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EXERCISE 11. An observer on the west-facing beach of a large lake is watching the beginning of a sunset. The water is

very smooth except for some areas with small ripples. The observer notices that some areas of the water

appear blue and some appear pink. Why does the water appear to be different colors in different areas?

2. When looking through a glass window to the outdoors at night, your sometimes see a double image of

yourself. Why?

3. Why do face masks make vision clearer under water? A face mask includes a flat piece of glass–the mask

does not have lenses like those in eyeglasses.

4. When a monochromatic light enters a rarer medium from a denser medium, what happens to the

(a) Velocity (b) Frequency (c) Wavelength (d) Amplitude

5. In dispersive materials, the angle of refraction for a light ray depends on the wavelength of the light. Does

the angle of reflection from the surface of the material depend on the wavelength ?

6. When a beam of light enters a glass prism with nonparallel sides, the spectrum of colours exiting the prism

is a testimonial to the dispersion occurring in the glass. Suppose a beam of light enters a slab of material

with parallel sides at an angle to the normal. When the beam exits the other side, traveling in the same

direction as the original beam, is there any evidence of dispersion?

7. Why does the focal length of a lens depend on the lens material, but the focal length for a mirror is

independent of the material from which the mirror is made?

8. A virtual image of often described as one through which light rays do not travel, as they do for a real image.

Can a virtual image be photographed?

9. The images formed by total internal reflection are much brighter than those formed by mirror or lenses.

Explain.

10. In an experiment with a lens, the object distance u versus image distance v data were obtained.

Analyze the following graphs.

(a) v1

versus u1

(b) uv versus (u – v) (c) uv

versus u .

11. Why are danger light are red, when the eye is most sensitive to yellow green ?

12. Why does a diamond "sparkle" more than a glass imitation cut to the same shape?

13. In some cars the right (passenger) side view mirror bears the notation : 'Objects in the mirror are closer

than they appear". What feature of the mirror requires this warning? What advantages does the mirror have

to compensate for this disadvantage? Do cars viewed in this mirror appear to be moving faster or slower

than they would if viewed in a plane mirror ?

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EXERCISE 2Conceptual Objective

1. A mirror is inclined at an angle of q with the horizontal. If a ray of light is incident at an angle q , then the angle madeby reflected ray with the horizontal is

(A) q (B) 2q (C) 2q

(D) none of these

2. A ray of light is incident at 50° on one of a pair of mirrors arranged at 60° to each other. The angle at whichthe ray is incident on the first mirror after being reflected from the second mirror is :(A) 80° (B) 70° (C) 60° (D) 50°

3. If the object is placed midway between two parallel mirrors separated by distance ‘b’. The general expressionfor the distance of the image from the object is : [ where n is an integer ](A) 4nb (B) 3nb (C) 2nb (D) nb

4. The image formed by a plane mirror(A) is always virtual (B) is always real (C) may be real (D) is never real

5. Image of the object is formed as shown in figure.

v

A

B

A'

B'

If the mirror starts moving towards the object with velocity v, then velocity of image will be(A) v towards right (B) v towards left(C) 2v towards right (D) 2v towards left

6. An object is placed between two plane mirrors as shown. The number of images formed is

///////

///////

///////

////////

//////

///

)45º)15º

O

(A) 4 (B) 5 (C) 6 (D) None7. The incorrect statement for a concave mirror producing a virtual image of the object is :

(A) The linear magnification is always greater than one except at the pole(B) The linear magnification is always less than one(C) The magnification tends to one as the object move nearer to the pole of the mirror(D) The distance of the object from the pole of the mirror is less than the focal length of mirror.

8. Which of the following is/are correct ?(A) The image and object are never on either side of focus in a spherical mirror.(B) A virtual image must be erect(C) An image formed in a plane mirror must have same speed as the object has(D) Laws of reflection are same for all wavelengths.

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9. A virtual object placed between the pole and the principal focus of a convex mirror produce an image whichis(A) real, magnified and upright (B) virtual, diminished and inverted(C) virtual, diminished and upright (D) real, diminished and inverted

10. Find the position of 1 cm tall object which is placed 8 cm infront of a concave mirror of radius of curvature24 cm

(A) 24 cm (B) 25 cm (C) 26 cm (D) 27 cm

11. A concave mirror has a focal length 20 cm. The distance between the two positions of the object for whichthe image size is double the object size is

(A) 20 cm (B) 40 cm (C) 30 cm (D) 60 cm

12. In a looking mirror or a window pane you find that your face appears larger than normal. The mirror orwindow pane is :

(A) Plane (B) Concave (C) Convex (D) None of the above

13. The figure shows the path of a ray of light as it passes through three different materials with refractiveindices n1 , n2 and n3 . The figure is drawn to scale . The refractive indices of the material satisfy the relation:

(A) n3 < n2 < n1 (B) n3 < n1 < n2 (C) n2 < n1 < n3 (D) n1 < n3 < n2

14. A ray of sunlight enters a spherical water droplet (n = 4/3) at an angle of incidence 53º measured withrespect to the normal to the surface . It is reflected from the back surface of the droplet and re-enters intoair. The angle between the incoming and outgoing ray is [Take sin 53º = 0.8]

(A) 15º (B) 34º (C) 138º (D) 30º

15. A parallel beam of light emerges from the opposite surface of the sphere when a point source of light lies atthe surface of the sphere. The refractive index of the sphere is (The ray are observed near normal)

(A) 3/2 (B) 5/3 (C) 2 (D) 5/2

16. A parallel beam of white light falls on a convex lens . Images of blue , red and green light are formed on otherside of the lens at distances x , y and z respectively from the pole of the lens . Then :

(A) x > y > z (B) x > z > y (C) y > z > x (D) none of these

17. The correct conclusion that can be drawn from these figures is :

(a) (b)

(A) m1 < m but m < m2 (B) m1 > m but m < m2

(C) m1 = m but m < m2 (D) m1 = m but m2 < m

18. An optical system consists of a thin convex lens of focal length 30 cm and a plane mirror placed 15 cmbehind the lens. An object is placed 15 cm in front of the lens. The distance of the final image from theobject is

(A) 60 cm (B) 30 cm (C) 75 cm (D) 45 cm

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19. A paraxial beam is incident on a glass (m = 1.5) hemisphere of radius R = 6 cm in air as shown. Thedistance of point of convergence F from the plane surface of hemisphere is

F

(A) 12 cm (B) 5.4 cm (C) 18 cm (D) 8 cm

20. A convex lens has a focal length 20 cm. The refractive index of material is m = 1.5. If this lens is immersedin a liquid of refractive index 1.8, it will behave as a

(A) convex lens of focal length 60 cm (B) concave lens of focal length 60 cm

(C) convex lens of focal length 120 cm (D) concave lens of focal length 120 cm

21. A particle executes SHM of amplitude 1cm along principal axis of a convex lens of focal length 12cm. Themean position of oscillation is at 20 cm from the lens. Find the amplitude of oscillation of the image of theparticle.

(A) 2 cm (B) 2.6 cm (C) 1 cm (D) 2.3 cm

22. Following figure shows three arrangements of lenses. The radii of curvature of all the curved surfaces aresame . The ratio of the equivalent focal length of combination P, Q and R is :

(A) 1 : 1 : 1 (B) 1 : 1 : – 1 (C) 2 : 1 : 1 (D) 2 : 1 : 2

23. A ray of light passes through a prism in a principle plane ; the deviation being equal to angle of incidencewhich is equal to 2a. It is given that a is the angle of prism and µ is the refractive index of the material ofprism, then

(A) 2

1µcos2 -

=a (B) 8

1µcos2 -

=a (C) 1µsin 2 -=a (D) 8

1µsin2 -

=a

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EXERCISE 3Conceptual Subjective

1. Two plane mirrors are inclined to each other at 30º. A ray is incident on M at 40º. Find deviation producedin it by three successive reflections due to mirrors.

2. Fig. shows a torch producing a straight light beam falling on a plane mirror at an angle 60º. The reflectedbeam makes a spot P on the screen along Y-axis. If at t = 0, mirror starts rotating about the hinge A withan angular velocity w = 1º per second clockwise, find the speed of the spot on the screen after time t = 15s.

3. Two plane mirrors form an angle of 120º . The distance between the two images of a point source formed bythem is 20 cm . Determine the distance from the light source to the point where the mirrors touch if it lieson the bisector of the angle formed by the mirrors .

4. If the least distance of distinct vision of a man is 0.25 metre. Then find the minimum distance at which heshould keep a plane mirror in order to see himself conveniently .

5. Find the magnitude of velocity of image with respect to object O.

6. A concave spherical mirror forms a threefold magnified inverted image of an object . What are the principalfocal length and the radius of curvature of the surface of the mirror if the distance from the object to theimage is 28 cm ?

7. A point is 35 cm along the optical axis from a spherical concave mirror having a focal length 25 cm .At what distance along the optical axis from the concave mirror should a plane mirror be placed for theimage it forms to coincide with the point source?

8. A concave mirror forms a real image three times larger than the object on a screen. Object and screen aremoved until the image becomes twice the size of object. If the shift of object is 6 cm, what is the shift of thescreen and the focal length of mirror ?

9. An object is present on the principal axis of a concave mirror of focal length 15 cm. Object is at a distanceof 20 cm from mirror. If velocity of object is 5cms–1 towards mirror and velocity of mirror is 5 cms–1 towardsobject then find velocity of image in mirror .

O

5cms-1 5cms-1

10. A plate with plane-parallel faces , having refractive index 1.8 rests on a plane mirror . A light ray is incidenton the upper face of the plate at 60º . How far from the entry point will the ray emerge after reflection by themirror if the plate is 6 cm thick ?

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11. A cubical vessel with non-transparent walls is so located that the eye of an observer does not see itsbottom , but sees all of the wall CD (as in figure) . Upto what height water should be poured into the vesselfor the observer to see an object O arranged at a distance of b = 10 cm from corner D ? The face of vesselis a = 40 cm .

12. A glass cube of edge 1 cm and m = 1.5 has a small spot at the centre . What parts of the cube face mustbe covered to prevent the spot from being seen , no matter what the direction of viewing ? What fraction ofthe cube surface must be covered . Neglect the case of internal reflection .

13. A hemispherical paper weight contains a small artificial flower of size 2 cm on its axis of symmetry at adistance 3 cm from the flat surface . What is the size of the flower as it appears to an observer when helooks at it along the axis of symmetry , (a) from top (b) from bottom ?

[Radius of the hemisphere is 10 cm , Index of refraction of glass = 1.5]

14. A candle is 2 m from a wall . When a converging lens is placed 40 cm from the candle between the candleand the wall , a sharp image of the candle is formed on the wall . Determine the optical power of the lens andits magnification .

15. A plano-convex lens with a radius of curvature of 30 cm and a refractive index of 1.5 produces a real imageof an object with a magnification equal to 2 . Find the distances of the object and the image from the lens.Draw the ray diagram .

16. An object of height 6 cm is set at right angles to the optical axis of a double convex lens of optical power5 D and 25 cm away from the lens . Determine the focal length of the lens , the position of the image , thelinear magnification of the lens and the height of the image formed by it .

17. The height of a candle flame is 5 cm . A lens produces an image of the flame 15 cm high on a screen .Without touching the lens, the candle is moved over a distance of l = 1.5 cm away from the lens and asharp image of the flame 10 cm high is obtained again after shifting the screen . Determine the focal lengthof the lens .

18. A pin is placed 10 cm infront of convex lens of focal length 20 cm made of material of refractive index 1.5 .The surface of the lens farther away from the pin is silvered and has a radius of curvature 22 cm . Determinethe position of the final image .

19. A convex lens of focal length 15 cm is placed in front of a convex mirror . Both are coaxial and the lens is5 cm from the apex of the mirror . When an object is placed on the axis at a distance of 20 cm from thelens, it is found that image coincides with the object . Calculate the radius of curvature of mirror .

20. A parallel beam of light travelling in water of refractive index 4/3 is refracted by a spherical air bubble ofradius 2 mm situated in water. Assuming the light rays to be paraxial, find the nature and position of theimage due to refraction at the first face .

HO2Bubble

21. The angle of refraction of a prism is 60º . A light ray emerges from the prism at the same angle as it isincident on it . The refractive index of the prism is 1.5 . Determine the angle by which the ray is deflectedfrom its initial direction as a result of its passage through the prism .

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EXERCISE 4Brainstorming Objective

1. Two mirrors are inclined at an angle q as shown in figure. Light ray is incident parallel to one of the mirrors.The ray will start retracing its path after third reflection if :

) q

(A) q = 45º (B) q = 30º (C) q = 60º (D) all three

2. The reflecting surface is represented by the equation 2x = y2 as shown in figure. A ray travelling horizontalbecomes vertical after reflection. The co-ordinates of the point of incidence can be

(A) (1/2, 1) (B) (1, 1/2) (C) (1/2, 1/2) (D) (–1/2, –1)3. By what angle mirror M2 is rotated, so that the light ray after reflection from both the mirrors become

horizontal ?

