ray; i.e., the ray drawn toward the center of curvature, which is then reflected back along the same path. Ray 2: the parallel ray; i.e., the incoming ray parallel to the main axis, which is then reflected along a path that extends to the focal point. Ray 3: the focal ray; i.e., the ray drawn toward the focal point, which is then reflected back parallel to the main axis. Diff:3 19) An object is placed 6 cm from a concave mirror of radius 4 cm. Graphically determine:

(a) the image position. (b) if the image is larger, smaller, or the same size as the object. (c) if the image is real or virtual.

Answer: (a) (shown)

(b) smaller

(c) real Diff:3

21) The rear-view mirrors on the passenger side of many new cars have a warning written on them: "OBJECTS IN MIRROR ARE CLOSER THAN THEY APPEAR." This implies that the mirror must be

A) concave. B) plane. C) convex. D) transparent.

Answer: C Diff: 1 22) If you stand in front of a concave mirror, exactly at its focal point,

A) you won't see your image because there is none. B) you will see your image, and you will appear smaller. C) you will see your image at your same height. D) you will see your image and you will appear larger. E) you won't see your image because it's focused at a different distance.

Answer: A (your image is at infinity. All you will see is a very very large blur) DiJf: 2 23) If you stand in front of a concave mirror, exactly at its center of curvature,

A) you will see your image and you will appear smaller. B) you will see your image and you will appear larger. C) you won't see your image because there is none. D) you won't see your image because it's focused at a different distance. E) you will see your image at your same height.

Answer: E (you are twice the focal length away. Try the math.) Diff: 2 24) If you stand in front of a convex mirror, at the same distance from it as its radius of curvature,

A) you won't see your image because there is none. B)you will see your image and you will appear larger. C) you will see your image and you will appear smaller. D) you will see your image at your same height. E) you won't see your image because it's focused at a different distance.

Answer: C Diff: 2 25) An object 2.0 cm tall is placed 24. cm in front of a convex mirror whose focal length is 30. cm.

(a) Where is the image formed? (b) How tall is it?

Answer: (a) 14. cm behind the mirror (b) 1.2 cm tall Di!!: 3 26) An object is placed 15. cm from a concave mirror of focal length +20. cm. If the object is 4.0 cm tall,

(a) where is the image formed? (b) how tall is it?

Answer: (a) 60. cm behind the mirror

(b) 16. cm tall Diff: 3

ADVANCED – Extra challenge

8) ADVANCED. At an amusement park you stand between two plane mirrors, which intersect at an angle of 60°. You are positioned at point P in the drawing here. You are 1.0 m from the nearest mirror, and 15° above it. What is the distance from you to the nearest image and to the second nearest image? Answer: 2.0 m ; 5.5 m Oiff:2 7) Two plane mirrors intersect at an angle of 120'. Draw ray diagrams to determine the locations of all the images formed by an object placed at a point P between the mirrors, closer to one mirror than the other. Answer: Oifj: 3 14) A man 190. cm tall stands 25. m from a plane wall mirror. One meter in front of him sits his dog, 30. cm tall. What minimum mirror size is needed for the man to see all of his dog's reflection? Answer: 18.8 cm tall DifJ: 2

12) A friend who is 180. cm tall stands 2.0 m from a plane wall mirror. You stand slightly behind him, 3.0 m from the wall mirror. How tall must the mirror be if you are to see all of your friend in the mirror? Answer: 1.08 meter Diff: 2

Chapter 18 Focused Review – Refraction and Lenses revised 04/18/11

Reference Information

Medium Index of refraction Medium Index of refraction

Vacuum 1.00000 Crown glass 1.52

Air 1.0003 Quartz 1.54

Water 1.33 Flint glass 1.61

Ethanol 1.36 Diamond 2.42

ROE Objectives

808. I can identify and describe refraction.

What causes refraction? When does is occur?

OPRF Physics Custom Objectives

1. I can locate angle of incidence and angle of refraction on a Snell’s law diagram.

What is a “normal line” in the context of Snell’s law?

2. I can define index of refraction mathematically and explain its meaning in my own words.

Given the speed of light in cubicblingonia is 2.5 x 108 m/s, the index of refraction in this substance is________.

3. I can predict what will happen when a ray of light traveling through a medium approaches the

boundary to another medium with a different index of refraction.

Explain how a mirage occurs, making mention of refractive index, temperature, and light rays.

4. I can define Snell’s law and use it to analyze different scenarios concerning refraction.

What is Snell’s law used for? Be specific in your description and use accurate

vocabulary.

5. I can describe total internal reflection in my own words and calculate “critical angle”.

How does a fiber optic cable work?

6. I can define dispersion ,recognize examples of dispersion, and explain its connection with the

concept of refraction.

Why does dispersion happen? Explain why different colors of light refract to varying degrees (no pun intended).

7. I can distinguish between the shape & characteristics of a concave lens versus those of a

convex lens.

What kind of images can concave lenses produce? Convex?

What kind of lens would you use for a magnifying glass and why? Use previous ray diagrams if you’re stuck.

8. I can interpret/comment on the numerical value of the focal length for a concave lens and for

a convex lens.

Which lens has a positive focal length? Negative?

9. I can interpret/comment on the numerical value of the image distance for a concave lens and

for a convex lens.

When could you get a negative image location? What does the negative mean?

10. I can interpret/comment on the numerical value of the magnification for a concave lens and for

a convex lens.

What does a negative magnification imply? Be precise in the wording of your

answer.

11. I can use the lens equation to make predictions about image position and other relevant

variables for a given optics scenario.

An object that is 30 cm tall is held 120 cm away from a convex lens of focal length of 40 cm. Does the image form on the same side as the object or on the opposite side? At what distance?

12. I can describe diagram how lenses relate to human vision and their applications for correction

common vision problems.

The image that your eye receives is ____________ a. Erect b. inverted c. could be either erect or inverted d. cannot determine

Light entering the eye focuses on a layer of light-sensitive tissue at the back of the eye called the ____________________.

13. I can draw a ray for convex and for concave lenses.

Complete the ray diagram for the lens below showing the image location, size and orientation.

Real or virtual

“Right-side-up” or inverted

Complete the ray diagram for the lens below showing the image location, size and orientation.

Real or virtual

22.1 Wave Fronts and Rays 2) The use of wave fronts and rays to describe optical phenomena is called

A) wave optics. B) geometrical optics. C) dispersive optics. D) quantum optics.

Answer: B Diff:l 22.3 Refraction 1) A ray of light, which is traveling in a vacuum, is incident on a glass plate (n = ng). For increasing angles of incidence, the angle of refraction

A) increases, approaching the limiting value of 90°. B) decreases, approaching the limiting value of zero degrees. C) increases, approaching the limiting value of sin-1(1/ng) degrees. D) increases, approaching the limiting value of sin-1(1/ng) degrees.

Answer: C Dif!' 2 Chapter 22 Reflection and Refraction of Light 2) Which of the following is equivalent to Snell's Law? (v is light velocity)

Answer: D Diff:2 3) A light beam having a wavelength of 470. nm in air is directed into glycerine (n = 1.47).

(a) What is the frequency of the light in the glycerine? (b) What is its wavelength in the glycerine? (c) If the incident angle is 75.0°,what is the refracted angle?

Answer: (a) 6.38 x 1014 Hz

(b) 320. nm (c) 41.1°

Diff: 3

4) As light refracts going from one medium to another, which of the following remains constant?

A) wavelength B) refractive index C) wave velocity D) frequency

Answer: D Diff: 2 6) How long does it take a light beam to cross a 6. m wide room? If the air were replaced with a transparent medium of index n, how much longer would it take? Answer: 2 x 10-8 s; n times longer Diff:3 7) When looking into a pond or lake of clear water, the apparent depth is what fraction of the actual depth? A) 1/4 B) 1/3 C) 1/2 D) 9/10 E) 3/4 Answer: E Diff:3 8)

Answer: B Diff: 2 9) If a transparent material has an index of refraction of 1.67, what is the speed of light in the material? Answer: 0.599c = 1.80 x 108 m/ s Diff: 2 10) Red light with a wavelength of 650. nm travels from air into a liquid with an index of 1.33. What is the frequency and wavelength in the liquid? Answer: 4.61 x 1014Hz and 489. nm Diff: 3

11) My flashlight beam makes an angle of 60. degrees with the surface of the water before it enters the water. In the water what angle does the beam make with the surface?

