Chapter 31: Properties of light

Section 31-1: The Speed of Light, and Concept Check 31-1

You are attempting to reproduce Fizeau’s determination of the speed of light. Using a wheel that has 720 teeth, light is observed when the wheel rotates and light is reflected between the teeth from a distant mirror. You assume that the time taken for the light to travel from the wheel to the mirror and back is the time for the wheel to rotate 1/720 of a revolution. You obtain a result for the speed of light which is 7 percent too low. What is the most likely source of error to account for this discrepancy?

A. You have miscounted the teeth.

B. You have not measured the angular speed correctly.

C. There are 720 teeth, but there are also 720 gaps, so the width of a tooth is less than 1/720 of the circumference of the wheel.

D. You have not measured the distance to the mirror correctly.

E. Light travels 7% slower in air than in a vacuum.

You are attempting to reproduce Fizeau’s determination of the speed of light. Using a wheel that has 720 teeth, light is observed when the wheel rotates and light is reflected between the teeth from a distant mirror. You assume that the time taken for the light to travel from the wheel to the mirror and back is the time for the wheel to rotate 1/720 of a revolution. You obtain a result for the speed of light which is 7 percent too low. What is the most likely source of error to account for this discrepancy?

A. You have miscounted the teeth.

B. You have not measured the angular speed correctly.

C. There are 720 teeth, but there are also 720 gaps, so the width of a tooth is less than 1/720 of the circumference of the wheel.

D. You have not measured the distance to the mirror correctly.

E. Light travels 7% slower in air than in a vacuum.

Mission Control sends a brief wake-up call to astronauts in a distant spaceship. Five seconds after the call is sent, Mission Control hears the waking groans of the astronauts. How far away (at most) from the earth is the spaceship?

A. 7.5 ×108 m

B. 15 × 108 m

C. 30 × 108 m

D. 45 × 108 m

E. There is no upper limit on the distance.

Mission Control sends a brief wake-up call to astronauts in a distant spaceship. Five seconds after the call is sent, Mission Control hears the waking groans of the astronauts. How far away (at most) from the earth is the spaceship?

A. 7.5 ×108 m

B. 15 × 108 m

C. 30 × 108 m

D. 45 × 108 m

E. There is no upper limit on the distance.

The speed of ultraviolet radiation in free space compared with the speed of visible radiation in free space is

A. greater.

B. the same.

C. less.

The speed of ultraviolet radiation in free space compared with the speed of visible radiation in free space is

A. greater.

B. the same.

C. less.

The speed of radio waves in free space compared with the speed of visible radiation in free space is

A. greater.

B. the same.

C. less.

The speed of radio waves in free space compared with the speed of visible radiation in free space is

A. greater.

B. the same.

C. less.

Ultra fast pulse lasers can emit pulses of the order 10 fs. The physical length of each pulse that is 10 fs long in duration is

A. 1.0 μm

B. 2.0 μm

C. 3.0 μm

D. 9.0 μm

E. 12.0 μm

Ultra fast pulse lasers can emit pulses of the order 10 fs. The physical length of each pulse that is 10 fs long in duration is

A. 1.0 μm

B. 2.0 μm

C. 3.0 μm

D. 9.0 μm

E. 12.0 μm

Chapter 31: Properties of light

Section 31-3: Reflection and Refraction

As light passes from one medium into another, the angle of refraction is smaller in the medium with the _____ index of refraction and _____ speed of light.

A. larger; lower

B. larger; higher

C. smaller; lower

D. smaller; higher

As light passes from one medium into another, the angle of refraction is smaller in the medium with the _____ index of refraction and _____ speed of light.

A. larger; lower

B. larger; higher

C. smaller; lower

D. smaller; higher

A glass block with index of refraction 1.50 is immersed in water whose index of refraction is 1.33. The critical angle at the glass–water interface is

A. 6.5º

B. 41.9º

C. 48.8º

D. 56.3º

E. 62.5º

A glass block with index of refraction 1.50 is immersed in water whose index of refraction is 1.33. The critical angle at the glass–water interface is

A. 6.5º

B. 41.9º

C. 48.8º

D. 56.3º

E. 62.5º

Which of the following statements is true about the speeds of the various colors of light in glass?