(A) 95º clockwise (B) 75º anticlockwise(C) 5º clockwise (D) 15º clockwise

4. If the equation of mirror is given by y = p2

sinpx (y > 0) then find the point on which horizontal ray

should be incident so that the reflected ray become perpendicular to the incident ray

(A) ÷÷ø

öççè

æ

p3,

31

(B) ÷÷ø

öççè

æ

p 31,3

(C) ÷÷ø

öççè

æ

p2,

21

(D) ÷÷ø

öççè

æ

p 21,2

5. The reflecting surface of a plane mirror is vertical. A particle is projected in a vertical plane which is alsoperpendicular to the mirror. The initial velocity of the particle is 10 m/s and the angle of projection is 60°.The point of projection is at a distance 5 m from the mirror. The particle moves towards the mirror. Justbefore the particle touches the mirror the velocity of approach of the particle and its image is :

(A) 10 m/s (B) 5 m/s (C) 310 m/s (D) 35 m/s

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6. A plane mirror lies in the x-y plane with its reflecting side on the +ve side of z-axis. A point at the coordinates(x, y, z) has a velocity whose component along x, y, and z directions are u, v and w, respectively. Thecoordinates of the image and its velocity components will be :

(A) (x, y, –z) and (u, v, –w) (B) (–x, –y, z) and (u, v, –w)

(C) (x, y, –z) and (–u, –v, w) (D) none of these

7. Sun rays are reflected from a horizontal mirror and fall on a vertical screen. A long object is placed perpen-dicular to mirror at large distance from the screen. If object is of length h then length of the shadow on thescreen will be

h

(A) of height h (B) of height 2h (C) inverted (D) erect8. An object is moving towards a mirror with a velocity v as shown in figure. If the collision between the mirror

and the object is perfectly elastic, then the velocity of the image after collision with mirror in vector form is

(q

v

y

x

(A) jv- (B) i2sinvj2cosv q+q- (C) iv- (D) ˆvcos vsin i- q + q9. There are two plane mirrors with reflecting surfaces facing each other. The mirrors are moving with speed

v away from each other. A point object is placed between the mirrrors. The velocity of the nth image will be(A) nv (B) 2nv (C) 3nv (D) 4nv

10. A ray of light is incident on a plane mirror along a line represented by kji ++ . The possible orientation ofthe vector which lies in the plane of the mirror for which the ray will retrace its path.

(A) k2j4i2 +- (B) kji -- (C) k2ji2 -+ (D) kji ---11. A body of mass 100 g is tied to one end of spring of constant 20 N/m it is released with spring unelongated.

The distance between pole of mirror and mean position of the body is 20 cm. The focal length ofconvex mirror is 10 cm. The length over which vibration of image takes place is -

//////////////////////////////////

O

20cm

(A) 10 cm (B) 50 cm (C) 1.14 cm (D) 0.33 cm

12. For a concave mirror for a certain position of object the magnification is 0.5 and for another position ofobject displaced from the former by 5cm the magnification is 0.25. The focal length of the concave mirroris(A) 2 cm (B) 2.5 cm (C) 3.0 cm (D) 3.5 cm

13. Two concave mirrors each of radius of curvature R situated at a distance d. A point object O is placed asshown with figure so that its image coincides with the object itself. Then d is equal to

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(A) R only (B) 2R

and R (C) 2R and 2R

(D) R and 2R

14. A concave mirror is placed on a horizontal surface and two thin uniform layers of different transparentliquids (which do not mix or interact) are present on the reflecting surface. The refractive indices of theupper and lower liquids are µ1 and µ2 respectively. The bright point source at a height ‘d’ (d is very large incomparison to the thickness of the film) above the mirror coincides with its own final image. The radius ofcurvature of the reflecting surface therefore is(A) µ1d/µ2 (B) µ1µ2d (C) µ1d (D) µ2d

15. A ray R1 is incident on the plane surface of the glass slab (kept in air) of refractive index 2 at angle ofincidence equal to the critical angle for this air glass system. The refracted ray R2 undergoes partialreflection & refraction at the other surface. The angle between reflected ray R3 and the refracted ray R4 atthe surface is:

R1

R2R3

R4

(A) 45º (B) 135º (C) 105º (D) 75º16. A ray of light travelling in a medium of refractive index m is incident at an angle q on a composite

transparent plate consisting of 50 plates of R.I. 1.01 m , 1.02 m , 1.03 m , ........ , 1.50 m . The ray emergesfrom the composite plate into a medium of refractive index 1.6 m at angle 'x' . Then :

(A) sin x = 50

5.101.1

÷øö

çèæ

sin q (B) sin x = 85

sin q

(C) sin x = 58

sin q (D) sin x = 50

01.15.1

÷øö

çèæ

sin q

17. A light ray is incident on a transparent sphere of index = 2 , at an angle of incidence = 45º . What is thedeviation of a tiny fraction of the ray , which enters the sphere , undergoes two internal reflections and thenrefracts out into air ?(A) 270º (B) 240º (C) 120º (D) 180º

18. An air bubble is inside water. The refractive index of water is 4/3. At what distance from the air bubbleshould a point object be placed so as to form a real image at the same distance from the bubble ?(A) 2R (B) 3R(C) 4R (D) the air bubble cannot form a real image

19. A concave spherical refracting surface separates two media glass and air (µglass = 1.5). If the image is to bereal, at what minimum distance u should the object be placed in air if R is the radius of curvature?(A) u < R (B) u > 2R (C) u < 2R (D) none of these

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20. The diagram shows a concavo-convex lens. What is the condition on the refractive indices so that the lensis diverging ?

(A) 2 m3 < m1 + m2 (B) 2 m3 > m1 + m2 (C) m3 > 2 (m1 – m2) (D) none of these21. Distance of an object from the first focus of an equiconvex lens is 10 cm and the distance of its real image

from second focus is 40 cm. The focal length of the lens is :(A) 25 cm (B) 10 cm (C) 20 cm (D) 40 cm

22. The greatest thickness of a plano-convex glass lens appears to be 2 cm when observed normally throughthe plane face, and when observed through the curved face the greatest thickness appears to be 20/9 cms,if real thickness is 3 cm then the radius of curvature of the spherical surface is :(A) 6.67 cm (B) 10.0 cm (C) 20.0 cm (D) 2.22 cm

23. Two point sources P and Q are 24 cm apart. Where should a convex lens of focal length 9 cm be placed inbetween them so that the images of both sources are formed at the same place ?(A) 3 cm from P (B) 15 cm from Q (C) 9 cm from Q (D) 18 cm from P

24. A real object is placed 1 cm above the optical axis of a convex lens of focal length 40 cm. The objectdistance is 60 cm. If the object now starts moving perpendicularly away from the optical axis with a speed= 10 cm/s, the speed of the image is

(A) 5 cm/sec (B) 10 cm/sec (C) 20 cm/sec (D) 40 cm/sec

25. Monochromatic light rays parallel to x-axis strike a convex lens AB. If the lens oscillates such that AB tiltsupto a small angle q (in radian) on either side of y-axis, then the length over which oscillation of image willtake place (f = focal length of the lens)

O

B

A

y

x

(A) fsecq (B) fsec2q (C) fq2/2 (D) the image will not move

26. A certain prism is found to produce a minimum deviation of 38º. It produces a deviation of 44º when theangle of incidence is either 42º or 62º. What is the angle of incidence when it is undergoing minimumdeviation ?

(A) 45º (B) 49º (C) 40º (D) 55º27. An equilateral prism ABC is placed in air with its base side BC

lying horizontally along X axis as shown in the figure. A ray given

by 3 Z + X = 10 is incident at a point P on face AB of the

prism. The value of m for which the ray grazes the face AC is :(0, 0, 0) 60º

A

B C X

Z

Y

P

(A) 12 (B)

23 (C)

32

(D) 13 .

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28. The refracting angle of a prism is 90º. If g is the angle of minimum deviation and b is the deviation of raywhich enters at grazing incidence. If µ is refractive index of material of the prism, then which of the following(s) is correct ?

(A) sing = sin2b (B) sing = cos2b (C) cosg = bm

cos (D) cosg = µsinb

29. For a prism kept in air it is found that for an angle of incidence 60º, all the three angles i.e., the angle ofrefraction ‘A’, angle of deviation ‘d’ and angle of emergence ‘e’ becomes equal. Then the refractive index ofthe prism is(A) 1.73 (B) 1.15 (C) 1.5 (D) 1.33

30. A beam of light, consisting of red, green and blue colours, is incident on a right-angled prism, as shown.The refractive indices of the material of the prism for the above red, green and blue wavelengths are 1.39,1.44 and 1.47 respectively. The prism will

(

45º

90º (45º

(A) separate part of the red colour from the green and blue colours(B) separate part of the blue colour from the red and green colours(C) separate all the three colours from one another(D) not separate even partially any colour from the other two colours

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EXERCISE 5Brainstorming Subjective

1. A small block of mass m and a concave mirror of radius R fitted with a stand, lie on a smooth horizontaltable with a separation d between them. The mirror together with its stand has a mass m. The block ispushed at t = 0 towards the mirror so that it starts moving towards the mirror at a constant speed V andcollides with it. The collision is perfectly elastic. Find the velocity of the image (a) at a time t < d/V, (b) ata time t > d/V.

2. An object is placed exactly midway between a concave mirror of radius of curvature 40 cm and a convexmirror of radius of curvature 30 cm . The mirrors face each other and are 50 cm apart . Determine the natureand position of the image formed by the successive reflections , first at the concave mirror and then at theconvex mirror .

3. A concave mirror is placed on the path of a converging bundle of rays so that the point of intersection of therays is behind the mirror at 20 cm from its pole . The rays reflected by the mirror converge at a point at adistance equal to half the focal length of the mirror. Determine the radius of curvature of the mirror .

4. Two spherical mirrors one convex and the other concave are each of the same radius ‘r’ . They are arrangedco-axially at a distance ‘2 r’ from each other . A small circle of radius ‘a’ is drawn on the convex mirror nearthe pole . Find the radii of the third image formed by successive reflections on the mirrors.

5. In the figure shown, S is a tiny bulb and on the far right side is a flat mirror. Black paint on right surface ofbulb blocks any light from the bulb reaching the flat mirror directly. When the concave mirror (f = 40 cm) isat a distance of 60 cm from the bulb, the real image of the bulb formed after one reflection from the concavemirror and then from flat mirror coincides with the bulb. Find the distance between the bulb and flat mirror.

6. A balloon is rising up along the axis of a concave mirror (reflecting surface facing up) of radius of curvature20 m . A ball is dropped from the balloon at a height of 15 m from the mirror when the balloon has velocity20 m/s . Find the velocity of the image of the ball formed by concave mirror after 4 seconds from instant ofdropping the ball .

7. A gun of mass M (without bullet) fires a bullet of mass ‘ m ‘ with a horizontal speed v. The gun is fitted witha concave mirror of focal length ‘ f ‘ facing towards the receding bullet. Find the speed of the image of thebullet just after the firing of the bullet .

8. Two rays are incident on a spherical mirror of radius R= 5 cm parallel to its optical axis at the distanceh1 = 0.5 cm and h2 = 3 cm. Find the distance Dx between the points at which these rays intersect theoptical axis after being reflected at the mirror .

9. A point source of light is placed a distance ‘h’ below the surface of a large deep lake . Show that thefraction ‘f’ of the light energy that escapes directly from the water surface is independent of ‘h’ and is

given by ; f = 21

– m2

112 -m , where m is the index of refraction of water .

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10. Given a glass slab placed on a table . The x-axis is along its length and y-axis is along the direction of the

thickness as shown in figure . The index of refraction of this glass slab varies as n = n0 / ÷øö

çèæ -

rx1 , where

n0 and ‘r’ are constants . A light beam enters from air perpendicular to the slab at O and emerges at apoint A at an angle a with the vertical . Find the index of the refraction nA at A .

d

11. A beam of parallel rays of width b propagates in glass at an angle q to its place face. Find the beam widthafter it goes over to air through this face. The refractive index of glass is µ]

12. A composite slab consisting of different media is placed infront of a concave mirror of radius of curvature150 cm. The whole arrangement is placed in water. An object O is placed at a distance 20 cm from theslab. The R.I. of different media are given in the diagram. Find the position of the final image formed by thesystem .

13. A concave mirror of radius of curvature 40 cm is filled with water (n = 4/3) upto a height of 12 cm. A pointobject O is kept on the principal axis of the mirror at height 13.5 cm from the water surface. Find theposition of the final image formed after refraction at water surface, reflection at mirror and again refraction atwater surface in succession .