A) 0° B) 30° C) 60° D) 22° E) 68°

Answer: E Diff: 2 12) A ray of light consisting of blue light (wavelength 480 nm) and red light (wavelength 670 nm) is incident on a thick piece of glass at 80°. What is the angular separation between the refracted red and refracted blue beams whiie they are in the glass? (The respective indices of refraction for the blue light and the red light are 1.4636and 1.4561.)

A) 0.277° B) 0.455° C) 0.330° D) 0.155° E) 0.341°

Answer: A Diff: 3 13) Which of the following materials has the slowest speed of light?

A) water B) oil C) air D) flint glass E) diamond

Answer: E Diff:l 14) Light of wavelength 550. nm in air is found to travel at 1.96x 108 m/ s in a certain liquid.

(a) Determine the index of refraction of the liquid, (b) Determine the frequency of the light in air.

Answer: (a) 1.53 (b) 5.45 x 1014 Hz Diff:3 15) A beam of light (f = 5 x 1014 Hz) enters a piece of glass (n = 1.5). What is the frequency of the light while it is in the glass?

A) 5 x 1014 Hz B) 7.5 x 1014 Hz C) 3.33 x 1014 Hz D) 5 x 1013 Hz E) 7.5 x 1013 Hz

Answer: A Diff: 1 16) A parallel light beam containing two wavelengths. 480. nm and 700. nm, strikes a plain piece of glass at an angle of incidence of 60°. The index of refraction of the glass is 1.4830 at 480. nm and 1.4760 at 700. nm. Determine the angle between the two beams in the glass. Answer: 0.196° Diff 3 17) An oil layer that is 5.0 cm thick is spread smoothly and evenly over the surface of water on a windless day. What is the angle of refraction in the water for a ray of light that has an angle of incidence of 45° as it enters the oil from the air above? (The index of refraction for oil is 1.15, and for water it is 1.33.)

A) 32.1° B) 27.2° C) 35.5° D) 25.6° E) 38.6°

Answer: A Diff: 2 18) A light beam composed of red and blue light is incident upon a rectangular glass plate, as shown. The light emerges into the air from point P as two separate beams A) that are parallel, with the red beam displaced below the blue beam. B) that are parallel, with the blue beam displaced below the red beam. C) that are not parallel, with the blue beam displaced below the red beam. D) that are not parallel, with the red beam displaced below the blue beam. Answer: B Diff:3 19) A ray of light, which is traveling in air, is incident on a glass plate at a 45° angle. The angle of refraction in the glass

A) is greater than 45°. B) is less than 45°. C) is equal to 45°. D) is unknown because it all depends on the index of refraction of glass. Answer: B Diff: 1 20) When a ray of light passes obliquely from one medium to another, which of the following changes?

A) direction of travel B) speed, direction of travel, but not wavelength C) wavelength D) wavelength, speed, & direction of travel E) speed

Answer: D Diff: 2 21) A point source of light is positioned 20.0m below the surface of a lake. What is the diameter of the largest circle on the surface of the water through which light can emerge? Answer: 45.6m Diff:2 22) A beam of light, traveling in air, strikes a plate of transparent material at an angle of incidence of 56°. It is observed that the reflected and refracted beams form an angle of 90°. What is the index of refraction of this material?

A) n = 1.43 B) n = 1.53 C) n = 1.40 D) n = 1.48 E) n = 1.44

Answer: D Diff:2 23) Shown here are some possible paths that a light ray can follow in going either from glass to air or from air into glass.

In the drawing you are not told whether the light is going from left to right or from right to left. Which path did the light follow?

A) path C B) path G C) path F D) path E E) path D

Answer: D Diff:2 24) When a beam of light (wavelength = 590 nrn), originally traveling in air, enters a piece of glass (index of refraction 1.50), its frequency

A) increases by a factor of 1.50. B) is reduced to 2/3 its original value. C) is unaffected.

D) increases by a factor of√

E) increases by a factor of.√

Answer: C Diff: 1 25) When a beam of light (wavelength = 590 nrn), originally traveling in air, enters a piece of glass (index of refraction 1.50), its wavelength

A) increases by a factor of 1.50. B) is reduced to 2/3 its original value. C) is unaffected.

D) increases by a factor of. .√ .

E) is reduced by a factor of. .√ . Answer: B Diff: 2 26) For all transparent material substances, the index of refraction

A) is less than 1. B) is greater than 1.

C) is equal to 1. D) could be greater than 1 or less than 1; it all depends on optical density.

Answer: B Diff: 1 27) The angle of incidence

A) is always greater than the angle of refraction. B) must equal the angle of refraction. C) is always less than the angle of refraction. D) may be greater than, less than, or equal to the angle of refraction.

Answer: D Diff 2 28) Light travels fastest

A) in a vacuum. B) through water. C) through glass. D) through diamond.

Answer: A Diff: 1 29) A light ray strikes a glass plate of thickness 0.80 cm at an angle of incidence of 60°. The index of refraction of the glass is 1.55. By how much is the beam displaced from its original line of travel after it has passed through the glass? Answer: 0.42 cm Diff3 31) The index of refraction of diamond is 2.42. This means that a given wavelength of light travels

A) 2.42 times faster in air than it does in diamond. B) 2.42 times faster in diamond than it does in vacuum. C) 2.42 times faster in vacuum than it does in diamond. D) 2.42 times faster in diamond than it does in air.

Answer: C Diff: 2 32) When a light wave enters into a medium of different optical density

A) its speed and frequency change. B) its speed and wavelength change. C) its frequency and wavelength change. D) its speed, frequency, and wavelength change.

Answer: B Diff: 2 33) Light of wavelength 550 nm in air is found to travel at 1.96x 108 ml s in a certain liquid.

Determine (a) the frequency of the light in the liquid. (b) the wavelength of the light in the liquid. Answer: (a) 5.45 x 1014Hz (b) 359. nm Diff:3 34) Index of refraction is which of the following? Answer: D Diff:2 35) Apparent depth is which of the following?

Answer: C Diff: 2 36) Optical density is directly proportional to

A) mass density. B) light speed. C) index of refraction. D) index of reflection.

Answer: C Diff:2 37) Snell's law is equivalent to which of the following?

Answer: B Diff:2 38) An index of refraction less than one for a medium would imply that A) refraction is not possible. B) the speed of light in the medium is greater than the speed of light in vacuum. C) the speed of light in the medium is the same as the speed of light in vacuum. D) reflection is not possible. Answer: B Diff: 1 39) A light beam enters water at an angle of incidence of 37°. Determine the angle of refraction. Answer: 26.9 ° Diff:2 22.4 Total Internal Reflection and Fiber Optics 1) Critical angle is which of the following?

Answer: E Diff: 1 2) The critical angle in ordinary glass is

A) greater than 45°. B) sin(1/n). C) less than 45°. D) 45°.

Answer: C Diff: 1

3) A light beam with wavelength 440. nm in a material then enters air and its wavelength becomes 577. nm. (a) What is the index of refraction for the material? (b) At what angle with the surface will the beam be totally reflected back in the material? Answer: (a) 1.31 (b) 40.30 Diff: 3 4) The critical angle is given by sinc(1/n1) for what condition? Answer: The second index n2 =1.00 Diff: 1 5) Fiber optics depends upon the phenomenon of

A) total internal reflection. B) diffuse reflection. C) polarization. D) dispersion.

Answer: A Diff: 1 6) When TOTAL REFLECTION occurs at a surface, the incident angle must be in the substance with the higher

A) speed of light. B) index of refraction. C) incident angle. D) c/n.

Answer: A Diff: 1 7) An optical fiber is 1.00 meter long and has a diameter of 20.0 flm. Its ends are perpendicular to its axis. Its index of refraction is 1.30.What is the minimum number of reflections a light ray entering one end will make before it emerges from the other end?

A) 2.42 x 105 B) 2.56 x 105 C) 2.02 x 105 D) 1.85 x 105 E) 2.85 x 105

Answer: D Diff: 3 8) Light in a transparent material (index of refraction 1.333)strikes the boundary with another transparent material (n = 1.010) . (a) What is the critical angle for total internal reflection?