A. All colors of light have the same speed in glass.

B. Violet has the highest speed, red the lowest.

C. Red has the highest speed, violet the lowest.

Which of the following statements is true about the speeds of the various colors of light in glass?

A. All colors of light have the same speed in glass.

B. Violet has the highest speed, red the lowest.

C. Red has the highest speed, violet the lowest.

A light wave traveling at speed v1 in medium 1 passes into medium 2 where its speed is v2. By which of the following equations is the frequency f1 of the wave in medium 1 related to its frequency f2 in medium 2?

A. f1v2 = f2v1

B. f1 = f2

C. f1v1 = f2v2

A light wave traveling at speed v1 in medium 1 passes into medium 2 where its speed is v2. By which of the following equations is the frequency f1 of the wave in medium 1 related to its frequency f2 in medium 2?

A. f1v2 = f2v1

B. f1 = f2

C. f1v1 = f2v2

Light that has been traveling in a medium with an index of refraction n2 is incident on the boundary surface of another medium with an index of refraction n1. Given a sufficient angle of incidence, which of the following conditions must be satisfied for total internal reflection to occur?

A. n1 < n2

B. n1 > n2

C. n1 = n2

Light that has been traveling in a medium with an index of refraction n2 is incident on the boundary surface of another medium with an index of refraction n1. Given a sufficient angle of incidence, which of the following conditions must be satisfied for total internal reflection to occur?

A. n1 < n2

B. n1 > n2

C. n1 = n2

You are trying to catch fish by using a spear. You observe a large fish a couple of meters in front of you and a meter below the water surface. In order to hit the fish with your spear you must aim (assume that the fish is stationary and does not swim away in fright)

A. directly at the point where you see the fish.

B. slightly above the point where you see the fish.

C. slightly below the point where you see the fish.

You are trying to catch fish by using a spear. You observe a large fish a couple of meters in front of you and a meter below the water surface. In order to hit the fish with your spear you must aim (assume that the fish is stationary and does not swim away in fright)

A. directly at the point where you see the fish.

B. slightly above the point where you see the fish.

C. slightly below the point where you see the fish.

You see a fish in water at an apparent depth of 1.83 m. The actual depth of the fish, if the index of refraction of the water relative to air is 4/3, must be

A. 3.81 cm

B. 61.0 cm

C. 1.37 m

D. 1.83 m

E. 2.44 m

You see a fish in water at an apparent depth of 1.83 m. The actual depth of the fish, if the index of refraction of the water relative to air is 4/3, must be

A. 3.81 cm

B. 61.0 cm

C. 1.37 m

D. 1.83 m

E. 2.44 m

A ray of light passes from air into water, striking the surface of the water with an angle of incidence of 45º. Which of the following four quantities change as the light enters the water: (1) wavelength, (2) frequency, (3) speed of propagation, and (4) direction of propagation?

A. 1 and 2 only

B. 2, 3, and 4 only

C. 1, 3, and 4 only

D. 3 and 4 only

E. 1, 2, 3, and 4

A ray of light passes from air into water, striking the surface of the water with an angle of incidence of 45º. Which of the following four quantities change as the light enters the water: (1) wavelength, (2) frequency, (3) speed of propagation, and (4) direction of propagation?

A. 1 and 2 only

B. 2, 3, and 4 only

C. 1, 3, and 4 only

D. 3 and 4 only

E. 1, 2, 3, and 4

A light ray makes an angle of 42º with the normal to a glass-water surface on the glass side of the surface. The angle q in the water is

A. 42º

B. 36º

C. 63º

D. 49º

E. 27º

A light ray makes an angle of 42º with the normal to a glass-water surface on the glass side of the surface. The angle q in the water is

A. 42º

B. 36º

C. 63º

D. 49º

E. 27º

In the laboratory you used the spectrometer to determine the indices of refraction of various wavelengths of light. Which curve could represent a plot of the index of refraction as a function of the wavelength of the light?

In the laboratory you used the spectrometer to determine the indices of refraction of various wavelengths of light. Which curve could represent a plot of the index of refraction as a function of the wavelength of the light?

Monochromatic light is incident on the prism at the proper angle for minimum deviation. The emergent ray passes through which point?