//////////////////////////////////////

///////

////////////////////////////////

O

13.5cm

14. A cylindrical glass rod of radius 0.1 m and refractive index 3 lies on horizontal plane mirror. A horizontalray of light moving perpendicular to the axis of the rod is incident on it. At what height from the mirror shouldthe ray be incident so that it leaves the rod at a height of 0.1 m above the plane mirror ? At what distancea second similar rod , parallel to the first be placed on the mirror, such that the emergent ray from thesecond rod is in line with the incident ray on the first rod?

15. The image S¢ of a point source S lying at a distance ‘b’ from a transparent sphere is formed by a smalldiaphragm only by rays close to the optical axis (as in figure) . Where will the image be after the sphereis cut into two parts perpendicular to the horizontal axis and the plane surface of the left half is silvered ?

ba

S

sourceS

length

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16. A ball is kept at a height h above the surface of a heavy transparent sphere made of a material of refractiveindex µ. The radius of the sphere is R. At t = 0, the ball is dropped to fall normally on the sphere. Find the

speed of the image formed as a function of time for gh2t < . Consider only the image by a single

refraction.

17. A point source is located at a distance of 20 cm from the front surface of symmetrical glass convex lens.The lens is 5 cm thick and the radii of curvature of its surfaces are also 5 cm . How far beyond the 2nd

surface of this lens is the image of the source formed? [ mg = 1.5 ]

18. A plano convex lens has a thickness of 4 cm . When placed on a horizontal table with the curved surfacein contact with it , the apparent depth of the bottom most point of the lens is found to be 3 cm . If the lensis inverted such that the plane face is in contact with the table , the apparent depth of the centre of theplane face of the lens is found to be 25/8 cm . Find m and R of the lens .

19. Two media each of refractive index 1.5 with plane parallel boundaries are separated by 100 cm . A convexlens of focal length 60 cm is placed midway between them with its principal axis normal to the boundaries.A luminous point object O is placed in one medium on the axis of the lens at a distance 125 cm from it .Find the position of its image formed as a result of refraction through the system .

20. Paraxial rays parallel to principal axis are falling on a thin equiconvex lens of radius of curvature R. Refractiveindex of the material of the lens is µ. If the image is formed after n total internal reflections, then find thedistance of final image from the lens.

21. A light ray parallel to the principal axis is incident (as shown in the figure) on a thin planoconvex lens withradius of curvature of its curved part equal to 10cm. Assuming that the refractive index of the material of thelens is 4/3 and medium on both sides of the lens is air, find the distance of the point from the right surfaceof lens where this ray meets the principal axis. Find your answer in the form X/7 cm and fill value of X.

22. A parallel beam of light is incident on a system consisting of three thin lenses with a common optical axis.The focal lengths of the lenses are equal to f1 = + 10 cm , f2 = – 20 cm and f3 = + 9 cm respectively.The distance between the first and the second lens is 15 cm and between the second and the third lens is5 cm . Find the position of the point at which the beam converges when it leaves the system of lenses .

23. A plano-convex lens is silvered on its plane-side and then it acts like a concave mirror of focal length 20 cm,when the convex side is silvered it acts like a concave mirror of 7 cm focal length. What is the refractiveindex of the lens ?

24. Consider a ‘beam expander’ which consists of two converging lenses of focal lengths40 cm and 100 cm having a common optical axis. A laser beam of diameter 4 mm isincident on the 40 cm focal length lens. Find the diameter of the final beam. (see figure)

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25. A convex lens of focal length 15 cm is split into two halves and the two halves are placed at a separation of120 cm. Between the two halves of convex lens a plane mirror is placed horizontally and at a distance of 4mm below the principal axis of the lens halves. An object AB of length 2mm is placed at a distance of 20cm from one half lens as shown in figure. The final image of the point A is formed at a distance of n/3 mmfrom the principle axis. Determine the value of n.

20cm 4 mm

120cm

f=15cm f=15cm

2mmB

A

26. A thin converging lens of focal length f = 1.5 m is placed along y-axis such that its optical centre coincideswith the origin. A small light source S is placed at (–2.0 m, 0.1m). Where should a plane mirror inclined at

an angle q, tan q = 0.3 be placed such that y co-ordinate of final image is 0.3 m, i.e., find d. Also find x-co-ordinate of final image.

XO

S

(q

d

Y

27. A thin convex lens of focal length f = 30 cm is cut into two pieces 8 mm above the optical axis. Theparts are then placed along x-axis as shown in the figure. An object is present on x axis at(–40 cm , 0) . Find distance (in mm) of the final image from x-axis.

y

90cm

O x

28. At what values of the refractive index of a rectangular prism can a ray travel as shown in figure . The sectionof the prism is an isosceles triangle and the ray is normally incident onto the face AB.

29. A ray of light is incident at an angle of 60º on one face of a prism which has an angle of 30º . The rayemerging out of the prism makes an angle of 30º with the incident ray . Show that the emergent ray isperpendicular to the face through which it emerges and calculate the refractive index of the material of theprism .

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30. Three isosceles right angles prisms of the refractive indices m1 , m2 and m3 are placed in contact with theirbases opposite as in figure . If a ray passes through the block of prisms so formed without being deviated,

show that 21m + 2

3m – 22m = 1 .

31. The figure shows the path of a ray passing through an equiangular prism PQR. It is incident on face PR atthe critical angle (slightly greater than C) for total internal reflection. If the angle a shown in the figure is 30°,determine the R.I. of the material of the prism .

32. An equilateral prism deviates a ray through 23º for two angles of incidence differing by 23º. Find µ of theprism ?

33. A direct-vision prism is made out of three prisms, each with a refracting angle of 60º, attached to each otheras shown in the figure. Light of a certain wavelength is incident on the first prism. The angle of incidence is30º and the ray leaves the third prism parallel to the direction of incidence. The refractive index of the glass

of the first and third prisms is 1.5. Find the refractive index of the material of the middle prism. ( )45.26 =

34. An equilateral prism provides the least deflection angle 45º in air. Find the refracting index of an unknownliquid in which same prism gives least deflection angle of 30º.

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EXERCISE 6NEW IIT-JEE PATTERN QUESTION

MULTIPLE CHOICE ANSWER TYPE1. Two plane mirrors at an angle such that a ray incident on a mirror undergoes a total deviation of 240º after

two reflections :(A) the angle between the mirror is 60º(B) the number of images formed by this system will be 5 , if an object is placed symmetrically between themirrors(C) the number of images will be 5 if an object is kept unsymmetrically between the mirrors(D) a ray will retrace its path after 2 successive reflections, if the angle of incidence on one mirror is 60º

2. A man of height 170 cm wants to see his complete image in a plane mirror (while standing) . His eyes areat a height of 160 cm from the ground. Then :(A) Minimum length of the mirror = 80 cm(B) Minimum length of the mirror = 85 cm(C) Bottom of the mirror should be at a height 80 cm(D) Bottom of the mirror should be at a height 85 cm

3. In the figure shown consider the first reflection at the plane mirror and second at the convex mirror. AB isobject.

(A) the second image is real, inverted of 1/5th magnification

(B) the second image is virtual and erect with magnification 1/5

(C) the second image moves towards the convex mirror

(D) the second image moves away from the convex mirror

4. The x-z plane separates two media A and B with refractive indices m1 and m2 respectively. A ray of light

travels from A to B . Its directions in the two media are given by the unit vectors, Arr

= jbia + and

Brr

= ji b+a where jandi are unit vectors in the x & y directions. Then :

(A) m1a = m2a (B) m1a = m2a (C) m1b = m2b (D) m1b = m2b

5. A ray of light is incident upon an air/water interface (it passes from air into water) at an angle of 45º . Whichof the following quantities change as the light enters the water ?

(A) Wavelength (B) Frequency

(C) Speed of propagation (D) Direction of propagation

6. A fish , F in the pond is at a depth of 0.8 m from the water surface and is moving vertically upwards withvelocity 2 m/s. At the same instant, a bird B is at a height of 6 m from the water surface and is movingdownwards with velocity 3 m/s. At this instant, both are on the same vertical line as shown in the figure .Which of the following statements are correct ?

(A) Height of B, observed by F (from itself) is equal to 5.30 m

(B) Depth of F, observed by B (from itself) is equal to 6.60 m

(C) Height of B, observed by F (from itself) is equal to 8.80 m

(D) None of the above

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7. A ray of light is incident normally on one face of 30º – 60º – 90º prism of refractive index 5/3 immersed inwater of refractive index 4/3 as shown in figure .

(A) The exit angle q2 of the ray is sin–1 ( )85

(B) The exit angle q2 of the ray is sin–1 ÷øöç

èæ

345

(C) Total internal reflection at point P ceases if the refractive index of water is increased to 32

5 by

dissolving some substance(D) Total internal reflection at point P ceases if the refractive index of water is increased to 5/6 by dissolving some substance

8. For refraction through a small angled prism , the angle of deviation :(A) increases with the increase in R.I. of prism(B) will decrease with the increase in R.I. of prism(C) is directly proportional to the angle of prism(D) will be 2d for a ray of R.I. = 2.4 , if it is d for a ray of R.I. = 1.2

9. Two convex lenses placed in contact form the image of a distantobject at P. If the lens B is moved to the right, then which is/arenot correct for the image?

(A) move to the left(B) move to the right(C) remain at P(D) move either to the left or right, depending upon focal length of the lenses

10. Which of the following can form diminished , virtual and erect image of your face ?(A) Converging mirror (B) Diverging mirror(C) Converging lens (D) Diverging lens

11. A convex lens forms an image of an object on a screen. The height of the image is 9 cm. The lens isnow displaced until an image is again obtained on the screen. Then height of this image is 4 cm . Thedistance between the object and the screen is 90 cm .(A) The distance between the two positions of the lens is 30 cm(B) The distance of the object from the lens in its first position is 36 cm(C) The height of the object is 6 cm(D) The focal length of the lens is 21.6 cm

12. The radius of curvature of the left and right surface of the concave lens are 10 cm and 15 cm respectively .The radius of curvature of the mirror is 15 cm.

Water( =4/3)m air

Glass ( =1.5)m

(A) equivalent focal length of the combination is – 18 cm(B) equivalent focal length of the combination is + 36 cm(C) the system behaves like a concave mirror(D) the system behaves like a convex mirror

13. Out of the following , select the correct statements :(A) A double convex air bubble in water would behave as a convergent lens(B) A convex lens of focal length f1 is placed in contact with a concave lens of focal length f2. The combinationwill act as a convex lens if f1 < f2.(C) An small object of linear dimensions L is placed along the axis of a thin lens placed in air. The size ofthe image is Lv2/u2.(D) The focal length of lens of power 200 D is 0.5 cm.

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14. A luminous point object is placed at O , whose image is formed at I as shown in the figure. AB is the opticalaxis.If height of object is equal to height of image, which of the following statements are correct ?

(A) If a lens is used to obtain image, the lens must be converging

(B) If a mirror is used to obtain image, the mirror must be a convex mirror having pole at the point of

intersection of lines OI and AB

(C) Position of principal focus of mirror cannot be found

(D) I is real image

15. A converging lens is used to form an image on a screen. When the upper half of the lens is covered by anopaque screen :

(A) Half of the image will disappear (B) Complete image will be formed

(C) Intensity of the image will increase (D) Intensity of the image will decrease

16. Which of the following statements are incorrect ?

(A) When a lens is dipped in water, magnitude of its focal length increases

(B) When a lens is dipped in water, magnitude of its focal length decreases

(C) When a spherical mirror is dipped in water, magnitude of its focal length increases

(D) When a lens is dipped in water magnitude of its focal length remains same

17. 'XX is the optic axis of an optical instrument. A is the position of a real point object. B is the position ofits image. Both the object and image are close to the optic axis and distance of the object from the opticaxis is greater than that of image. The optical instrument can possibly be

(A) diverging lens (B) converging lens (C) concave mirror (D) convex mirror18. In displacement method, the distance between object and screen is 96 cm. The ratio of length of two

images formed by a convex lens placed between them is 4.84.

(A) Ratio of the length of object to the length of shorter image is 11/5

(B) Distance between the two positions of the lens is 36 cm

(C) Focal length of the lens is 22.5 cm

(D) Distance of the lens from the shorter image is 30 cm

19. An object O is kept infront of a converging lens of focal length 30 cm behind which there is a plane mirrorat 15 cm from the lens.