(b) By what percent does the wavelength change going from the 1st to the 2nd material? Answer: (al 49.26° (b) 32.0% Diff: 3 9) For certain angles, TOTAL INTERNAL REFLECTION can occur when light tries to pass from one medium to another which has

A) a larger index of refraction. B) a smaller index of refraction. C) the same index of refraction. D) an index of refraction which is sin-1(45°). E) an index of refraction which is sin-1(n).

Answer: B Diff:l 10) The critical angle for a beam of light passing from water into air is 48.8'. This means that all light rays with an angle of incidence greater than this angle will be

A) absorbed. B) totally transmitted. C) partially reflected and partially transmitted. D) totally reflected.

Answer: D Diff:l 11 ) A ray of light (inc) enters a 45° - 90° glass prism from air (bottom left), as shown. In what direction does the light re-emerge back into the air?

A) D B) B C) A D) C E) E

Answer: E Diff: 2

12) The end of a cylindrical plastic rod is polished and cut perpendicular to the axis of the cylinder. Determine the minimum index of refraction so that a light ray entering the end of the rod will always be totally internally reflected within the rod, i.e., it will never escape the rod until it comes to the other end. Answer: 1.414 Diff:2 13) Mirages are due to

A) reflection. B) polarization. C) refraction. D) dispersion. E) total internal reflection.

Answer: C Diff: 1 14) A light ray enters a glass enclosed fishtank. From air it enters the glass at 20.0° with respect to the surface, then emerges into the water. The index for glass is 1.50 and for water 1.33.

(a) What is the angle of refraction in the glass? (b) What is the angle of refraction in the water? (c) Is there any incident angle in air for which the ray will not enter the water due to total

internal reflection? Answer: (a) 39° (b) 45° (c) no Diff: 3 15) Fiberscopes are based on the physical phenomena called

A) diffusion. B) dispersion. C) total internal reflection. D) absorption. E) polarization.

Answer: C Diff: 1 16) A light ray emerges from the bottom of a 45° glass prism into air, as shown in the sketch.

From which direction was the ray incident on the prism?

A) A B) B C) C D) D

Answer: D Diff: 2 17) What is the critical angle for light traveling from crown glass (n; 1.52) into water (n; 1.33)?

A) 66° B) 42° C) 57° D) 48° E) 61°

Answer: E Diff: 2 22.5 Dispersion 1) The person who proved that white light is composed of light of different colors is

A) Willebrod Snell. B) Christen Huygens. C) Isaac Newton. D) General Electric. E) Thomas Edison.

Answer: C Diff: J 2) In common transparent media, as the frequency of light increases, the index of refraction

A) increases. B) stays constant. C) decreases. D) varies as the sine of the incident angle.

Answer: A Diff: 1 4) You can only see a rainbow if

A) the sun is behind you. B) the sun is in front of you. C) the sun is 90° to the side. D) the sun is 180° to the side.

Answer: A

Diff: 1 5) White light is

A) dichromatic. B) monochromatic. C) achromamtic. D) polychromatic.

Answer: D Diff: 1 6) Rainbows are caused by sunlight being

A) dispersed. B) dispersed, refracted, & reflected. C) refracted. D) reflected. E) refracted & reflected but not dispersed.

Answer: B Diff: 1 7) The color on the outer edge of the primary rainbow is

A) white B) red C) violet D) yellow E) green

Answer: B Diff: 1 8) White light, coming from medium 1 (index of refraction n1), will disperse upon entering medium 2 (index of refraction n2) when

A) (n2 > n1). B) (n2 < n1). C)(n2 = n1). D) (n2 > n1) or (n2 < n1).

Answer:D Diff: 2 9) When the index of refraction of a transparent material varies with wavelength, the material exhibits

A) density variation. B) polarization. C) dispersion. D) reflection. E) total internal reflection.

Answer: C

Diff: 1 10) Which of the following colors undergoes the greatest REFRACTION when passing from air into glass?

A) yellow B) red C) blue D) orange E) green

Answer: C Diff: 1 11 ) White light is

A) light of wavelength 550 nm, in the middle of the visible spectrum. B) the term used to describe very bright light. C) a mixture of red, green, and blue light. D) a mixture of all frequencies. E) the opposite (or complementary color) of black light.

Answer: C or D Diff: 1 12) Laser light is

A) invisible in air. B) monochromatic. C) dispersive. D) created by total reflection.

Answer: B Diff: 1 13) When white light enters a more optically dense medium than that from which it came, the green color component refracts____________ the red color component.

A) more than B) the same as C) less than

Answer: A Diff: 1 14) White light is

A) the absence of color. B) polychromatic. C) monochromatic.

Answer: B Diff: 1 15) Which color of light undergoes the greatest refraction when passing from air to glass?

A) yellow B) red C) green D) blue E) cyan

Answer: D Diff:l 16) More of the rainbow can be seen from the ground when

A) the sun is higher. B) there is an eclipse. C) the sun is lower. D) the sun is in front of you.

Answer: C Diff: 1 17) A beam of white light is incident on a thick glass plate with parallel sides, at an angle between 0° and 90° with the normal. Which color emerges from the other side first? A) red B) green C) violet D) none of the other choices; all colors emerge at the same time Answer: A Diff: 2 18) The color on the outer edge of a rainbow is _____for the primary rainbows and ___for the secondary.

A) violet, red B) violet, violet C) red, violet D) green, yellow E) red, red

Answer: C Diff: 1 19) The index of refraction for a certain material is 1.399 for red light and 1.432 for blue light. Find the angle separating the two refracted colors if the:

(a) angle of incidence is 30°. (b) angle of incidence is 60°.

Answer: (a) 0.500 (b) 1.040 Diff:3

23.3 Lenses 1) A lens projects an image of a man as seen in the figure. Rays marked A, B, and C travel to the lens from the man's ear.

Draw the three refracted rays as they proceed to the right of the lens; noting that A is parallel to the axis, B goes through the center of the lens, C proceeds to the bottom of the lens, and the point marked f is the focal point of the lens. Answer: Diff: 3 2) In a single-lens reflex camera the lens-film distance may be varied by sliding the lens forward or backward with respect to the camera housing. If, with such a camera, a fuzzy picture is obtained, this means that

A) the lens was too far from the film. B) too little light was incident on the film. C) the lens was too close to the film. D) one cannot say which of the other reasons is valid. E) too much light was incident on the film.

Answer: D (most likely A or C, but can’t be sure.) Diff: 2 3) A 3.0 cm tall statue is 48. cm in front of a biconvex lens (focal length 20. cm).

(a) Is the image real or virtual? (b) How far is the image from the lens?

(c) Is the image upright or inverted? (d) How high is the image?

Answer: (a) real

(b) 34.cm (c) inverted (d) 2.1cm

Diff:3 5) A slide projector is designed with its lens 6.0 m from the screen. The projected image is 1.5m square of a slide object 2.5 cm square.

(a) What is the object distance from the lens? (b) What should be the lens focal length? (c) What is the lens POWER?

Answer: (a) 10. cm

(b) f = 9.8 cm (c) 10.2 Diopters

Diff:3 6) The image of the rare stamp you see through a magnifying glass is

A) always the same orientation as the stamp. B) always upside-down compared to the stamp. C) either the same orientation or upside-down, depending on how close the stamp is to the

glass. D) either the same orientation or upside-down, depending on the thickness of the glass used.

Answer: C (although D is true to some extent) Diff: 2 9) Consider a converging lens forming an image on a screen. What property of the image would be affeeled by covering the top half of the lens? Answer: It would be half as bright since half of the light gets through the lens. Same image. Diff: 2 10) A lamp is placed 1m from a screen. Between the lamp and the screen is placed a converging lens of focal length 24 cm. The filament of the lamp can be imaged on the screen. As the lens position is varied with respect to the lamp,

A) a sharp image will be seen when the lens is 60 cm from the lamp. B) a sharp image will be seen when the lens is 40 cm from the lamp. c) no sharp image will be seen for any lens position. D) a sharp image will be seen when the lens is halfway between the lamp and the screen. E) a sharp image will be seen when the lens is either 40 cm from the lamp or 60 cm from the

lamp, but not otherwise.