Monochromatic light is incident on the prism at the proper angle for minimum deviation. The emergent ray passes through which point?

Light travels in a medium of index of refraction n', passes into a medium of index n", where n" > n', and then into air, where nair < n' < n". Which ray correctly shows the light path?

Light travels in a medium of index of refraction n', passes into a medium of index n", where n" > n', and then into air, where nair < n' < n". Which ray correctly shows the light path?

Light from an underwater source at O impinges upon a water-air interface. Which label shows the critical angle?

Light from an underwater source at O impinges upon a water-air interface. Which label shows the critical angle?

The light ray that passes through the prism and emerges at the angle of minimum deviation for that color is A. red

B. yellowC. greenD. blueE. violet

The light ray that passes through the prism and emerges at the angle of minimum deviation for that color is A. red

B. yellowC. greenD. blueE. violet

An air prism is immersed in water. A ray of monochromatic light strikes one face as shown. Which arrow shows the emerging ray?

An air prism is immersed in water. A ray of monochromatic light strikes one face as shown. Which arrow shows the emerging ray?

Which label shows the angle of minimum deviation?

Which label shows the angle of minimum deviation?

The figure shows the electric field strength versus distance for light that is normally incident on and transmitted through a refractive medium. The index of refraction of this medium is

A. 1.0

B. 1.5

C. 2.0

D. 0.67

E. 3.0

The figure shows the electric field strength versus distance for light that is normally incident on and transmitted through a refractive medium. The index of refraction of this medium is

A. 1.0

B. 1.5

C. 2.0

D. 0.67

E. 3.0

A ray of light in glass is incident on a glass–air interface as shown. You would expect a ray to pass through

A. point 1 only.

B. point 3 only.

C. point 4 only.

D. points 2 and 4.

E. points 1 and 4.

A ray of light in glass is incident on a glass–air interface as shown. You would expect a ray to pass through

A. point 1 only.

B. point 3 only.

C. point 4 only.

D. points 2 and 4.

E. points 1 and 4.

The rays in the figure are reflected and refracted at the front and back surfaces of the glass. Which of the following is true of the angles of these rays relative to normal?

A. 1 = 2 = 3 = 4

B. 1 = 2; 3 = 4; but 1 ≠ 3

C. 1 = 2 = 3; but 4 ≠ 1

D. 1 = 4; but 2 ≠ 4

E. 1 ≠ 2 ≠ 3 ≠ 4

The rays in the figure are reflected and refracted at the front and back surfaces of the glass. Which of the following is true of the angles of these rays relative to normal?

A. 1 = 2 = 3 = 4

B. 1 = 2; 3 = 4; but 1 ≠ 3

C. 1 = 2 = 3; but 4 ≠ 1

D. 1 = 4; but 2 ≠ 4

E. 1 ≠ 2 ≠ 3 ≠ 4

A plane wavefront of light (AA') approaches an air–water interface as shown. n < n'. Which diagram best shows the refracted wave?

A plane wavefront of light (AA') approaches an air–water interface as shown. n < n'. Which diagram best shows the refracted wave?

A fiber optic is made by cladding a thin fiber core of refractive index n1 = 1.45 with a material of refractive index n2 = 1.38. What is the critical angle at the core-cladding interface?

A. 44º

B. 46º

C. 55º

D. 72º

E. None of these is correct.

A fiber optic is made by cladding a thin fiber core of refractive index n1 = 1.45 with a material of refractive index n2 = 1.38. What is the critical angle at the core-cladding interface?

A. 44º

B. 46º

C. 55º

D. 72º

E. None of these is correct.

A fiber optic is made by cladding a thin fiber core of refractive index n1 = 1.45 with a material of refractive index n2 = 1.38. What is the maximum incident angle, θ, so that the light ray is totally internally reflected inside the fiber?

A. 24.1º

B. 26.4º

C. 28.2º

D. 30.3º

E. 32.7º

n2n1

air

A fiber optic is made by cladding a thin fiber core of refractive index n1 = 1.45 with a material of refractive index n2 = 1.38. What is the maximum incident angle, θ, so that the light ray is totally internally reflected inside the fiber?