15cm15cm

O

30cm

(A) the final image is formed at 60 cm from the lens towards right of it

(B) the final image is at 60 cm from lens towards left of it

(C) the final image is real

(D) the final image is virtual

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20. A thin symmetric double-convex lens of power P is cut into three parts A , B and C as shown . The powerof :

B C

A

(A) A is P (B) A is 2P (C) B is P (D) B is P/4

21. Two refracting media are separated by a spherical interface as shown in the figure. PP’ is the principal axis,µ1 and µ2 are the refractive indices of medium of incidence and medium of refraction respectively. Then :

µ2 µ1

P P’

(A) if µ2 > µ1 , then there cannot be a real image of real object(B) if µ2 > µ1 , then there cannot be a real image of virtual object(C) if µ1 > µ2 , then there cannot be a virtual image of virtual object(D) if µ1 > µ2 , then there cannot be a real image of real object.

REASONING TYPE22. Statement-1 :

Geometrical optics can be regarded as the limiting case of wave opticsStatement-2 :When size of obstacle or opening is very large compared to the wavelength of light then wave nature can beignored and light can be assumed to be travelling in straight line.

23. Statement-1 :A ray of light reflected successively from three mutually perpendicular mirrors reverses itspathStatement-2 : Whenever light is reflected from an optically denser medium, the reflected ray undergoes anabrupt phase change of p radians

24. Statement-1 :For observing traffic at our back, we prefer to use a convex mirror.Statement-2 :A convex mirror has a more larger field of view than a plane mirror or concave mirror.

25. Statement-1 :A virtual image can be photographed.Statement-2 :Only a real image can be formed on a screen.

26. Statement-1 :A convex lens may be diverging.Statement-2 :The nature of a lens depends upon the refractive indices of the material of lens and surrounding mediumbesides geometry.

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78

27. Statement-1 : Law of reflection is applicable for all type of mirrors.Statement-2 : Rays which are parallel to principle axis are known as paraxial rays.

28. Statement-1 :If a plane glass slab is placed on the letters of different colours then all the letters appear to be raised up tothe same height.Statement-2 :Refractive index of a medium depends upon wavelength of light.

29. Statement-1 :

The formula, isµdepthApparent

depthalRe= valid for normal incidence.

Statement-2 :

Normal view favours to take approximation úû

ùêë

é»»

rtanrsinitanisin

, where i and r are angle of incidence & angle of

refraction, to derive the relation µ = depthApparentdepthalRe

.

30. Statement-1 :When a glass prism is immersed in water, the deviation caused by prism decreases.Statement-2 :Refractive index of glass prism relative to water is less than relative to air.

31. Statement-1 :When white light passes through a prism, deviation of violet light is more than green light.Statement-2 :In a prism average deviation is measured as deviation of yellow light.

32. Statement-1 :The power of a thin lens depends upon the surrounding medium.Statement-2 :Power of a thin lens = µ/F.

33. Statement-1 : The focal length of lens does not change when red light is replaced by blue light.Statement-2 : The focal length of lens depends on the colour of light used.

34. Statement-1 : Sun glasses have zero power even though their surfaces are curved.

Statement - 2 : Both the surfaces of the sun glasses are curved in the same direction with same radii.

35. Statement-1 :The image formed by total internal reflection is much brighter than those formed by mirror orlenses.

Statement-2 : There is no loss of intensity in total internal reflection.

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LINKED COMPREHENSION TYPEWrite Up-1

A man is standing in a room and a plane mirror is fixed on the wall in front of him. The height of the wall isH. Man has to see the complete image of wall behind him at a time.

36. When the man is standing near wall i.e. at position 1, the minimum length of the mirror required is :(A) H (B) H/2 (C) H/3 (D) H/4

37. When the man is standing at the middle of the room i.e. at position 2, the minimum length of the mirrorrequired is :(A) H (B) H/2 (C) H/3 (D) H/4

38. When the man is at position 3, the minimum length of the mirror required is :(A) H (B) H/2 (C) H/3 (D) H/4

Write Up-2

A projectile is projected at an angle f , with a speed u in the vertical plane and there is a plane mirror OM,in which image of the projectile is observed.

fq

M

O

u

39. At a particular instant, image of the projectile appears to be at rest with respect to object. At this momentspeed of the projectile is

(A) sin

sinu q

f (B) ( )( )

sinsinu q f

f q f+- (C)

sinsin

u fq

(D) cos

cosu f

q

40. The image will have maximum velocity with respect to object when the particle has speed

(A) ( )

( )cos

cosu q f

f q+

- (B) cos

sinu f

q(C)

sincos

u fq

(D) sin

cosu q

f

41. The path of the image as seen by the projectile will be

(A) straight line (B) parabola (C) circle (D) ellipseWrite Up-3

Spherical aberration in spherical mirrors is a defect which is due to dependence of focal length ‘f’ on angleof incidence ‘q’ as shown in figure is given by

q-= sec2RRf

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where R is radius of curvature of mirror and q is the angle of incidence. The rays which are closed toprincipal axis are called paraxial rays and the rays far away from principal axis are called marginal rays. Asa result of above dependence different rays are brought to focus at different points and the image of a pointobject is on a point.

42. If fp and fm represent the focal length of paraxial and marginal rays respectively, then correct relationship is(A) fp = fm (B) fp > fm (C) fp < fm (D) none

43. If angle of incidence is 60°, then focal length of this ray is :(A) R (B) R/2 (C) 2R (D) 0

44. The total deviation suffered by the ray falling on mirror at an angle of incidence equal to 60° is(A) 180° (B) 90° (C) Can’t be determined (D) none

45. For paraxial rays, focal length approximately is :(A) R (B) R/2 (C) 2R (D) none

46. Which of the following statements are correct regarding spherical aberration :(A) It can be completely eliminated(B) It can’t be completely eliminated but it can be minimized by allowing either paraxial or marginal rays tohit the mirror(C) It is reduced by taking large aperture mirrors(D) none

Write Up-4An object is present on the principal axis of a concave mirror at a distance 30 cm from it. Focal length ofmirror is 20 cm.

O

30cm

47. Image formed by mirror is :(A) At a distance 60 cm in front of mirror(B) At a distance 60 cm behind the mirror(C) At a distance 12 cm in front of mirror(D) At a distance 12 cm behind the mirror.

48. If object starts moving with 2 cms–1 along principal axis towards the mirror then :(A) image starts moving with 8 cms–1 away from the mirror(B) image starts moving with 8 cms–1 towards the mirror(C) image starts moving with 4 cms–1 towards the mirror(D) image starts moving with 4 cms–1 away from the mirror

49. If object starts moving with 2 cms–1 perpendicular to principal axis above the principal axis then :(A) image moves with velocity 4 cms–1 below the principal axis(B) image moves with velocity 4 cms–1 above the principal axis(C) image moves with velocity 8 cms–1 below the principal axis(D) image moves with velocity 8 cms–1 above the principal axis

PHYSICS

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Write Up-5The figure shows a ray incident at an angle i = p/3. If the plot drawn shows the variation of |r – i| versus

2

1

mm

= k, (r = angle of refraction)

i

µ1

µ2

50. The value of k1 is :

(A) 32

(B) 1 (C) 31

(D) 23

51. The value of q1 is :

(A) p/3 (B) p/2 (C) p/6 (D) zero52. The value of k2 is:

(A) 1 (B) 2 (C) 1/2 (D) none

Write Up-6A point object is placed on the optical axis of an equiconvex glass lens of focal length 7.5 cm. The distanceof object from the lens is 20 cm as shown in figure.

53. The lens is splitted along two halves along the plane YY¢ and right half is shifted towards right by 30 cmkeeping the left half fixed at its position as shown in figure II. What is the shift in location of image?

(A) 28 cm (B) 48 cm (C) 62 cm (D) 10 cm

54. The right half lens is further displaced perpendicular to line XX¢ by 6 mm as shown in figure III. What isfurther shift in image from its earlier position (position in figure II)?

(A) 6 mm (B) 4 mm (C) 3 mm (D) 2mm

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55. The two halves are grouped together as in figure II and space is filled with water as shown in figure IV. Whatis shift in position of image from its position of figure (II) (mg = 3/2, mw = 4/3)

(A) 7.5 cm (B) 10.7 cm (C) 0.7 cm (D) 17.5 cmWrite Up-7

" Figure shows a convex lens of focal length 15 cm. A point object is placed on the principle axis of lens ata distance 20 cm from it as shown. On the other side of lens two observer eyes O1 and O2 are situated ata distance 100 cm from the lens at some distance above and below the principle axis.

Activity I : Now half position of lens below principle axis is painted blackActivity II : After this , lens is cut along its horizontal diameter and upper part of it is raised up slightly invertical direction.

56. In initial setup before the activities which of the following statement is correct?(A) Observer O1 will see a real image at 60 cm from the lens but observer O2 will not be able to see it.(B) Observer O2 will see a real image at 60 cm from the lens but observer O1 will not be able to see it.(C) Both the observers will see a real image at 60 cm from lens irrespective the positions of O1 and O2.(D) Both the observers may or may not be able to see the image at 60 cm from lens depending on thepositions of O1 and O2.

57. After activity - I , which of the following observer will not be able to see the image of object , if before thisactivity both were seeing the image?(A) O1 (B) O2(C) both O1 & O2 (D) neither O1 nor O2

58. After activity - I , for which observer the intensity of image will be reduced to half.(A) for O1 (B) for O2(C) both for O1 & O2 (D) neither for O1 nor for O2

59. After activity - II , which of the following statements is correct?(A) An image will be seen by both the observers , no matter what will be the displacement of lens(B) An image will still be formed at a distance 60 cm from the lens(C) An image will still be formed at the same position where it was before activity - II(D) None of these

60. If from the initial setup directly activity - II is executed skipping activity - I , how many images may be seenby the observers.(A) 1 (B) 2 (C) 3 (D) 4

Write Up-8

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White light is incident on a glass prism such that dispersion takes place. Light with different wavelengthsare travelling in different directions and with different speeds. So, different coloured rays are deviated indifferent directions from original direction of incident white light. Now, answer the following questions.

61. If Vr and Rr are the angles of refraction for violet and red rays inside the prism, then :

(A) V Rr r> (B) V Rr r< (C) V Rr r= (D) None

62. If Vm and Rm are the refractive indices for violet and red rays, then :

(A) V Rm m> (B) V Rm m< (C) V Rm m= (D) None

63. If Vd and Rd are the angles of deviation of violet and red rays with respect to incident direction of whitelight, then :

(A) V Rd d> (B) V Rd d< (C) V Rd d= (D) None

64. If VC and RC are the speeds of violet and red rays inside the prism, then :

(A) V RC C> (B) V RC C< (C) V RC C= (D) NoneWrite Up-9

Real images of an object are formed on the screen for two positions of a lens separated by a distance 60cm.

65. If the distance between object and screen is 180 cm then, the focal length of the lens is :(A) 40 cm (B) 25 cm (C) 14 cm (D) 20 cm

66. The ratio between the sizes of the two images will be :(A) 1/3 (B) 3 (C) 1/4 (D) 1/2

67. The images in the two cases have sizes 0.4 cm and 0.9 cm. The size of the object will be :(A) 0.36 cm (B) 0.6 cm (C) 1.5 cm (D) 0.9 cm

MATRIX MATCH TYPE68. A plane mirror is arranged parallel to the screen and a point source S is kept on the screen as shown in

figure. The mirror is moving near the screen.Corresponding to the direction of motion of the mirror matchthe column. (Consider the moment the motion starts)

Column - I Column- II(A) Direction of motion of mirror along 1 (p) length of spot increases(B) Direction of motion of mirror along 2 (q) length of spot decreases(C) Direction of motion of mirror along 3 (r) length of spot does not change(D) Direction of motion of mirror along 4 (s) brightness of spot increases

69. Angle between two mirrors ‘q’ and location of object is given in column I and some possible number ofimages are given in column II. Match the two columns.Column I Column - II(A) q = 60º and object is not on bisector (p) 4(B) q = 72º and object is on bisector (q) 5(C) q = 45º and object is on bisector (r) 7(D) q = 50º and object is on bisector (s) 8

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84

70. A point object is placed in front of a plane mirror as shown and moving with velocity 3 m/s towardsmirror. Mirror is moving with speed 2 m/s towards object, then

Column 1 Column 2(A) speed of image w.r.t. ground (p) 10 m/s(B) speed of image w.r.t. mirror (q) 5 m/s(C) speed of image w.r.t. object (r) 14 m/s(D) speed of mirror w.r.t. object (s) 7 m/s

71. A plane mirror is placed in x-z plane with its reflecting surface facing towards negative y-axis. The mirror ismoving parallel to positive x-axis with a speed of 5 m/s. A point object P is moving in front of the mirror with

a velocity ( ) ( ) ( )ˆ ˆ ˆ3m / s i 4m / s j 5m / s k+ + , then

Column-I Column-II

(A) Velocity of image (p) ( ) ( ) ( )ˆ ˆ ˆ2m / s i 4m / s j 5m / s k- + +

(B) Velocity of image w.r.t. mirror (q) ( ) ˆ8m / s j-

(C) Velocity of image w.r.t. object (r) ( ) ( ) ( )ˆ ˆ ˆ3m / s i 4m / s j 5m / s k+ - +

(D) Velocity of object w.r.t. mirror (s) ( ) ( ) ( )ˆ ˆ ˆ2m / s i 4m / s j 5m / s k- + - +72. A concave mirror forms image ‘I’ of an object ‘O’ as shown in figure. At the given position of object it starts

moving along one of the paths which causes motion of its image also. Match the line of motion of imagewith the direction of motion of object.