Answer: E Diff: 2 12) When an object is placed 60. cm from a converging lens, it forms a real image. When the object is moved to 40. cm from the lens, the image moves 10. cm farther from the lens. What is the focal length of the lens?

a. 42cm b. 50cm c. 40cm d. 20cm e. 30cm

Answer: A Diff: 2 15) Is it possible to see a virtual image?

A) no, since virtual images do not really exist B) no, since the rays that seem to emanate from a virtual image do not in fact emanate from

the image C) yes, since the rays that appear to emanate from a virtual image can be focused on the

retina just like those from an illuminated object D) yes, since almost everything we see is virtual because most things do not themselves give

off light, but only reflect light coming from some other source E) yes, but only indirectly in the sense that if the virtual image is formed on a sheet of

photographic film, one could later look at the picture formed Answer: D Diff: 2 16) How far from a lens of focal length 50.0 mm must the object be placed if it is to form a virtual image magnified in size by a factor of three?

A) 33.3 mm B) 48.0 mm C) 38.3 mm D) 42.2 mm E) 54.4 mm

Answer: A Diff: 2 17) A slide projector has a lens of focal length 150. mm. An image 100. cm x 100. cm is formed of a slide whose dimensions are 50.0 mm x 50.0 mm. How far from the lens must the screen be placed? Answer: 3.15 m Diff:2 18) Two thin lenses, of focal lengths f1 and f2, placed in contact with each other are equivalent to a single lens of focal length

A) f1 + f2. B) 1/ ( f1 + f2).

C) f1f2/ (f1 + f2). 0) ( f1 +f2)/ f1f2. E) (l/f1) + 0/f2).

Answer: C Diff: 2 21) How does the thickness of a lens relate to it being converging or diverging? Answer: A converging lens is thicker at its center than it is at its edges and a diverging lens is thinner at its center than it is at its edges. Diff: 1 22) A camera with a telephoto lens of focal length 125.mm is used to take a photograph of a plant 1.8m tall. The plant is 5.0 m from the lens.

(a) What must be the distance between the lens and the camera film if the image is sharply focused?

(b) How tall is the image? Answer: (a) 128.mm from lens to film

(b) 45. mm tall Diff: 3 23) Where must an object be placed with respect to a converging lens of focal length 30 cm if the image is to be virtual, and three times as large as the object? Answer: 20 cm from the lens Diff: 2 25) In using ray tracing to graphically locate the image of an object that is placed in front of a lens, describe three simple rays that you could draw that pass by the head of the object. Answer: Ray 1: the vertex ray; i.e., the ray passing through the center of the lens, which emerges undeflected. Ray 2: the parallel ray; i.e., the incoming ray parallel to the main axis, which is then refracted along a path that extends to the focal point.

Ray 3: the focal ray; i.e., the ray drawn toward the focal point, which is then refracted parallel to the main axis.

Diff: 3 26) How far from a 50. mm focal length lens, such as is used in many 35. mm cameras, must an object be positioned if it is to form a real image magnified in size by a factor of three?

A) 58. mm B) 76. mm

C) 46.mm D) 67. mm E) 52. Mm

Answer: D Diff:2 28) An object is placed 9.5cm from a lens of focal length 24 cm.

(a) Where is the image formed? (b) What is the magnification?

Answer: (a) 16=from the lens on the same side as the object

(b) m = 1.7 DifI: 3 29) The images formed by double concave lenses

A) are always virtual. B) could be real or virtual, but always real when the object is placed at the focal point. C) could be real or virtual; it depends on whether the object distance is smaller or greater than

the focal length. D) are always real.

Answer: C Diff: 2 2) Spherical lenses suffer from

A) both spherical and chromatic aberration. B) spherical aberration, but not chromatic aberration. C) neither spherical nor chromatic aberration. D) chromatic aberration, but not spherical aberration.

Answer: A Diff: 1 3) If the refractive index of the glass in a lens varies with wavelength, then which of the following results?

A) spherical aberration B) light scattering C) total reflection D) astigmatism E) chromatic aberration

Answer: E Diff: 1 4) Spherical aberration can occur in

A) mirrors and lenses.

B) mirrors but not lenses. C) lenses but not mirrors.

Answer: A Diff:l 5) Chromatic aberration occurs because of

A) polarization. B) spherical surfaces. C) dispersion. D) internal reflection. E) astigma tism.

Answer: C Diff:1 6) When two parallel white rays pass through the outer edges of a converging glass lens, chromatic aberration will cause colors to appear on the screen in what order, from the top down?

A) red, blue, red, blue B) blue, red, blue, red C) red, blue, blue, red D) blue, red, red, blue E) blue, blue, red, red

Answer: D Diff:2 7) Compare two diverging lenses similar except that lens B is rated at 20 Diopters, whereas lens A is rated at 10 Diopters. The focal length of lens B is

A) twice the focal length of lens A. B) one-fourth of the focal length of lens A. C) one-half of the focal length of lens A. D) 1/..j2 of the focal length of lens A. E) four times the focal length of lens A.

Answer: C Diff: 1 8) Why do large aperture telescopes use a mirror instead of a lens to focus light? Answer: Large mirrors are much cheaper than lenses (the largest lens has a 1 m diameter) and mirrors have an added advantage of no chromatic aberration. Lenses have to be supported from the sides, so they can deform. Mirrors can be supported from underneath, so they won’t deform as much. Diff: 2

Advanced 7) A fish appears to be at the center of a spherical fish bowl. We know light rays leaving the bowl refract at the glass surface so where actually is the fish? (assume the water and glass have n = 1.33)

A) 1.33R behind the glass B) at the center C) R/1.33 behind the glass D) half way to the center

Answer: B Diff: 2 4) Light from an object proceeds through 3 lenses, each with magnification 2, -4, 0.2 respectively. The overall magnification is

A) 2 - 4 + 0.2 = -1.8. B) 2 x (-4) x 0.2 = -1.6. C) 2/(-4)/0.2 = -2.5. D) +8/5. E) +5/8.

Answer: B Diff: 2 24) The simplest type of camera is a pin-hole camera; you might have even made one. It consists of a box with a single pinhole in it, and a piece of film on the inner side opposite the hole. Suppose you photograph your friend with it. Your friend's image on the film will appear

A) upside down because light travels in a straight line. B) right side up because light travels in a straight line. C) upside down because light refracts at the pinhole. D) right side up because light refracts at the pinhole.

Answer: A Diff: 1 20) The power of the human eye is approximately how many Diopters? (hint: estimate the size of the eyeball)

A) 1 B) 4 C) -25 D) -4 E) 25

Answer: E Diff:2

Not covered

9) What POWER lens placed next to a lens of 25. cm focal length would produce a combination with an effective INFINITE focal length? Answer: -4.0 Diopters Diff: 2 10) A converging lens with the same curvature on both sides and focal length 25. cm is to be made from crown glass (n = 1.52).What radius of curvature is required for each face? Answer: 26. cm Diff: 2 11) A 4.0 cm high object is 20. cm in front of a 1.333 Diopter plano-convex lens.

(a) Find the image position. Real or Virtual? (b) Find the image size. Erect or Inverted?

Answer: (a) 60. cm in front of lens; virtual image

(b) 12. cm high; erect Diff: 3 12) Take the lens maker equation and show that a lens which has been turned around (surface 1 becomes 2 and 2 becomes 1) has the same focal length. Answer: 1/ f=(n-l)(l! Rl - I/R2) A sign change occurs when 1 and 2 are exchanged, and the radii themselves change sign because the center of curvature moves to other side of surface. These sign changes cancel each other out and yield the same f. Diff:3 14) A double convex lens has faces of radii 18.0 em and 20.0 em. When an object is placed 24.0 cm from the lens, a real image is formed 32.0 em from the lens. Determine: (a) the focal length of the lens. (b) the index of refraction of the lens material. Answer: (a) 13.7 em (b) n = 1.69 Diff:3 15) A double convex (convex-convex) thin lens has radii of curvature 46. cm, and is made of glass of index of refraction n = 1.60. What is the focal length?

A) 36. cm B) infinite C) 46. cm D) 18. cm

E) 30. Cm

Answer: E Diff: 2 16) What kind of lens is it that has a power of +10 Diopters and a first surface center of curvature in front of the lens?