A. 24.1º

B. 26.4º

C. 28.2º

D. 30.3º

E. 32.7º

n2n1

air

Chapter 31: Properties of light

Section 31-4: Polarization

Light is an electromagnetic wave. When visible light is plane polarized,

A. the electric-field vector is parallel to the magnetic-field vector.

B. the electric-field vector is parallel to the direction of propagation.

C. the electric-field vector is in a fixed direction perpendicular to the direction of propagation, but the magnetic-field vector may be in any direction.

D. the electric-field vector is in a fixed direction perpendicular to the direction of propagation, and the magnetic-field vector is perpendicular to the electric-field vector.

E. None of these is correct.

Light is an electromagnetic wave. When visible light is plane polarized,

A. the electric-field vector is parallel to the magnetic-field vector.

B. the electric-field vector is parallel to the direction of propagation.

C. the electric-field vector is in a fixed direction perpendicular to the direction of propagation, but the magnetic-field vector may be in any direction.

D. the electric-field vector is in a fixed direction perpendicular to the direction of propagation, and the magnetic-field vector is perpendicular to the electric-field vector.

E. None of these is correct.

Two polarizers have their transmission axes at an angle θ. Unpolarized light of intensity I is incident on the first polarizer. What is the intensity of the light transmitted by the second polarizer?

A. I cos2 θ

B. 0.5I cos2 θ

C. 0.25I cos2 θ

D. I cos θ

E. 0.25I cos θ

Two polarizers have their transmission axes at an angle θ. Unpolarized light of intensity I is incident on the first polarizer. What is the intensity of the light transmitted by the second polarizer?

A. I cos2 θ

B. 0.5I cos2 θ

C. 0.25I cos2 θ

D. I cos θ

E. 0.25I cos θ

Which of the following is not a phenomenon by which polarized light can be produced from unpolarized light?

A. absorption

B. reflection

C. birefringence

D. diffraction

E. scattering

Which of the following is not a phenomenon by which polarized light can be produced from unpolarized light?

A. absorption

B. reflection

C. birefringence

D. diffraction

E. scattering

The index of refraction of a sample of glass cannot be determined by measuring the

A. Brewster's angle.

B. critical angle.

C. angle of minimum deviation.

D. ratio of true to apparent depth.

E. angle of dispersion between red and violet light.

The index of refraction of a sample of glass cannot be determined by measuring the

A. Brewster's angle.

B. critical angle.

C. angle of minimum deviation.

D. ratio of true to apparent depth.

E. angle of dispersion between red and violet light.

If you look at a dot on a piece of paper through a calcite crystal lying on the paper, you will see two images of the dot, one of which appears to be nearer to you than the other. From this evidence you can conclude that

A. the beams from both images are polarized.

B. calcite has different indices of refraction for the two beams.

C. there is interference between the two beams.

D. the calcite has increased the resolving power of your eye.

E. the appearance is due to diffraction.

If you look at a dot on a piece of paper through a calcite crystal lying on the paper, you will see two images of the dot, one of which appears to be nearer to you than the other. From this evidence you can conclude that

A. the beams from both images are polarized.

B. calcite has different indices of refraction for the two beams.

C. there is interference between the two beams.

D. the calcite has increased the resolving power of your eye.

E. the appearance is due to diffraction.

What taking a picture of a highly reflecting surface, it is desirable to use a polarizer in front of the camera to cut down on the “glare”. Suppose you are taking a picture of a lake where the water is very still. The polarizing axis of the polarizer should ideally be oriented

A. horizontally.

B. vertically.

What taking a picture of a highly reflecting surface, it is desirable to use a polarizer in front of the camera to cut down on the “glare”. Suppose you are taking a picture of a lake where the water is very still. The polarizing axis of the polarizer should ideally be oriented