PQRS I

B

C A

D

O

Column I Column II(direction of motion of object) (Line of motion of image)(A) Along A (p) on line P(B) Along B (q) on line Q(C) Along C (r) on line R(D) Along D (s) on line S

73. For a concave mirror of focal length 20 cm, match the following. (Consider the case of real object only)Column I Column II(Object distance) (Nature of image)

(A) 10 cm (p) Magnified, inverted & real(B) 30 cm (q) Equal size, inverted & real(C) 40 cm (r) Smaller, inverted & real(D) 50 cm (s) Magnified, erect & virtual

74. A white light ray is incident on a glass prism, and it creates four refracted rays A,B,C and D. Match therefracted rays with the colours given (1 & D are rays due to total internal reflection)

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Column – I (Ray) Column – II ( Colour)(A) A (p) Red

(B) B (q) green(C) C (r) yellow(D) D (s) blue

75. There is a equi biconvex lens, made of refractive index 3/2 and radius of curvature 60 cm.Column – I Column – II

(A) Its focal length is (p) Infinite(B) When placed in a liquid of m = 5/2, (q) less than 60 cm

its focal length is(C) When placed in a liquid of m = 5/4, (r) more than 60 cm

its focal length is(D) When placed in a liquid of m = 3/2, (s) 60 cm

its focal length is76. A convex lens forms an image of an object on a screen. The height of the image is 9 cm. The lens is now

displaced until an image is again obtained on the screen. The height of the image is 4 cm. The distancebetween object and screen is 90 cm.

Column – I Column – II(A) The distance of object from lens for 1st position (p) 6 cm(B) Height of the object (q) 36 cm(C) Focal length of the lens is (r) 21.6 cm(D) Product of magnifications in the two cases (s) Unity.

77. Consider the following diagram representing magnification against image distance for a real object for aconvex lens:

q

m

v

Column – I Column – II

(A) Focal length of the lens (p) Inverse of slope of line.(B) Intercept on V-axis (q) Unity(C) Magnitude of intercept on m-axis (r) Focal length(D) Slope of the line (s) Inverse of the focal length.

78. Column – I(Arrangement) Column – II(Number of images formed)

(A) 120°

OObject (p) 1

(B)

m1

m3

object m2

(q) 2

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86

(C) m1

object m2

(r) 3

(D)

object

(s) 4

79. Regarding power of an optical instrument, match the following table.Column (I) Column (II)

(A) Convex mirror (p) Positive(B) Diverging lens (q) Negative(C) Concave mirror (r) Infinite(D) Plane glass plate (s) Zero

80. Column – I Column – II(A) Converging system (p) convex lens(B) Diverging system (q) concave lens(C) Virtual Image is formed by (r) concave mirror(D) Magnification < 1 is possible with (s) convex mirror

81. In Column I are shown four diagrams of real object point O, image point I and principal axis(optical axis).Select the proper optical system from Column II which can produce the required image. (Image may bereal or virtual)

Column I Column II

(A) (p) Diverging lens

(B) (q) Converging lens

(C) (r) Concave mirror

(D) (s) Convex mirror

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EXERCISE 7CBSE FLASH BACK

1. Why convex mirror is used as a rear view mirror in vehicles ?

orIf you are driving a car, what type of mirror would you prefer to use for observing traffic at your back ?

2. Is it possible to find the nature of mirror (plane or concave or convex) just with the help of the nature of theimage of an object ?

orHow can you conclude about the nature of mirror without touching it ?

3. What happens to the image if aperture of a spherical mirror is large ?

4. Define the refraction index of glass in terms of velocity of light.

5. What is the speed of light in glass having refractive index 1.5.

6. Calculate speed of light in a medium, where critical angle is 45º.

7. An object is placed at the focus of a concave lens. Where will its image be formed?

8. A concave mirror and a convex lens are held in water. What changes, if any, do you expect in theirrespective focal lengths as compared to their values in air.

9. Two thin lenses of powers +7D and –3D are in contact. What is the focal length of the combination ?

10. A thin prism of angle 60º gives a deviation of 30º. What is the refractive index of the material of the prism.

11. State the condition for total internal reflection. Calculate the speed of light in medium where critical angle is45º.

12. A ray of light when moves from denser to rarer medium undergoes total internal reflection. Derive theexpression for critical angle in terms of speed of light in the respective media.

13. Write thin lens formula for a convex lens and draw the graph showing the variation of u and v for a convexlens.

14. Violet light is incident on a thin convex lens. If this light is replaced by red light, explain with reason, howthe power of this lens would change?

15. The image of a candle is formed by a convex lens on a screen. The lower half of the lens is painted blackto make it completely opaque. Draw the ray diagram to show the image formation. How will this image bedifferent from the one obtained when the lens is not painted black?

16. Derive the expression :

Ruv1212 m-m

=m

-m

When refraction occurs from rarer to denser medium at convex spherical refracting surface (m1 < m2).

17. Derive expression for lens maker's formula

( ) ÷÷ø

öççè

æ--m=

21 R1

R11

f1

where the letters have their usual meanings.

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88

18. Draw a ray diagram of real image of the same size as that of the object placed in front of a converging lens.Using this ray diagram establish the relation between u, v and f in this lens.

19. Derive the formula for the focal length of a combination of two thin lenses placed in contact.

20. Describe a compound microscope and find an expression for its magnifying power.

21. Describe an astronomical telescope and find and expression for its magnifying power.

22. Draw a labelled ray diagram for a reflecting type telescope. Write four advantages of a reflecting typetelescope over a refracting type telescope.

23. Draw a graph to show the angle of deviation d with variation of the angle of incidence i for a monochromatic

ray of light passing through a prism of refracting angle A. Deduce the relation

mAsin2Asin2

+ dæ öç ÷è øm =

24. Explain, how two thin prisms can be combined to produce dispersion without deviation of the mean light.Obtain a formula for the resultant dispersion.

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EXERCISE 8AIEEE FLASH BACK

1. A candle placed 25 cm from a lens, forms an image on a screen placed 75 cm on the other end of the lens.The focal length and type of the lens should be: [AIEEE 2003](A) + 18.75 cm and convex lens (B) – 18.75 cm and concave lens(C) + 20.25 cm and convex lens (D) – 20.25 cm and concave lens

2. A light ray is incident perpendicular to one face of a 90º prism and is totally internally reflected at the glass-air interface. If the angle of reflection is 45º, we conclude that the refractive index n is: [AIEEE 2004]

45º

45º

(A) n < 21

(B) n > 2 (C) n > 21

(D) n < 2

3. A plano-convex lens of refractive index 1.5 and radius of curvature 30 cm is silvered at the curved surface.Now this lens has been used to form the image of an object. At what distance from this lens an object beplaced in order to have a real image of the size of the object? [AIEEE 2004](A) 20 cm (B) 30 cm (C) 60 cm (D) 80 cm

4. A fish looking up through the water sees the outside world contained in a circular horizon. If the refractiveindex of water is 4/3 and the fish is 12 cm below the surface, the radius of this circle in cm is:

[AIEEE 2005]

q

q

R

12 cm

(A) 36 5 (B) 4 5 (C) 36 7 (D) 36/ 7

5. A thin glass (refractive index 1.5) lens has optical power of – 5D in air. Its optical power in a liquid mediumwith refractive index 1.6 will be: [AIEEE 2005](A) 25 D (B) – 25 D (C) 0.625 D (D) – 1 D

6. The refractive index of glass is 1.520 for red light and 1.525 for blue light. Let D1 and D2 be the angles ofminimum deviation for red light and blue light respectively in a prism of this glass. Then:[AIEEE 2006](A) D1 > D2 (B) D1 < D2 (C) D1 = D2

(D) D1 can be less than or greater than depending upon the angle of prism7. Two lenses of power – 15 D and + 5 D are in contact with each other. The focal length of the combination

is: [AIEEE 2007](A) + 10 cm (B) – 20 cm (C) – 10 cm (D) + 20 cm

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90

8. A student measures the focal length of convex lens by putting an object pin at a distance 'u' from thelens and measuring the distance 'v' of the image pin. The graph between 'u' and 'v' plotted by thestudent should-look like. [AIEEE-2008]

(A)

u (cm)o

v (cm)

(B)

u (cm)o

v (cm)

(C)

u (cm)o

v (cm)

(D)

u (cm)o

v (cm)

9. In an opitcs experiment, with the position of the object fixed, a student varies the position of a convexlens and for each position, the screen is adjusted to get a clear image of the object. A graph betweenthe object distance u and the image distance v, from the lens, is plotted using the same scale for thetwo axes. A straight line passing through the origin and making an angle of 45º with the x-axis meetsthe experimental curve at P. The corrdinates of P will be [AIEEE-2009]

(A) (4f, 4f) (B) (2f, 2f) (C) f f,2 2

æ öç ÷è ø

(D) (f, f)

10. A car is fitted with a convex side-view mirror of focal length 20cm . A second car 2.8m behind the firstcar is overtaking the first car at a relative speed of 15m/s. The speed of the image of the second caras seen in the mirror of the first one is [AIEEE-2011]

(A) 1 m / s

10 (B) 1 m / s

15 (C) 10m/s (D) 15m/s

11. Let the x-z plane be the boundary between two transparent media. Medium 1 in z 0³ has refractive

index of 2 and medium 2 with z < 0 has a refractive in index of 3 . A ray of light in medium 1 given

by the vector ˆ ˆ ˆA 6 3i 8 3j 10k= + -r

in incident on the plane of separation. The angle of refractionin medium 2 is [AIEEE-2011](A) 30º (B) 45º (C) 60º (D) 75º

12. An object 2.4 m in front of a lens forms a sharp image on a film 12 cm behind the lens. A glass plate1 cm thick, of refractive index 1.50 is interposed between lens and film with its plane faces parallel to film.At what distance (from lens) should object be shifted to be in sharp focus on film? [AIEEE-2012](A) 3.2 m (B) 5.6 m (C) 7.2 m (D) 2.4 m

13. The graph between angle of deviation ( )d and angle of incidence (i) for a triangular prism is represented

by : [JEE-Main-2013]

(A)

O i

d(B)

O i

d

(C)

O i

d

(D)

O i

d

14. Diameter of a plano - convex lens is 6 cm and thickness at the centre is 3 mm. If speed of light in materialof lens is 2×108 m/s, the focal length of the lens is : [JEE-Main-2013](A) 15 cm (B) 20 cm (C) 30 cm (D) 10 cm

PHYSICS

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So

EXERCISE 9IIT-JEE OBJECTIVE FLASH BACK

OBJECTIVE PROBLEMS (only one option is correct)

1. When a ray of light enters a glass slab from air : [1980, 1M](A) its wavelength decreases(B) its wavelength increases(C) its frequency increases(D) neither its wavelength nor its frequency changes

2. A glass prism of refractive index 1.5 is immersed in water (refractive index 4/3). A light beamincident normally on the face AB is totally reflected to reach the face BC if : [1981, 3M]

(A) sinq > 8/9 (B) 2/3 < sinq < 8/9(C) sinq < 2/3 (D) none of these

3. A convex lens of focal length 40 cm is in contact with a concave lens of focal length 25 cm. The power of thecombination is : [1982, 3M](A) –1.5 D (B) –6.5 D (C) +6.5 D (D) +6.67 D

4. A ray of light from a denser medium strikes a rarer medium at an angle of incidence i (seefigure). The reflected and refracted rays make an angle of 90° with each other. The anglesof reflection and refraction are r and r’. The critical angle is : [1983, 1M]

(A) sin–1(tan r) (B) sin–1(cot i) (C) sin–1(tan r¢) (D) tan–1(sin i)

5. A short linear object of length b lies along the axis of a concave mirror of focal length f at a distance u fromthe pole of the mirror. The size of the image is approximately equal to : [1988, 2M]

(A) 2/1

ffub ÷

øö

çèæ -

(B) 2/1

fufb ÷

øö

çèæ

-(C) ÷

øö

çèæ -

ffub (D)

2

fufb ÷

øö

çèæ

-

6. A beam of light consisting of red, green and blue colours is incident on a right-angled prism. The refractive indices of the material of the prism for the above red,green and blue wavelengths are 1.39, 1.44 and 1.47 respectively. The prism will :

(A) separate the red colour from the green and blue colours(B) separate the blue colour from the red and green colours(C) separate all the three colours from one another(D) not separate even partially any colour from the other two colours. [1989, 2M]