A) double convex B) double concave C) converging meniscus D) plano concave E) plano convex

Answer: C Diff: 2

19) Two thin double-convex (convex-convex) lenses are placed in contact. If each has a focal length of 20. cm, how would you expect the combination to function? A) about like a single lens of focal length 40. cm B) about like a single lens of focal length 20. cm C) about like a single lens of focal length slightly greater than 20. cm 0) about like a single lens of focal length less than 20. cm Answer: 0 Diff:2 23.5 The Lens Maker's Equation 1 ) A +20 Diopter lens has what power in water? A) greater than 20. D B) the same 20. D Answer: C Diff: 2 C) less than 20. D 2) A plano-convex lens is to have a focal length of 40 em. It is made of glass of index of refraction 1.65. What radius of curvature is required? M~rm m~rm 011rm ~nrm m~rm Answer: B Diff: 2 408 Test Item File 3) A camera uses a biconvex lens made of glass with an index of refraction of 1.60 and has a radius of curvature of 12. cm for the 1st surface and 24. cm for the 2nd. (a) What is the focal length of this lens when used in air? (b) If used under water (n = 1.33), what is the focal length? Answer: (a) 13. cm (b) 39. cm Diff: 3 4) What is the FOCAL LENGTH of a lens whose two radii of curvatures are equal (RI =R2)? A) zero B) 2R2 / (n-I) C) infinite E) 1/ (2R2)

Answer: C Diff: 2 5) The curved surface of a 50. cm focal length "plano-convex" lens has a radius of curvature of 30. cm. What is the refractive index of the glass? Answer: n = 1.6 Diff: 2 6) What Diopter takes an object at 47. cm and forms an upright image 23. cm from the lens?

A) +2.20 B) -0.022 0 C) -2.2 0 D) 2.2 x 102 0 E) +0.0220

Answer: C Diff: 2 5) A person looks straight down into a large cube of glass. Three cm below the surface is a bubble. How far below the surface does the bubble appear to the person?

Answer: 2.0 cm below Diff:3 11 ) An object is placed at the origin. A converging lens of focal length 10mm is placed at x = 40 mm on the x axis. A second converging lens of focal length 20 mm is placed at x = 90 mm. Graphically determine the size and location of the final image. Answer: Diff:2

30) A buoy, used to mark a harbor channel, consists of a weighted rod 2.00 m in length. 1.50 m of the rod is immersed in water and 0.500 m extends above the surface. If sunlight is incident on the water with an angle of incidence of 40.0°, what is the length of the shadow of the buoy on the level bottom of the harbor? Answer: 1.25 m Diff: 2 20) A diverging lens (f = -4 cm) is positioned 2 cm to the left of a converging lens (f = +6 cm). A 1-mm diameter beam of parallel light rays is incident on the diverging lens from the left. After leaving the converging lens, the outgoing rays

A) diverge. B) converge. C) form a parallel beam of diameter 0 > 1 mm. D) form a parallel beam of diameter 0 < 1 mm. E) will travel back toward the light source.

Answer: C Diff: 2 27) Two very thin lenses, each with focal length 20. cm, are placed in contact. What is the focal length of this compound lens? N~= ~ill= C)n= ~m= mn= Answer: B Diff: 2 13) A concave meniscus lens with an index of refraction of 1.48 has radii of 6.0 cm and 4.0 cm (see figure). What is the power of the lens in DIOPTERS? A) -0.040

B) -20. C) -0.25 D) -0.20 E) -4.0

Answer: E Diff: 2 8) Describe a double convex lens made with n = 1.45 glass having radii of 27. cm. Answer: converging lens of power 3.3 Diopters (30.cm focal length) Diff: 2

Chapter 20 Review Questions

20.1 I can define the basics of electrostatics, conservation and charge interactions

1. If an object is attracted by a positively charged rod, we can be sure that the body is: a) negatively charged b) losing electrons c) either neutral or negative

2. As a positively charged object is brought steadily nearer to (but not touching) the knob of a

positively charged electroscope, the leaves of the electroscope: a) are not effected b) spread apart more c) come closer together

3. Like charges repel, whereas opposite charges attract.

a) True b) False

4. Electric charge can be created and destroyed, but the charges must be created and destroyed

in pairs (one + and one - )

a) True b) False

5. Electric forces can be either repulsive or attractive, whereas gravitational force is always:

a. Attractive b. Repulsive c. both a and b d. neither a nor b

6. Metals contain _____ electrons; rubber has _____ electrons. a. bound, free b. free, bound c. excess, insufficient

7. Charge carriers in a metal are electrons rather than protons, because electrons are

a) relatively far from a nucleus. b) loosely bound. c) Both a and b d) none of the above

20.2 Describe three methods of charging (friction, conduction, and induction)

8. A plastic ruler is rubbed with a towel and becomes charged. The towel is brought near an electroscope (like my pop can electropscope) and it is found to be charged. If I then bring my ruler to the electroscope, it should be: a) Neutral (not charged) b) oppositely charged as the towel c) the same charge as the towel

9. When a person standing on the ground touches a rod that is positively charged, the person:

a) gives the rod extra electrons b) gives the rod extra protons c) accepts the rods extra protons d) accepts the rods extra electrons

10. Objects can be charged by

a) touching (conduction) b) induction. c) friction. d) all of the above e) none of the above

11. Bring a charged object near a conductor and then momentarily ground it by touching one part. This demonstrates charge by

a) Induction. b) electrification. c) polarization. d) deduction.

12. Pie tins fly off the Van de Graaff generator because the generator charges them and then repel each other.

a. True b. False

13. Charged objects are attracted to neutral objects because of polarization

a. True b. False

20.3 Draw the redistribution of electric charges on a neutral object when a charged object is brought near and explain why an attractive force results from bringing a charged object near a neutral object.

14. A negatively charged balloon sticks to a wooden door. However, an uncharged balloon does not stick to a wooden door. What is the nature of the charge on the wooden door? a) Electrically neutral b) Positively charged c) Negatively charged d) Cannot be determined

20.4 Calculate the electric force between charged objects

15. What is the force between two small charged spheres that have charges of 2.0x10–7 C and 3 10–7 C and are placed 30 cm apart in air? a) 6 x 10-7 N b) 0.006 N c) 0.6 N

16. A charge of +6mC is 40cm from a charge of +8mC. What is the magnitude of the force

between them?

a. 2.7x106 N b. 2.7x108 N c. 1.4x106 N d. 1.4x108 N

20.5 Determine the new electric force on charged objects after they touch and are then separated.

17. One metal sphere has a charge of +10C and another has a charge of +8C. They are allowed to touch and are separated to a distance of one meter. What is the force between them?

a) 7.29 x 1011 N b) 7.29 N c) 7.29 x 106N

20.6 Predict electrostatic force and strength of electric field based on relationship between variables

18. Particle A has twice as much charge as particle B. Compared to the force on particle A, the force on particle B is

a) two times as much. b) four times as much. c) the same. d) half as much. e) none of the above

19. _____ vary/varies inversely as the square of the distance between two point objects.

a. Gravitational force b. Electric force c. Neither a nor b d. Both a and b

20. If the distance between two charges becomes 1/6 as much, what is the new force between

them?

a. 1/36 N b. 36 times as much as the original force c. 6 N d. 6 times the original force

1. Electrons carry a

a. positive charge. b. Negative charge c. neutral charge. d. variable charge.

Answer: B Diff: 1 3) Since there is a universal Law of Conservation of Charge

A) charges can be annihilated but not created. B) charges cannot be created or destroyed. C) charges can be created and destroyed.

Answer: C Diff:2 4) Which is true?

A) Unlike charges repel. B) All charges attract. C) Unlike charges attract. D) Like charges attract.

Answer: C Dijf: 1 5) A neutral atom has

A) equal numbers of electrons, protons, and neutrons. B) equal numbers of protons and neutrons. C) equal numbers of electrons and neutrons. D) equal numbers of electrons and protons. E) zero neutrons.

Answer: D Dijf: 1 7) Charge is

A) invariant. B) conserved C) quantized. D) invariant, conserved, and quantized

Answer: D Diff:l 10) The two types of charge (plus and minus) were named by

A) Lord Rutherford. B) Benjamin Franklin. C) Albert Einstein. D) Richard Feynman. E) Newton.