A. horizontally.

B. vertically.

In any wave motion, dependence of velocity on wavelength is called

A. polarization

B. deviation

C. dispersion

D. diffraction

E. scattering

In any wave motion, dependence of velocity on wavelength is called

A. polarization

B. deviation

C. dispersion

D. diffraction

E. scattering

Polarized light cannot be produced by

A. dispersion

B. dichroism

C. reflection

D. scattering

E. refraction

Polarized light cannot be produced by

A. dispersion

B. dichroism

C. reflection

D. scattering

E. refraction

One would not attempt to polarize light by

A. selective absorption.

B. reflection from a surface.

C. passage through a narrow slit.

D. scattering.

E. double refraction.

One would not attempt to polarize light by

A. selective absorption.

B. reflection from a surface.

C. passage through a narrow slit.

D. scattering.

E. double refraction.

Light is circularly polarized if

A. the cross section of a spherical wave front is polarized.

B. it consists of two plane-polarized waves that are out of phase with each other by 90º.

C. it is refracted by a medium that has a high index of refraction.

D. it is reflected at the critical angle and polarized.

E. it is polarized by scattering from molecules.

Light is circularly polarized if

A. the cross section of a spherical wave front is polarized.

B. it consists of two plane-polarized waves that are out of phase with each other by 90º.

C. it is refracted by a medium that has a high index of refraction.

D. it is reflected at the critical angle and polarized.

E. it is polarized by scattering from molecules.

The optical phenomenon that is usually cited as demonstrating the transverse wave nature of light is

A. dispersion

B. interference

C. reflection

D. polarization

E. refraction

The optical phenomenon that is usually cited as demonstrating the transverse wave nature of light is

A. dispersion

B. interference

C. reflection

D. polarization

E. refraction

A ray of light (ab) is incident on the surface of a piece of glass at such an angle that the reflected ray (bc) is totally polarized. The directed line segment that represents the refracted ray is

A. 1

B. 2

C. 3

D. 4

E. None of these is correct.

A ray of light (ab) is incident on the surface of a piece of glass at such an angle that the reflected ray (bc) is totally polarized. The directed line segment that represents the refracted ray is

A. 1

B. 2

C. 3

D. 4

E. None of these is correct.

Of the following quantities, the one that is independent of the frequency of light is the

A. polarizing angle.

B. critical angle.

C. angle of minimum deviation.

D. angle of refraction.

E. angle of reflection.

Of the following quantities, the one that is independent of the frequency of light is the

A. polarizing angle.

B. critical angle.

C. angle of minimum deviation.

D. angle of refraction.

E. angle of reflection.

A ray of unpolarized light is incident on a glass block at an angle of incidence in such a way that the reflected ray is completely plane polarized. Which ray best represents the refracted ray?

A ray of unpolarized light is incident on a glass block at an angle of incidence in such a way that the reflected ray is completely plane polarized. Which ray best represents the refracted ray?

Sound waves differ from light waves in many respects. One important difference is that sound waves cannot

A. be refracted.

B. be reflected.

C. show interference.

D. show diffraction.

E. be polarized.

Sound waves differ from light waves in many respects. One important difference is that sound waves cannot

A. be refracted.

B. be reflected.

C. show interference.

D. show diffraction.

E. be polarized.

Which of the following is not a property of all waves?

A. refraction

B. diffraction

C. reflection

D. interference

E. polarization

Which of the following is not a property of all waves?

A. refraction

B. diffraction

C. reflection

D. interference

E. polarization

When light is reflected from a plane surface of glass at the polarizing angle, the

A. reflected ray is at right angles to the incident ray.

B. angle of reflection is equal to the angle of refraction.

C. incident ray is at right angles to the refracted ray.

D. reflected ray is at right angles to the refracted ray.

E. intensity of the reflected light is a maximum.

When light is reflected from a plane surface of glass at the polarizing angle, the

A. reflected ray is at right angles to the incident ray.

B. angle of reflection is equal to the angle of refraction.

C. incident ray is at right angles to the refracted ray.

D. reflected ray is at right angles to the refracted ray.

E. intensity of the reflected light is a maximum.

The angle of incidence that will cause the unpolarized light to be reflected as completely plane-polarized light is called

A. Brewster's angle.

B. Young's angle.

C. Snells's angle.

D. Huygens' angle.

E. Fraunhofer's angle.

The angle of incidence that will cause the unpolarized light to be reflected as completely plane-polarized light is called

A. Brewster's angle.

B. Young's angle.

C. Snells's angle.

D. Huygens' angle.

E. Fraunhofer's angle.

If the index of refraction of a glass plate is 1.45, the angle of incidence that will cause the unpolarized light to be reflected as completely plane polarized light is