7. A thin prism P1 with angle 4° and made from glass of refractive index 1.54 is combined with another thinprism P2 made from glass of refractive index 1.72 to produce dispersion without deviation. The angle of theprism P2 is : [1990, 2M](A) 5.33° (B) 4° (C) 3° (D) 2.6°

8. Two thin convex lenses of focal lengths f1 and f2 are separatedby a horizontal distance d (where d < f1, d < f2) and their centresare displaced by a vertical separation D as shown in the figure .Taking the origin of coordinates, O, at the centre of the first lens,the x and y-coordinates of the focal point of this lens system, fora parallel beam of rays coming from the left, are given by :

PHYSICS

92

(A) D=+

= y,ff

ffx21

21(B)

2121

21

ffy,

dff)df(fx

+D

=-+

+=

(C) dff)df(y,

dff)df(dffx

21

1

21

121

-+-D

=-+

-+= (D) 0y,

dff)df(dffx

21

121 =-+

-+= [1993, 2M]

9. An isosceles prism of angle 120° has a refractive index 1.44. Two parallel rays ofmonochromatic light enter the prism parallel to each other in air as shown. The raysemerge from the opposite face

(A) are parallel to each other(B) are diverging(C) make an angle 2 [sin–1(0.72) – 30°] with each other(D) make an angle 2 sin–1(0.72) with each other [1995, 2M]

10. A diminished image of an object is to be obtained on a screen 1 m from it. This can be achieved byappropriate placing : [1995, 2M](A) a concave mirror of suitable focal length (B) a convex mirror of suitable focal length(C) a convex lens of focal length less than 0.25 m (D) a convex lens of suitable focal length

11. A real image of a distant object is formed by a planoconvex lens on its principal axis. Sphericalaberration : [1998, 2M](A) is absent(B) is smaller if the curved surface of the lens faces the object(C) is smaller if the plane surface of the lens faces the object(D) is the same whichever side of the lens faces the object

12. A concave mirror is placed on a horizontal table with its axis directed vertically upwards. Let O be the poleof the mirror and C its centre of curvature. A point object is placed at C. It has a real image, also located atC. If the mirror is now filled with water, the image will be : [1998, 2M](A) real and will remain at C (B) real and located at a point between C and ¥(C) virtual and located at a point between C and O(D) real and located at a point between C and O

13. A spherical surface of radius of curvature R, separates air (refractive index 1.0) from glass (refractive index1.5). The centre of curvature is in the glass. A point object P placed in air is found to have a real image Qin the glass. The line PQ cuts the surface at a point O and PO = OQ. The distance PO is equal to :

[1998, 2M](A) 5R (B) 3R (C) 2R (D) 1.5R

14. A concave lens of glass, refractive index 1.5 has both surfaces of same radius of curvature R. On immersionin a medium of refractive index 1.75, it will behave as a : [1999, 2M](A) convergent lens of focal length 3.5 R (B) convergent lens of focal length 3 R(C) divergent lens of focal length 3.5 R (D) divergent lens of focal length 3 R

15. In a compound microscope, the intermediate image is : [2000, 2M](A) virtual, erect and magnified (B) real, erect and magnified(C) real, inverted and magnified (D) virtual, erect and reduced

16. A hollow double concave lens is made of very thin transparent material. It can be filled with air or either oftwo liquids L1 or L2 having refracting indices n1 and n2 respectively (n2 > n1 > 1). The lens will diverge aparallel beam of light if it is filled with : [2000, 2M](A) air and placed in air (B) air and immersed in L1(C) L1 and immersed in L2 (D) L2 and immersed in L1

17. A diverging beam of light from a point source S having divergence angle a fallssymmetrically on a glass slab as shown. The angles of incidence of the twoextreme rays are equal. If the thickness of the glass slab is t and its refractiveindex is n, then the divergence angle of the emergent beam is :

[2000, 2M]

(A) zero (B) a (C) sin–1(1/n) (D) 2sin–1(1/n)

PHYSICS

93

18. A point source of light B, placed at a distance L in front of the centre of a plane mirrorof width d, hangs vertically on a wall. A man walks in front of the mirror along a lineparallel to the mirror at a distance 2L from it as shown. The greatest distance overwhich he can see the image of the light source in the mirror is

(A) d/2 (B) d(C) 2d (D) 3d [2000, 2M]

19. A rectangular glass slab ABCD of refractive index n1 is immersed in water ofrefractive index n2 (n1 > n2). A ray of light is incident at the surface AB of theslab as shown. The maximum value of the angle of incidence amax, such thatthe ray comes out only from the surface CD, is given by :

(A) úû

ùêë

é÷÷ø

öççè

æ --

1

21

2

11

nnsincos

nnsin (B) ú

û

ùêë

é÷÷ø

öççè

æ --

2

11

1

n1sincosnsin

(C) ÷÷ø

öççè

æ-

2

11

nnsin (D) ÷÷

ø

öççè

æ-

1

21

nnsin [2000, 2M]

20. A ray of light passes through four transparent media with refractive indices m1, m2,m3 and m4 as shown in the figure. The surfaces of all media are parallel. If theemergent ray CD is parallel to the incident ray AB, we must have : [2001, 2M]

(A) m1 = m2 (B) m2 = m3 (C) m3 = m4 (D) m4 = m1

21. A given ray of light suffers minimum deviation in an equilateral prism P. Additionalprism Q and R of identical shape and of the same material as P are now added asshown in the figure. The ray will suffer : [2001, 2M]

(A) greater deviation (B) no deviation(C) same deviation as before (D) total internal reflection

22. An observer can see through a pin-hole the top end of a thin rod of height h,placed as shown in the figure. The beaker height is 3h and its radius h. Whenthe beaker is filled with a liquid up to a height 2h, he can see the lower end of therod. Then the refractive index of the liquid is : [2002, 2M]

(A) 25

(B) 25

(C) 23

(D) 23

23. Which one of the following spherical lenses does not exhibit dispersion? The radii of curvature of thesurfaces of the lenses are as given in the diagrams : [2002, 2M]

(A) (B) (C) (D)

24. Two plane mirrors A and B are aligned parallel to each other, as shown inthe figure. A light ray is incident at an angle 30° at a point just inside oneend of A. The plane of incidence coincides with the plane of the figure. Themaximum number of times the ray undergoes reflections (including thefirst one) before it emerges out is : [2002, 2M]

(A) 28 (B) 30 (C) 32 (D) 34

PHYSICS

94

25. The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and the image at adistance of 26 cm from the convex lens, calculate the new size of the image :(A) 1.25 cm (B) 2.5 cm (C) 1.05 cm (D) 2 cm [2003, 2M]

26. A ray of light is incident at the glass-water interface at an angle i, it emergesfinally parallel to the surface of water, then the value of mg would be :

(A) (4/3) sin i (B) 1/sin i(C) 4/3 (D) 1 [2003, 2M ]

27. White light is incident on the interface of glass and air as shown in the figure. Ifgreen light is just totally internally reflected, then the emerging ray in air contains

[2004, 2M]

(A) yellow, orange, red (B) violet, indigo, blue(C) all colours (D) all colours except green

28. A ray of light is incident on an equilateral glass prism placed on a horizontal table.For minimum deviation, which of the following is true? [2004, 2M]

(A) PQ is horizontal (B) QR is horizontal(C) RS is horizontal (D) Either PQ or RS is horizontal

29. A point object is placed at the centre of a glass sphere of radius 6 cm and refractive index 1.5. The distanceof the virtual image from the surface of the sphere is : [2004, 2M](A) 2 cm (B) 4 cm (C) 6 cm (D) 12 cm

30. A container is filled with water (m = 1.33) upto a height of 33.25 cm. A concavemirror is placed 15 cm above the water level and the image of an object placed atthe bottom is formed 25 cm below the water level. The focal length of the mirroris : [2004, 2M]

(A) 10 cm (B) 15 cm(C) 20 cm (D) 25 cm

31. A convex lens is in contact with concave lens. The magnitude of the ratio of their focal length is 2/3. Theirequivalent focal length is 30 cm. What are their individual focal lengths? [2005, 2M](A) –75, 50 (B) –10, 15 (C) 75, 50 (D) –15, 10

32. Focal length of the plano-convex lens is 15 cm. The object is at A as shown in thefigure. The plane side is silvered. The image is [2006, 3M]

A 20 cm (A) 60 cm to the left of lens (B) 12 cm to the left of lens(C) 60 cm to the right of lens (D) 30 cm to the left of lens

33. Light from Sun falls on a biconvex lens of focal length f and the circular image of radius r is formed on thefocal plane of the lens. Then which of the following statement is correct? [2006, 3M](A) Area of image is pr2 and area is directly proportional to f

(B) Area of image is pr2 and area is directly proportional to f2

(C) Intensity of image increases if f is increased.(D) If lower half of the lens is covered with black paper, area will become half.

34. In an experiment to determine the focal length (f) of a concave mirror by the u-v method, a student placesthe object pin A on the principal axis at a distance x from the pole P. The student looks at the pin and itsinverted image from a distance keeping his/her eye in line with PA. When the student shifts his/her eyetowards left, the image appears to the right of the object pin. Then, [2007, 3M](A) x < f (B) f < x < 2f (C) x = 2f (D) x > 2f

PHYSICS

95

35. A ray of light travelling in water is incident on its surface open to air. The angle of incidence is q, which isless than the critical angle. Then there will be [2007, 3M](A) only a reflected ray and no refracted ray(B) only a refracted ray and no reflected ray(C) a reflected ray & a refracted ray and the Ð between them would be less than 180º – 2q(D) a reflected ray & a refracted ray and the Ð between them would be greater than 180º – 2q

36. Two beams of red and violet colours are made to pass separately through a prism (angle of the prismis 60º). In the position of minimum deviation, the angle of refraction will be [2008, IIT](A) 30º for both the colours (B) greater for the violet colour(C) greater for the red colour (D) equal but not 30º for both the colours

37. A light beam is traveling from Region I to Region IV (Refer figure). The refractive index in Regions I, II,

III and IV are n0, 0 0n n

,2 6 and 0n

8 , respectively. The angle of incidence q for which the beam just

misses entering Region IV is [2008, IIT]Figure

qn0

Region I Region II Region III Region IV

n2

0 n6

0 n8

0

0 0.2m 0.6m

(A) 1 3sin

4- æ ö

ç ÷è ø

(B) 1 1sin

8- æ ö

ç ÷è ø

(C) 1 1sin

4- æ ö

ç ÷è ø

(D) 1 1sin

3- æ ö

ç ÷è ø

Multiple Correct Answer Type

38. A converging lens is used to form an image on a screen. When the upper half of the lens is covered by anopaque screen : [1986, 2M](A) half of the image will disappear (B) complete image will be formed(C) intensity of the image will increase (D) intensity of the image will decrease

39. A planet is observed by an astronomical refracting telescope having an objective of focal length 16 m andan eye piece of focal length 2 cm : [1992, 2M](A) the distance between the objective and the eye piece is 16.02 m(B) the angular magnification of the planet is –800(C) the image of the plane is inverted(D) the objective is larger than the eye piece

40. Which of the following form(s) a virtual and erect image for all positions of the object? [1996, 2M](A) Convex lens (B) Concave lens (C) Convex mirror (D) Concave mirror

41. A ray of light travelling in a transparent medium falls on a surface separating the medium from air at anangle of incident 45°. The ray undergoes total internal reflection. If n is the refractive index of the mediumwith respect to air, select the possible value (s) of n from the following : [1998, 2M](A) 1.3 (B) 1.4 (C) 1.5 (D) 1.6

REASONING TYPE42. STATEMENT - 1

The formula connecting u, v and f for a spherical mirror is valid only for mirrors whose sizes are very smallcompared to their radii of curvature. [2007, 3M]becauseSTATEMENT - 2Laws of reflection are strictly valid for plane surface, but not for large spherical surfaces.(A) Statement- 1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement -1(B) Statement -1 is True, Statement -2 is True ; Statement -2 is NOT a correct explanation for Statement - 1(C) Statement - 1 is True, Statement- 2 is False(D) Statement -1 is False, Statement -2 is True

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96

FILL IN THE BLANKS

43. A light wave of frequency 5 × 1014 Hz enters a medium of refractive index 1.5. In the medium the velocity ofthe light wave is .................. and its wavelength is .................... [1983, 2M]

44. A convex lens A of focal length 20 cm and a concave lens B of focal length 5 cm are kept along the sameaxis with a distance d between them. If a parallel beam of light falling on A leaves B are parallel beam, thend is equal to ......... cm. [1985, 2M]

45. A monochromatic beam of light of wavelength 6000Å in vacuum enters a medium of refractive index 1.5. Inthe medium its wavelength is ............., its frequency is ................. [1985, 2M]

46. A thin lens of refractive index 1.5 has a focal length of 15 cm in air. When the lens is placed in a medium ofrefractive index 4/3, its focal length will become ............. cm. [1987, 2M]

47. A slab of material of refractive index 2 shown in figure has a curved surfaceAPB of radius of curvature 10 cm and a plane surface CD. On the left of APBis air and on the right of CD is water with refractive indices as given in thefigure. An object O is placed at a distance of 15 cm from the pole P as shown.The distance of the final image of O from P, as viewed from the left is...................... [1991, 2M]

48. A thin rod of length f/3 is placed along the optic axis of a concave mirror of focal length f such that its imagewhich is real and elongated, just touches the rod. The magnification is ........... [1991, 1M]

49. A ray of light undergoes deviation of 30° when incident on an equilateral prism of refractive index .2 Theangle made by the ray inside the prism with the base of the prism is ................ [1992, 1M]

50. The resolving power of electron microscope is higher that of an optical microscope because the wavelengthof electrons is .............. than the wavelength of visible light. [1992, 1M]

51. If e0 and m0 are, respectively, the electric permittivity and magnetic permeability of free space, e and m thecorresponding quantities in a medium, the index of refraction of the medium in terms of the above parametersis .......................... [1992, 1M]

52. A light of wavelength 6000Å in air, enters a medium with refractive index 1.5. Inside the medium its frequencyis ................. Hz and its wavelength is .................Å. [1997, 2M]

53. Two thin lenses, when in contact, produce a combination of power +10 diopters. When they are 0.25 mapart, the power reduces to +6 diopters. The focal length of the lenses are .........m and ..............m.