Answer: B Diff:l 11) Can you get an electric shock by touching a charged insulator?

A) only if you are insulated B) yes C) no

Answer: B Diff:l 1) A glass rod is rubbed with a piece of silk. During the process the glass rod acquires a positive charge and the silk

A) acquires a positive charge also. B) remains neutral. C) acquires a negative charge. D) could either be positively charged or negatively charged. It depends on how hard the rod

was rubbed. Answer: C Diff:l 2) Explain how objects can get charged by FRICTION. Answer: When two dissimilar materials are rubbed together, one literally rubs or tears electrons off the one type of molecule, leaving it positively charged, and the other material acquires the extra electrons, thereby becoming negative. Diff: 2

3) The charge carried by one electron is e = -1.6 x 10-19 C. The number of excess electrons necessary to produce a charge of 1.0 C is

A) 6.3 x 1018. B) 1.6 x 1019. C) 6.3 x 109. D) 6.3 x 106. E) 1.6 x 1018.

Answer: A Diff:2 4) When an electron is removed from a neutral atom, it becomes

A) a positive ion. B) a negative ion. C) heavier. D) a bipolar atom. E) more massive.

Answer: A Diff:l 15.3 Electric Force Choose from the following:

(a) C2/N-m2 (b) N-m2/C2 (c) coulomb (d) N/C (e) dimensionless (f) j/C2

1) The Coulomb constant has which of the following units? Answer: (b) N-m2/C2 Oiff 1 4) Consider a container of 2.0 grams of hydrogen (one gram mole). Suppose you removed all the electrons and moved them to the other side of the Earth (Earth diameter 12740. km). (12.04 x 1023 electrons) (a) How much charge is left behind? (b) What is the attractive force between the protons here and the electrons at the other side of the Earth? Answer: (a) 1.9 x 105 Coulombs (b) 2.1 x 106 Newtons = 2.1 x 102 tons!

Oiff3 6) Ben Franklin named charges "plus" and "minus". Suppose he had gotten it reversed and had called plus charges "minus" and called minus "plus", what would have been the consequences? Answer: Like charges would still repel, unlike charges would attract. Coulomb's Law would still describe the electric force. Oiff: 3 9) Only gravitation determines the planetary orbits. Why aren't the other fundamental forces (and electromagnetism in particular) important for the motions? Answer: Only gravity and electromagnetism are long range, however the planets and satellites are electrically neutral. The planets do not have "negative mass" to neutralize the positive mass so gravity predominates. Oif!: 2 10) The force which binds, or holds, atoms together to form molecules is

A) gravitational. B) magnetic. C) friction. D) nuclear. E) electrical.

Answer: E Diff: 1 11) How far apart should two protons be if the electrical force of repulsion is equal to the weight (attraction to the Earth) of one of the protons? Answer: 12. cm Oif!: 2 12) A charged rod will attract a thin stream of water falling from a faucet even though the water is neutral, it has no net charge. How can the rod attract the water? Answer: The Coulomb force of the rod polarizes each molecule of water (one sign of charge is attracted and the opposite sign is repelled). The charge that is attracted feels a slightly larger attraction than the opposite charge is repelled because it is at a slightly different distance from the rod. 0if!:2 13) Two charged objects attract each other with a force F. What happens to the force between them if one charge is doubled, the other charge is tripled, and the separation distance between their centers is reduced to one-fourth its original value? The force is now equal to

A) 24 F. B) 6/16 F. C) 16F.

D) 96 F. E) 8/22 F.

Answer: D Diff:2 15) Two charged objects attract each other with a certain force. If the charges on both objects are doubled with no change in separation, the force between them

A) becomes zero. B) doubles. C) halves. D) quadruples. E) increases, but we can't say how much without knowing the distance between them.

Answer: D Diff:2 18) Consider point charges of +Q and +4Q which are separated by 3 m. At what point, on a line between the two charges, would it be possible to place a charge of -Q such that the electrostatic force acting on it would be zero?

A) 3/5 m from the +Q charge B) 1m from the +Q charge C) 1m from the +4Q charge D) 3 m from the +4Q charge E) There is no such point possible.

Answer: B Oiff: 2 20) Two charges are separated by 5.0 meters and attract one another. If one charge is halved, the other tripled, and the distance quartered, by what factor does the attraction change?

A) 48 B) 3 C) 2 D) 24 E) 16

Answer: D Oiff 2 22) Sphere A carries a net charge and sphere B is neutral. They are placed near each other on an insulated table. Which statement best describes the electrostatic force between them?

A) There is no force between them since one is neutral.

B) There is a force of repulsion between them. C) There is a force of attraction between them. D) The force is attractive if A is charged positively and repulsive if A is charged negatively.

Answer: C Diff 2 23) Charge +2q is placed at the origin and charge -q is placed at x = 2a. Where can a third positive charge +q be placed so that the force on it is zero? Answer: x = 6.83a Diff: 3 Choose from the following: (a) C2/N-m2 (d) N/C (b) N-m2/C2 (e) dimensionless (c) coulomb (f) J /C2 25) Charge has which of the units shown above? Answer: (c) coulomb Diff: 1 26) An electron and a proton are separated by a distance of 1 m. What happens to the size of the force on the proton if the electron is moved 0.5 m closer to the proton?

A) It increases to 4 times its original value. B) It decreases to one-half its original value. C) It increases to 2 times its original value. D) It decreases to one-fourth its original value. E) It increases to 8 times its original value.

Answer: A Diff:2

Advanced 16) One kilogram is hung from a string and it stretches 4.0 cm. A charge of 3.0 µC is placed on the kilogram. How much charge must be placed 4.0 cm below the kg (before it moves) so that the kg moves up by 1.0 cm to a new equilibrium position? Answer: 0.23 µC Diff: 2

19) A point charge of +Q is placed at the center of a square, and a second point charge of -Q is placed at the upper-left comer. It is observed that an electrostatic force of 2 N acts on the positive charge at the center. What is the magnitude of the force that acts on the center charge if a third charge of -Q is placed at the lower-left comer?

A) zero

B) √ N C) 4 N

D) √ Answer: C Oiff: 2 21) Two volleyballs, each of mass 0.300 kg, are charged by an electrostatic generator. Each is attached to an identical string and suspended from the same point. They repel each other and hang with separation 50.0cm. The length of the string from the point of support to the center of a ball is 250. cm. Determine the charge on each ball. Answer: 2.86 µC Diff: 2

3) Consider an equilateral triangle with charges 69. µc,24 µc,and 24 µC at each respective vertex. Each charge is 31.cm from its neighbors. (a) What is the magnitude of the total electrostatic force on the 69. µC charge? (b) If the charges were 3.5 times farther apart, what would be the force on the 69. µC charge? Answer: (a) 48. Newton (b) 3.9 N Diff3

2) Consider the x-axis with 4.0 µC at x = 1.0 meter and -2.0 µC at the origin. Where should 6.0 µC be placed so that the net force on it is zero? Answer: x = -2.4 meter Oiff: 2 5) There is a 5.0 µC charge at each of 3 corners of a square (each side 70. mm long). What is the force on +6.0 µC placed at the center of the square? Answer: 28. Newtons toward the empty corner Oiff: 2

14) A point charge of +Q is placed at the centroid of an equilateral triangle. When a second charge of +Q is placed at one of the triangle's vertices, an electrostatic force of 4 N acts on it. What is the magnitude of the force that acts on the center charge when a third charge of +Q is placed at one of the other vertices?

A) zero B) 4 N C) 8 N D) 16 N

Answer: B Diff: 3

17) A proton and electron are separated by 3.5 run.

(a) What is the magnitude of the force on the electron? (b) What is the magnitude of the force on the proton? (c) What is the electric field of the proton at the electron position?

Answer: (a) 19. pN / C

(b) 19. pN/C (c) 1.2 x 108 N/C away from proton

Oiff 3 4) The statement that "the number of field lines passing through a surface is proportional to the net charge enclosed" is known as

A) Franklin"s Law. B) The Law of Enclosure. C) Coulomb's Law. D) Gauss"s Law. E) Faraday's Law.