A. 8.25º

B. 34.6º

C. 45.0º

D. 55.4º

E. 81.7º

If the index of refraction of a glass plate is 1.45, the angle of incidence that will cause the unpolarized light to be reflected as completely plane polarized light is

A. 8.25º

B. 34.6º

C. 45.0º

D. 55.4º

E. 81.7º

The plane of polarization of the reflected light lies

A. parallel to the screen.

B. at 45º with respect to the screen.

C. perpendicular to the screen.

The plane of polarization of the reflected light lies

A. parallel to the screen.

B. at 45º with respect to the screen.

C. perpendicular to the screen.

Chapter 31: Properties of light

Section 31-5: Derivation of the Laws of Reflection and Refraction

Huygens' theory for the construction of wavefronts states that

A. the angle of incidence is always less than the angle of refraction.

B. the time required for light to travel from one point to another is either a maximum or minimum.

C. only parallel light produces interference and diffraction.

D. each point on a wavefront is itself the source of a secondary spherical wave.

E. all wavefronts are spherical.

Huygens' theory for the construction of wavefronts states that

A. the angle of incidence is always less than the angle of refraction.

B. the time required for light to travel from one point to another is either a maximum or minimum.

C. only parallel light produces interference and diffraction.

D. each point on a wavefront is itself the source of a secondary spherical wave.

E. all wavefronts are spherical.

The principle of superposition states: A. The effect observed at each point of a wave made up

of two or more waves is the sum of the effects that the individual waves would produce at that point.

B. Huygens' wavelets cannot be allowed to extend across regions where the phase velocity of the wave changes abruptly.

C. Sources of radiation whose phase angles are maintained at constant differences are said to be coherent.

D. A characteristic phenomenon of wave propagation is the tendency of a wave to expand around and behind any obstacles it chances to encounter.

E. A good source of waves at a particular frequency is a good detector of waves at the same frequency.

The principle of superposition states: A. The effect observed at each point of a wave made

up of two or more waves is the sum of the effects that the individual waves would produce at that point.

B. Huygens' wavelets cannot be allowed to extend across regions where the phase velocity of the wave changes abruptly.

C. Sources of radiation whose phase angles are maintained at constant differences are said to be coherent.

D. A characteristic phenomenon of wave propagation is the tendency of a wave to expand around and behind any obstacles it chances to encounter.

E. A good source of waves at a particular frequency is a good detector of waves at the same frequency.

"To find the value of the resultant displacement for overlapping waves at any point at a particular instant, it is only necessary to add the values of the displacements for the individual waves." This is a statement of

A. Huygens' principle.

B. the principle of superposition.

C. Bernoulli's principle.

D. the principle of dispersion.

E. Newton's theory of light.

"To find the value of the resultant displacement for overlapping waves at any point at a particular instant, it is only necessary to add the values of the displacements for the individual waves." This is a statement of

A. Huygens' principle.

B. the principle of superposition.

C. Bernoulli's principle.

D. the principle of dispersion.

E. Newton's theory of light.

A light wave is like a sound wave in that both

A. are longitudinal waves.

B. are means of transmitting energy.

C. are transverse waves.

D. require a material medium for propagation.

E. have the same velocity in air.

A light wave is like a sound wave in that both

A. are longitudinal waves.

B. are means of transmitting energy.

C. are transverse waves.

D. require a material medium for propagation.

E. have the same velocity in air.

Chapter 31: Properties of light

Section 31-8: Sources of Light

If the wavelength l of the incident light is large compared with the size of an atom, the probability of elastic scattering upon the atom varies as

A. λ

B. λ4

C. λ–4

D. λ2

E. λ–3

If the wavelength l of the incident light is large compared with the size of an atom, the probability of elastic scattering upon the atom varies as

A. λ

B. λ4

C. λ–4

D. λ2

E. λ–3

The lifetime of a typical excited atomic energy state is of the order of

A. 10–6 s

B. 10–7 s

C. 10–8 s

D. 10–9 s

E. 10–10 s

The lifetime of a typical excited atomic energy state is of the order of

A. 10–6 s

B. 10–7 s

C. 10–8 s

D. 10–9 s

E. 10–10 s