[1997, 2M]

54. A ray of light is incident normally on one of the faces of a prism of apex angle 30° and refractive index .2The angle of deviation of the ray is ........................ degrees. [1997, 2M]

TRUE/FALSE

55. The intensity of light at a distance r from the axis of a long cylindrical source is inversely proportional to r.[1981, 2M]

56. A convex lens of focal length 1 m and a concave lens of focal length 0.25 m are kept 0.75 m apart. A parallelbeam of light first passes through the convex lens, then through the concave lens and comes to a focus 0.5m away from the concave lens. [1983, 2M]

57. A beam of white light passing through a hollow prism given no spectrum. [1993, 2M]58. A parallel beam of white light falls on a combination of a concave and a convex lens, both of the same

material. Their focal lengths are 15 cm and 30 cm respectively for the mean wavelength in white light. Onthe same side of the lens system, one sees coloured patterns with violet colour nearer to the lens.

[1988, 2M]MATRIX MATCH TYPE59. Column 1 Column 2 [2006, 6M]

(a) Angular magnification (P) Dispersion of lenses(b) Sharpness of the image (Q) f0 and fe

(c) Light gathering power (R) Aperture of lenses(d) Length of telescope (S) Spherical aberration

PHYSICS

97

60. An optical component and an object S placed along its optic axis are given in Column I . Thedistance between the object and the component can be varied. The properties of images are given inColumn II. Match all the properties of images from Column II with the appropriate componentsgiven in Column I. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrixgiven in the ORS. [2008, IIT]Column I Column II

(A) S

(p) Real image

(B)

S(q) Virtual image

(C) S

(r) Magnified image

(D) S

(s) Image at infinity

61. Two transparent media of refractive indices m1 and m3 have a solid lens shaped transparent material ofrefractive index m2 between them as shown in figure in column-II. A ray traversing these media is alsoshown in the figure. In column-I different relationships between m1, m2 and m3 are given. Match them to theydiagrams shown in column-II.

Column-I Column-II

(A) m1 < m2 (p) m3 m2 m1

(B) m1 > m2 (q) m2m3 m1

(C) m2 = m3 (r) m2m3 m1

(D) m2 > m3 (s) m2m3 m1

(t) m2m3 m1

PHYSICS

98

62. The focal length of a thin biconvex lens is 20cm. When an object is moved from a distance of 25cm in front

of it to 50cm, the magnitficaiton of its image charges from m25 to m50. The ratio 25

50

mm is [2010]

63. A biconvex lens of focal length 15cm is in front of a plane mirror. The distance between the lens and themirror is 10cm. A small object is kept at a distance of 30cm from the lens. The final image is(A) virtual and at a distance of 16cm from the mirror [2010](B) real and at a distance of 16cm from the mirror(C) virtual and at a distance of 20cm from the mirror(D) real and at a distance of 20cm from the mirror

64. A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident

angle of 60º (see figure) If the refractive index of the material of the prism is 3 , which of the followingis (are) correct ? [2010]

60º

90º 75º

135ºC

B

DA

P

O(A) the ray gets totally internally reflected at face CD(B) the ray comes out through face AD(C) the angle between the incident ray and the emergent ray is 90º(D) the angle between the incident ray and the emergent ray is 120º

65. A light ray traveling in glass medium is incident on glass-air interface at an angle of incidence q. Thereflected (R) and transmitted (T) intensities, both as function of q, are plotted. The correct sketch is[2011]

(A)

90ºq0

100º

inte

nsity T

R (B)

90ºq0

100º

inte

nsity T

R (C)

90ºq0

100º

inte

nsity T

R (D)

90ºq0

100º

inte

nsity T

R

66. A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractiveindex n of the first lens is 1.5 and that of the second lens is 1.2. Both the curved surfaces areof the same radius of curvature R = 14cm. For this bi-convex lens, for an object distance of 40cm,the image distance will be [2012]

n=1.2n=1.5

R=14cm(A) –280.0cm (B) 40.0cm (C) 21.5cm (D) 13.3cm

67. A ray of light travelling in the direction ( )1 ˆ ˆi 3j2

+ is incident on a plane mirror. After reflection, it travels

along the direction ( )1 ˆ ˆi 3j2

- . The angle of incidence is [JEE-Advanced-2013]

(A) 30° (B) 45° (C) 60° (D) 75°

68. The image of an object, formed by a plano-convex lens at a distance of 8m behind the lens, is real and is

one-third the size of the object. The wavelength of light inside the lens is 23 times the wavelength in free

space. The radius of the curved surface of the lens is [JEE-Advanced-2013](A) 1 m (B) 2 m (C) 3 m (D) 6 m

PHYSICS

99

69. A right angles prism of refractive index m1 is placed in a rectangular block of refractive index m2, which issurrounded by a medium of refractive index m3, as shown in the figure. A ray of light 'e' enters therectangular block at normal incidence. Depending upon the relationships between m1, m2 and m3 it takesone of the four possible paths 'ef', 'eg' 'eh' or 'ei'. [JEE-Advanced-2013]

Match the paths in List I with conditions of refractive indices in List II and select the corret answer using thecodes given below the lists :

List I List II

P. e ® f 1. 1 22m > mQ. e ® g 2. m2 > m1 and m2 > m3

R. e ® h 3. m1 = m2

S. e ® i 4. 2 1 22m < m < m and m2 > m3

Codes :P Q R S

(A) 2 3 1 4(B) 1 2 4 3(C) 4 1 2 3(D) 2 3 4 1

PHYSICS

100

EXERCISE 10(SUBJECTIVE PROBLEMS) IIT-JEE SUBJECTIVE

1. The convex surface of a thin concavo-convex lens of glass of refractive index 1.5 has a radius of curvature20 cm. The concave surface has a radius of curvature 60 cm. The convex side is silvered and placed on ahorizontal surface. [1981, 2M](i) Where should a pin be placed on the optic axis such that its image is formed atthe same place?(ii) If the concave part is filled with water of refractive index 4/3, find the distancethrough which the pin should be moved, so that the image of the pin again coincideswith the pin.

2. A plano-convex lens has a thickness of 4 cm. When placed on a horizontal table, with the curved surfacein contact with it, the apparent depth of the bottom most point of the lens is found to be 3 cm. If the lens isinverted such that the plane face is in contact with the table, the apparent depth of the centre of the planeface is found to be 25/8 cm. Find the focal length of the lens. Assume thickness to be negligible whilefinding its focal length. [1984, 6M]

3. Monochromatic light is incident on a plane interface AB between two media ofrefractive indices n1 and n2 (n2 > n1) at an angle of incidence q as shown in thefigure. The angle q is infinitesimally greater than the critical angle for the twomedia so that total internal reflection takes place. Now if a transparent slab DEFGof uniform thickness and of refractive index n3 is introduced on the interface (asshown in the figure), show that for any value of n3 all light will ultimately be reflectedback again into medium II. Consider separately the cases :(i) n3 < n1 and (ii) n3 > n1. [1986, 6M]

4. A right prism is to be made by selecting a proper material and the angle A and B)AB( £ , as shown in figure. It is desired that a ray of light incident on the face

AB emerges parallel to the incident direction after two internal reflections.[1987, 7M]

(i) What should be the minimum refractive index n for this to be possible?(ii) For n = 5/3 is it possible to achieve this with the angle B equal to 30 degrees?

5. A parallel beam of light travelling in water (refractive index = 4/3) is refracted by a spherical air bubble ofradius 2 mm situated in water. Assuming the light rays to be paraxial. [1988, 6M](i) Find the position of the image due to refraction at the first surface and the position of the final image.(ii) Draw a ray diagram showing the positions of both the images.

6. Two parallel beams of light P and Q (separation d) containing radiationsof wavelengths 4000Å and 5000Å (which are mutually coherent ineach wavelength separately) are incident normally on a prism as shownin figure. The refractive index of the prism as a function of wavelength

is given by the relation, m(l) = 2

b20.1l

+ where l is in Å and b is

positive constant. The value of b is such that the condition for totalreflection at the face AC is just satisfied for one wavelength and is notsatisfied for the other [1991, 2+2+4M]

(a) Find the value of b.(b) Find the deviation of the beams transmitted through the face AC.

PHYSICS

101

7. Light is incident at an angle a on one planar end of transparent cylindrical rod of refractive index n.Determine the least value of n so that the light entering the rod does not emerge from the curved surface ofthe rod irrespective to the value of a. [1992, 8M]

8. An image Y is formed of point object X by a lens whose optic axis is AB as shownin figure. Draw a ray diagram to locate the lens and its focus. If the image Y of theobject X is formed by a concave mirror (having the same optic axis as AB) insteadof lens, draw another ray diagram to locate the mirror and its focus. Write down thesteps of construction of the ray diagrams. [1994, 6M]

9. A ray of light travelling in air is incident at grazing angle (incident angle = 90°)on a long rectangular slab of a transparent medium of thickness t = 1.0 m. Thepoint of incidence is the origin A(0, 0). The medium has a variable index of

refraction n(y) given by 2/12/3 ]1ky[)y(n += where k = 1.0 (meter)–3/2. Therefractive index of air is 1.0. [1995, 10M]

The refractive index of air is 1.0.(a) Obtain a relation between the slope of the trajectory of the ray at a point B(x, y) in the medium and theincident angle at the point.(b) Obtain an equation for the trajectory y(x) of the ray in the medium.(c) Determine the co-ordinates (x1, y1) of the point P, where the ray intersects the upper surface of the slab-air boundary.(d) Indicate the path of the ray subsequently.

10. A right angle prism (45°-90°-45°) of refractive index n has a plane of refractiveindex n1(n1 < n) cemented to its diagonal face. The assembly is in air. The ray isincident on AB. [1996, 3M]

(i) Calculate the angle of incidence at AB for which the ray strikes the diagonalface at the critical angle.(ii) Assuming n = 1.352, calculate the angle of incidence at AB for which therefracted ray passes through the diagonal face undeviated.