Answer: D Diff: 2 14) Consider charges 15.µCand 15. µC at two vertices of an equilateral triangle, the length of the triangle legs being 27.cm. (a) What is the magnitude of the electric field at the unoccupied third vertex? (b) If the triangle were 2.5 times larger, what would be the electric field then? Answer: (a) 5.7x 105N/ C (b) 9.1x 104N/C Diff:3 1) A positive charge is enclosed in a hollow metallic sphere that is not grounded. At a point directly above the hollow sphere, the electric field caused by the enclosed positive charge has

A) diminished to zero. B) diminished somewhat. C) increased somewhat. D) not changed.

Answer: D Diff: 1 2) A positive point charge is enclosed in a hollow metallic sphere that is grounded. At a point directly above the hollow sphere, the electric field caused by the enclosed positive charge has

A) diminished to zero. B) diminished somewhat. C) increased somewhat. D) not changed.

Answer: A

Diff:2 3) The lightning rod was invented by

A) Dr. Frankenstein. B) Albert Einstein. C) Isaac Newton. D) Ben Franklin. E) Michael Faraday.

Answer: D Diff: 1 15.5 Conductors and Electric Fields 1 ) The electric field at the surface of a conductor is

A) always zero. B) perpendicular to the surface. C) parallel to the surface. D) never zero.

Answer: B Diff J 2) To be more effective, how should one shape the tip of a lightning rod?

A) sharpened to a point B) with a rounded tip (hemispherical) C) flat (cut off perpendicular to the rod axis)

Answer: A Diff J 3) A solid metal ball is inserted into a uniform electric field. The field lines near the ball

A) move away from the ball. B) reverse direction. C) bend toward the ball. D) are unaffected. E) are in the downward direction.

Answer: C Diff 2 4) Several electrons are placed on a hollow metal sphere. They

A) clump together on the sphere's inner surface. B) clump together on the sphere's outer surface. C) become uniformly distributed on the sphere's outer surface. D) become uniformly distributed on the sphere's inner surface.

Answer: C Diff: J

5) A hollow metallic sphere is placed in a region permeated by a uniform electric field that is directed upward. Which statement is correct concerning the electric field in the sphere's interior?

A) The field is zero everywhere in the interior. B) The field is directed upward. C) The field is directed downward. D) The field is zero only at the sphere's exact center.

Answer: A Diff: 1 Test Item File 6) Which of the following is an accurate statement?

A) If a solid metal sphere carries a net charge, the charge will move to the sphere surface. B) If a solid metal sphere carries a net charge, the charge will be uniformly distributed

throughout the volume of the sphere. C) The electric field at the surface of a conductor is not necessarily perpendicular to the

surface in all cases. D) A conductor cannot carry a net charge.

Answer: A Diff:2 7) An electron placed in an electric field will feel a force that felt by a proton placed in that same field. A) perpendicular to B) in the same direction as C) in the opposite direction as D) smaller than Answer: C Diff: 1 8) A solid block of metal is placed in a uniform electric field. Which statement is correct concerning the electric field in the block's interior?

A) The interior field points in a direction opposite to the exterior field. B) There is no electric field in the block's interior. C) The interior field points in a direction that is parallel to the exterior field. D) The interior field points in a direction that is at right angles to the exterior field.

Answer: B Diff:l 9) If a solid metal sphere and a hollow metal sphere of equal diameters are each given the same

charge, the electric field ( ⃑ ) midway between the sphere center and the surface is A) greater for the solid sphere than for the hollow sphere. B) greater for the hollow sphere than for the solid sphere. C) zero for both. D) equal in magnitude for both, but one is opposite in direction from the other.

Answer: C Diff: 1

17) An electron, free to move when placed in an electric field, moves

A) along the field line, opposite the field. B) along the field line, in the field direction. C) perpendicular to the field line. D) unaffected by the field.

Answer: A Oiff: 1 18) A metal sphere of radius 2.0 cm carries a charge of 3.0 µc. What is the electric field 6.0 cm from the center of the sphere? Answer: 7.5 x 106V/m Oiff: 2 19) An electric dipole placed into a non-uniform electric field feels a net force

A) parallel to the field. B) perpendicular to the field. C) of zero magnitude. D) 45°with respect to the field.

Answer: A Diff:2

(a) C2/N-m2 (d) N/C (b) N-m2/C2 (e) dimensionless (c) coulomb (f) J /C2 24) The permittivity has which of the units shown above? Answer: (a) C2/N-m2 Diff: 1 1) Consider an equilateral triangle of side 20. cm. A charge of +2.0 µC is placed at one vertex and charges of -4.0 µC are placed at the other two vertices. Determine the magnitude and direction of the electric field at the center of the triangle.

Answer: 2.7 x 106 V/m Diff: 2 2) Which of the following does not have dimensions of an electric field?

A) N/C B) Kg-m/(C-s2) C) N/Cm

Answer: C Diff: 1 3) Two large parallel metal plates are uniformly and oppositely charged and the electric field between them is 7.6 x 106 N/ C. (a) What is the charge density on each plate? (b) If the very large charged plates are moved 2 times farther apart, what is the electric field between the plates now?

Answer: (a) (b) 7.6 x 106 N/C, unchanged Diff:3 4) In electricity, what quantity is analogous to the "acceleration of gravity" g (which is a force per unit mass)?

A) electric force B) electric field C) electric potential D) electric charge E) an electric dipole

Answer: B Diff:l 5) Thirty microcoulombs of NEGATIVE charge experiences an electrostatic force of 27. mN. What is the magnitude and direction of the electric field? Answer: 0.90 kN/C (or kV/m) in the direction opposite the force Diff:2 6) A force of 6.0 N acts on a charge of 3.0 µC when it is placed in a uniform electric field. What is the magnitude of this electric field?

A)18. µN/C B)2.0µN/C C) 0.5 µN/C D)3.5 µN/C E)O.5N/C

Answer: B Di!!: 2 7) Electric dipoles always consist of two charges that are

A) equal in magnitude; both are negative. B) equal in magnitude; opposite in sign. C) unequal in magnitude; opposite in sign. D) equal in magnitude; both are positive.

Answer: B Diff:1 8) Which of the following is a vector?

A) electric constant k B) electric charge C) electric field D) electric potential

Answer: C Diff: 1 9) Two stationary point charges q1 and q2 are shown in the sketch along with some electric field lines representing the field between them. What can you deduce from the sketch?

A) q1 is negative and q2 is positive; the magnitudes are equal. B) q1 and q2 have the same sign; the magnitudes are equal. C) q1 is positive and q2 is negative; the magnitude of q1 is greater than the magnitude of q2. D) q1 and q2 have the same sign; the magnitude of q is greater than the magnitude of q2.

Answer: C Diff: 2 10) The electric field shown

A) increases to the right. B) increases down.

C) decreases to the right. D) decreases down. E) is uniform.

Answer: A Oiff: 1 11) Which of the following makes an approximate uniform electric field?

A) a metal charged cylinder B) a very long line of positive charge C) very large, closely separated, parallel oppositely charged plates D) two long parallel, closely separated, oppositely charged lines of charge

Answer: C Oiff: 1 12) Electric field lines

A) are closer together the stronger the field. B) start on negative charges and end on positive charges. C) were invented by Isaac Newton. D) are perpendicular to the lines of force. E) were discovered by Franklin.

Answer: A Oiff:l 13) Electric field lines

A) circle clockwise around positive charges. B) circle counter-clockwise around positive charges. C) radiate outward from negative charges. D) radiate outward from positive charges.

Answer: D Oiff:l Choose from the fol/owing: (a) C2/N-m2 (d) N/C (b) N-m2/C2 (e) dimensionless (c) coulomb (f) J /C2 15) Electric field has which of the units shown above? Answer: (d) N/C Oiff 1 16) An electric dipole placed into a uniform electric field feels a net force

A) along the field. B) opposite the field. C) perpendicular to the field. D) of zero magnitude.

Answer: D Diff:l

17) A proton and electron are separated by 3.5 run.

(a) What is the magnitude of the force on the electron? (b) What is the magnitude of the force on the proton? (c) What is the electric field of the proton at the electron position?

Answer: (a) 19. pN / C

(b) 19. pN/C (c) 1.2 x 108 N/C away from proton

Oiff 3 4) The statement that "the number of field lines passing through a surface is proportional to the net charge enclosed" is known as

A) Franklin"s Law. B) The Law of Enclosure. C) Coulomb's Law. D) Gauss"s Law. E) Faraday's Law.

Answer: D Diff: 2 14) Consider charges 15.µCand 15. µC at two vertices of an equilateral triangle, the length of the triangle legs being 27.cm. (a) What is the magnitude of the electric field at the unoccupied third vertex? (b) If the triangle were 2.5 times larger, what would be the electric field then? Answer: (a) 5.7x 105N/ C (b) 9.1x 104N/C Diff:3 1) A positive charge is enclosed in a hollow metallic sphere that is not grounded. At a point directly above the hollow sphere, the electric field caused by the enclosed positive charge has

A) diminished to zero. B) diminished somewhat. C) increased somewhat. D) not changed.

Answer: D Diff: 1 2) A positive point charge is enclosed in a hollow metallic sphere that is grounded. At a point directly above the hollow sphere, the electric field caused by the enclosed positive charge has

A) diminished to zero. B) diminished somewhat. C) increased somewhat. D) not changed.

Answer: A

Diff:2 3) The lightning rod was invented by

A) Dr. Frankenstein. B) Albert Einstein. C) Isaac Newton. D) Ben Franklin. E) Michael Faraday.

Answer: D Diff: 1 15.5 Conductors and Electric Fields 1 ) The electric field at the surface of a conductor is

A) always zero. B) perpendicular to the surface. C) parallel to the surface. D) never zero.

Answer: B Diff J 2) To be more effective, how should one shape the tip of a lightning rod?

A) sharpened to a point B) with a rounded tip (hemispherical) C) flat (cut off perpendicular to the rod axis)

Answer: A Diff J 3) A solid metal ball is inserted into a uniform electric field. The field lines near the ball

A) move away from the ball. B) reverse direction. C) bend toward the ball. D) are unaffected. E) are in the downward direction.

Answer: C Diff 2 4) Several electrons are placed on a hollow metal sphere. They

A) clump together on the sphere's inner surface. B) clump together on the sphere's outer surface. C) become uniformly distributed on the sphere's outer surface. D) become uniformly distributed on the sphere's inner surface.

Answer: C Diff: J

5) A hollow metallic sphere is placed in a region permeated by a uniform electric field that is directed upward. Which statement is correct concerning the electric field in the sphere's interior?

A) The field is zero everywhere in the interior. B) The field is directed upward. C) The field is directed downward. D) The field is zero only at the sphere's exact center.

Answer: A Diff: 1 Test Item File 6) Which of the following is an accurate statement?

A) If a solid metal sphere carries a net charge, the charge will move to the sphere surface. B) If a solid metal sphere carries a net charge, the charge will be uniformly distributed

throughout the volume of the sphere. C) The electric field at the surface of a conductor is not necessarily perpendicular to the

surface in all cases. D) A conductor cannot carry a net charge.

Answer: A Diff:2 7) An electron placed in an electric field will feel a force that felt by a proton placed in that same field. A) perpendicular to B) in the same direction as C) in the opposite direction as D) smaller than Answer: C Diff: 1 8) A solid block of metal is placed in a uniform electric field. Which statement is correct concerning the electric field in the block's interior?

A) The interior field points in a direction opposite to the exterior field. B) There is no electric field in the block's interior. C) The interior field points in a direction that is parallel to the exterior field. D) The interior field points in a direction that is at right angles to the exterior field.

Answer: B Diff:l 9) If a solid metal sphere and a hollow metal sphere of equal diameters are each given the same

charge, the electric field ( ⃑ ) midway between the sphere center and the surface is A) greater for the solid sphere than for the hollow sphere. B) greater for the hollow sphere than for the solid sphere. C) zero for both. D) equal in magnitude for both, but one is opposite in direction from the other.

Answer: C Diff: 1

17) An electron, free to move when placed in an electric field, moves

A) along the field line, opposite the field. B) along the field line, in the field direction. C) perpendicular to the field line. D) unaffected by the field.

Answer: A Oiff: 1 18) A metal sphere of radius 2.0 cm carries a charge of 3.0 µc. What is the electric field 6.0 cm from the center of the sphere? Answer: 7.5 x 106V/m Oiff: 2 19) An electric dipole placed into a non-uniform electric field feels a net force

A) parallel to the field. B) perpendicular to the field. C) of zero magnitude. D) 45°with respect to the field.

Answer: A Diff:2

(a) C2/N-m2 (d) N/C (b) N-m2/C2 (e) dimensionless (c) coulomb (f) J /C2 24) The permittivity has which of the units shown above? Answer: (a) C2/N-m2 Diff: 1 1) Consider an equilateral triangle of side 20. cm. A charge of +2.0 µC is placed at one vertex and charges of -4.0 µC are placed at the other two vertices. Determine the magnitude and direction of the electric field at the center of the triangle.

Answer: 2.7 x 106 V/m Diff: 2 2) Which of the following does not have dimensions of an electric field?

A) N/C B) Kg-m/(C-s2) C) N/Cm

Answer: C Diff: 1 3) Two large parallel metal plates are uniformly and oppositely charged and the electric field between them is 7.6 x 106 N/ C. (a) What is the charge density on each plate? (b) If the very large charged plates are moved 2 times farther apart, what is the electric field between the plates now?

Answer: (a) (b) 7.6 x 106 N/C, unchanged Diff:3 4) In electricity, what quantity is analogous to the "acceleration of gravity" g (which is a force per unit mass)?

A) electric force B) electric field C) electric potential D) electric charge E) an electric dipole

Answer: B Diff:l 5) Thirty microcoulombs of NEGATIVE charge experiences an electrostatic force of 27. mN. What is the magnitude and direction of the electric field? Answer: 0.90 kN/C (or kV/m) in the direction opposite the force Diff:2 6) A force of 6.0 N acts on a charge of 3.0 µC when it is placed in a uniform electric field. What is the magnitude of this electric field?

A)18. µN/C B)2.0µN/C C) 0.5 µN/C D)3.5 µN/C E)O.5N/C

Answer: B Di!!: 2 7) Electric dipoles always consist of two charges that are

A) equal in magnitude; both are negative. B) equal in magnitude; opposite in sign. C) unequal in magnitude; opposite in sign. D) equal in magnitude; both are positive.

Answer: B Diff:1 8) Which of the following is a vector?

A) electric constant k B) electric charge C) electric field D) electric potential

Answer: C Diff: 1 9) Two stationary point charges q1 and q2 are shown in the sketch along with some electric field lines representing the field between them. What can you deduce from the sketch?

A) q1 is negative and q2 is positive; the magnitudes are equal. B) q1 and q2 have the same sign; the magnitudes are equal. C) q1 is positive and q2 is negative; the magnitude of q1 is greater than the magnitude of q2. D) q1 and q2 have the same sign; the magnitude of q is greater than the magnitude of q2.

Answer: C Diff: 2 10) The electric field shown

A) increases to the right. B) increases down.

C) decreases to the right. D) decreases down. E) is uniform.

Answer: A Oiff: 1 11) Which of the following makes an approximate uniform electric field?

A) a metal charged cylinder B) a very long line of positive charge C) very large, closely separated, parallel oppositely charged plates D) two long parallel, closely separated, oppositely charged lines of charge

Answer: C Oiff: 1 12) Electric field lines

A) are closer together the stronger the field. B) start on negative charges and end on positive charges. C) were invented by Isaac Newton. D) are perpendicular to the lines of force. E) were discovered by Franklin.

Answer: A Oiff:l 13) Electric field lines

A) circle clockwise around positive charges. B) circle counter-clockwise around positive charges. C) radiate outward from negative charges. D) radiate outward from positive charges.

Answer: D Oiff:l Choose from the fol/owing: (a) C2/N-m2 (d) N/C (b) N-m2/C2 (e) dimensionless (c) coulomb (f) J /C2 15) Electric field has which of the units shown above? Answer: (d) N/C Oiff 1 16) An electric dipole placed into a uniform electric field feels a net force

A) along the field. B) opposite the field. C) perpendicular to the field. D) of zero magnitude.

Answer: D Diff:l