11. A thin plano-convex lens of focal length f is split into two halves. One of the halves isshifted along the optical axis. The separation between object and image planes is1.8m. The magnification of the image formed by one of the half lens is 2. Find thefocal length of the lens and separation between the halves. Draw the ray diagram forimage formation. [1996, 5M]

12. A thin equiconvex lens of glass of refractive index m = 3/2 and of focal length 0.3m in air is sealed into an opening at one end of a tank filled with water m = 4/3. Onthe opposite side of the lens, a mirror is placed inside the tank on the tank wallperpendicular to the lens axis, as shown in figure. The separation between thelens and the mirror is 0.8 m. A small object is placed outside the tank in front ofthe lens at a distance of 0.9 m from the lens along its axis. Find the position(relative to the lens) of the image of the object formed by the system. [1997C, 5M]

13. A prism of refractive index n1 and another prism of refractive index n2 are stucktogether with a gap as shown in the figure. The angles of the prism are asshown. n1 and n2 depend on l, the wavelength of light according to :

2

4

1108.1020.1n

l´

+= ,

PHYSICS

102

n2 = 145 + 4

21.80 10´

l and where l is in nm

(a) Calculate the wavelength l0 for which rays incident at any angle on theinterface BC pass through without bending at that interface.(b) For light of wavelength l0, find the angle of incidence i on the face AC such that the deviation producedby the combination of prisms is minimum. [1998, 8M]

14. The x-y plane is the boundary between two transparent media. Medium-1 with 0z ³ has a refractive index

2 and medium-2 with 0z £ has a refractive index 3 . A ray of light in medium-1 given by vector

k10j38i36A -+=r

is incident on the plane of separation. Find the unit vector in the direction ofthe separation. Find the unit vector in the direction of the refracted ray in medium-2. [1999, 10M]

15. A quarter cylinder of radius R and refractive index 1.5 is placed on atable. A point object P is kept at a distance of mR from it. Find the valueof m for which a ray from P will emerge parallel to the table as shown infigure. [1999, 5M]

16. A convex lens of focal length 15 cm and a concave mirror of focal length 30 cm are kept with their optic axisPQ and RS parallel but separated in vertical direction by 0.6 cm as shown. The distancebetween the lens and mirror is 30 cm. An upright object AB of height1.2 cm is placed on the optic axis PQ of the lens at a distance of 20cm from the lens. If A¢B¢ is the image after refraction from the lensand the reflection from the mirror, find the distance of A¢B¢ from thepole of the mirror and obtain its magnification. Also locate positions ofA¢ and B¢ with respect to the optic axis RS. [2000, 6M]

17. The refractive indices of the crown glass for blue and red light are 1.51 and 1.49 respectively and those ofthe flint glass are 1.77 and 1.73 respectively. An isosceles prism of angle 6° is made of crown glass. Abeam of white light is incident at a small angle on this prism. The other flint glass isosceles prism iscombined with the crown glass prism such that there is no deviation of the incident light. [2001, 5M](i) Determine the angle of the flint glass prism.(ii) Calculate the net dispersion of the combined system.

18. A thin biconvex lens of refractive index 3/2 is placed on a horizontal plane mirror as shown in the figure. Thespace between the lens and the mirror is then filled with water of refractive index 4/3. It is foundthat when a point object is placed 15 cm above the lens on its principalaxis, the object coincides with its own image. On repeating with anotherliquid, the object and the image again coincide at a distance 25 cm fromthe lens. Calculate the refractive index of the liquid. [2001, 5M]

19. In the figure, light is incident on the thin lens as shown. The radius of curvaturefor both the surface is R. Determine the focal length of this system.

[2003, 2M]

20. A prism of refracting angle 30° is coated with a thin film of transparent material ofrefractive index 2.2 on face AC of the prism. A light of wavelength 6600Å is incident onface AB such that angle of incidence is 60°. Find the angle of emergence

[2003, 4M]

PHYSICS

103

21. Figure shows an irregular block of material of refractive index 2 . A ray oflight strikes the face AB as shown in the figure. After refraction it is incidenton a spherical surface CD of radius of curvature 0.4 m and enters a mediumof refractive index 1.514 to meet PQ at E. Find the distance OE upto twoplaces of decimal [2004, 2M]

22. An object is approaching a thin convex lens of focal length 0.3 m with a speed of 0.01 m/s. Find themagnitude of the rates of change of position and lateral magnification of image when the object is at adistance of 0.4 m from the lens. [2004, 4M]

23. AB and CD are two slabs. The medium between the slabs has refractiveindex 2. Find the minimum angle of incidence of Q, so that the ray istotally reflected by both the slabs. [2005, 2M]

24. A ray of light is incident on a prism ABC of refractive index 3 as shown infigure.

(a) Find the angle of incidence for which the deviation of light ray by the prismABC is minimum.(b) By what angle the second prism must be rotated, so that the final raysuffer net minimum deviation ? [2005, 4M]

PHYSICS

104

EXERCISE 11INTEGER TYPE QUESTION

1. A concave mirror of focal length 20 cm is cut into two parts from themiddle and the two parts are moved perpendicularly by a distance 1cm from the previous principal axis AB. Find the distance between theimages formed by the two parts? (in cm)

2. A balloon is rising up along the axis of a concave mirror of radius of curvature 20 m. A ball is droppedfrom the balloon at a height 15 m from the mirror when the balloon has velocity 20 m/s. Find the speedof the image of the ball formed by concave mirror after 4 seconds? (answer in multiple of 10) [Take :g=10 m/s2]

3. A ray of light falls on a transparent sphere with centre at C as shown infigure. The ray emerges from the sphere parallel to line AB. Find therefractive index of the sphere is n . Find the value of n.

4. An equilateral prism deviates a ray through 23° for two angles of incidence differing by 23°. If m of the

prism is 43N

. Find the value of N.

5. A thief is running away in a car with velocity of 20 m/s. A police jeep is following him, which is sightedby thief in his rear view mirror which is a convex mirror of focal length 10 m. He observes that theimage of jeep is moving towards him with a velocity of 1 cm/s. If the magnification of the mirror for thejeep at that time is 1/10. Find rate (per second) at which magnification is changing. Assume that policejeep is on axis of the mirror. (answer in multiple of 10–1)

6. A surveyor on one bank of canal observed the image of the 4 inch and 17 ft marks on a vertical staff,which is partially immersed in the water and held against the bank directly opposite to him, coincides.If the 17ft mark and the surveyor’s eye are both 6ft above the water level, estimate the width of thecanal, assuming that the refractive index of the water is 4/3. (in the multiple of 2 feet)

7. A ray of light travelling in air is incident at grazing angle (incidence angle = 90°) on a medium whoserefractive index depends on the depth of the medium. The trajectory of the light in the medium is aparabola, y = 2x2. Find, at a depth of 1 m in the medium, the refractive index of the medium.

PHYSICS

105

8. The refractive indices of the crown glass for violet and red lights are 1.51 and 1.49 respectively andthose of the flint glass are 1.77 and 1.73 respectively. A prism of angle 6° is made of crown glass. Abeam of white light is incident at a small angle on this prism. The other thin flint glass prism is combinedwith the crown glass prism such that the net mean deviation is 1.5° anticlockwise. Determine the angle(in degree) of the flint glass prism.

9. A plane mirror 50 cm long , is hung parallel to a vertical wall of a room, with its lower edge 50 cmabove the ground. A man stands infront of the mirror at a distance 2 m away from the mirror. If his eyesare at a height 1.8 m above the ground, find the length of the floor between him & the mirror, visible tohim reflected from the mirror. (nearest integer value)

10. In figure shown AB is a plane mirror of length 40cm placed at a height 40cm from ground. There is alight source S at a point on the ground. Find the minimum height of a man (eye height) required to seethe image of the source if he is standing at a point A on ground shown in figure. (in the muliple of 20cm)

PHYSICS

106

PP- ANSWER KEYPP-1

1. B 2. B 3. A 4. B 5. C 6. A

7. C 8. B 9. D 10. C

PP-2

1. CD 2. A 3. C 4. D 5. C 6. A

7. C 8. A 9. D 10. B

PP-3

1. C 2. D 3. C 4. A 5. A 6. B

7. B 8. D 9. C 10. D

PP-4

1. A 2. B 3. C 4. B 5. ABC 6. D

7. D 8. A 9. B 10. A

PP-5

1. A 2. C 3. A 4. A 5. A 6. B

7. C 8. A 9. A 10. C

PP-6

1. B 2. A 3. B 4. C 5. B 6. A

7. A 8. A 9. C 10. C

PP-7

1. B 2. A 3. C 4. C 5. D 6. C

7. D 8. A

PHYSICS

107

PP-8

1. A 2. D 3. C 4. A 5. B 6. A

7. B 8. A 9. BC 10. B 11. B 12. C

13. D

PP-9

1. B 2. A 3. C 4. C 5. B 6. C

7. B 8. C 9. B 10. A

PP-10

1. A 2. D 3. A 4. A 5. B 6. C

7. A 8. B 9. D 10. D 11. C

PP-11

1. B 2. C 3. A 4. C 5. B

6. D 7. B

PP-12

1. C 2. AB 3. D 4. C 5. D 6. C

7. B 8. D 9. D 10. C

PP-13

1. A 2. A 3. A 4. D 5. B 6. C

7. B 8. A 9. C 10. C

PP-14

1. A 2. D 3. C 4. C 5. C 6. D

7. B 8. C 9. D 10. C

PHYSICS

108

ANSWER SHEETExercise - 02

1. D 2. B 3. D 4. C 5. D

6. B 7. B 8. D 9. A 10. A

11. A 12. B 13. A 14. C 15. C

16. C 17. C 18. C 19. D 20. B

21. D 22. A 23. B

Exercise - 03

1. 200° ACW, 160° CW 2. 2p/15 m/s

3. 11.5 cm 4. 0.125 M

5. 34 m/s 6. 10.5 cm, 21 cm

7. 61.25 cm 8. 36 cm, 16 cm

9. 95 cms–1 towards left 10. 6.6 cm

11. h = 323

2310-

cm 12. 0.688 cm

13. (a) 2348

cm (b) 34

cm 14. About 3.1 D

15. F = 60, u = 90, v = 180 16. 20 cm, 1 m, 4, 24 cm

17. 9 cm 18. 11 cm19. 55 cm 20. virtual, 6 mm from the surface of the bubble on water side21. 38° = dm = 2 sin–1 (3/4) –60

Exercise - 041. B 2. A 3. C 4. C 5. A

6. A 7. B 8. A 9. B 10. A

11. C 12. B 13. D 14. D 15. C

16. B 17. A 18. D 19. D 20. B

21. C 22. B 23. D 24. C 25. C

26. B 27. B 28. A 29. A 30. A

PHYSICS

109

Exercise - 05

1. (a) ( )[ ]22

RVtd2VR

--(b)

( )[ ] úúû

ù

êêë

é

--- 2

2

RdVt2R1V 2. 100 cm, 21.43 cm

3. R = 0.40 m 4.41aa3 = 5. 30 cm

6. 80 m/s 7. vMm21 ÷

øö

çèæ + 8. 0.625 cm

10. nA = a+ 220 sinn 11.

qqm-

sincos1b 22

12. On the object itself

13. 36 cm from the surface of water 14. 0.1 m, 0.1 ± 0.086 m, 0.3155 m

15. At a distance b from the sphere on the opposite side. 16. ( )2

2

2

Rgt21h1

gtR

úû

ùêë

é-÷

øö

çèæ --m

m

17. 6.25 cm 18. m = 4/3, R = 25 cm. 19. 200 cm, with respect to lens

20. [ ]1n2R

-m+m 21. 130 22. Infinity

23. 20/13 = 1.538 24. 1 cm 25. 826. d = 5.0 m, x co-ordinate of final image = 4.0 m 27. 12 mm

28. m > 2 29. 1.732 31. 7 / 3

32.435

33. 1.95 34. m = 258

Exercise - 061. A,B,C,D 2. B,C 3. B,C 4. A

5. A,C,D 6. B,C 7. A,C 8. A,C

9. A,C,D 10. B,D 11. B,C,D 12. A,C

13. B,C,D 14. A,D 15. B,D 16. B,C,D

17. B,D 18. A,B,D 19. B,C 20. A

21. A, C 22. A 23. B 24. A

25. B 26. A 27. C 28. D

29. A 30. A 31. B 32. C

33. D 34. A 35. A 36. B

37. C 38. D 39. D 40. B

41. A 42. B 43. D 44. A

PHYSICS

110

45. B 46. B 47. A 48. A

49. A 50. D 51. C 52. A

53. A 54. B 55. C 56. D

57. A 58. D 59. B 60. B

61. B 62. B 63. A 64. B

65. A 66. C 67. B

68. A - r,s, B - r, C - r, D - r, s 69. A - q, B - q, C - r, D - s

70. A - s, B - q, C - p, D - q 71. A - r, B - s, C - q, D - p

72. A - s, B - p, C - s, D - p 73. A - s, B - p, C - q, D - r

74. A-p, B-r, c-q, D-s 75. A - s, B - q, C - r, D - p, r

76. A - q, B - p, C - r, D - s 77. A - p, b - r, c - q, d - s

78. A - q, r, B - r, C - p, D - q 79. A - q, B - q, C - p, D - s

80. A - p,q,r; B - p,q,s; C - p,q,r,s; D - p,q,r,s 81. A - p, s, B - q, r, C - q,D - q, r

Exercise - 081. A 2. B 3. A 4. D 5. C6. B 7. C 8. C 9. B 10. B11. B 12. A 13. C 14. C

Exercise - 091. A 2. A 3. A 4. A

5. D 6. A 7. C 8. C

9. C 10. C 11. B 12. D

13. A 14. A 15. C 16. D

17. B 18. D 19. A 20. D

21. C 22. B 23. C 24. B

25. B 26. B 27. A 28. B

29. C 30. C 31. D 32. B

33. B 34. B 35. C 36. A

37. B 38. B, D 39. A, B, C, D 40. B, C

41. C, D 42. C

Fill in the blanks43. 2 × 108 m/s, 4 × 10–7 m 44. 15 45. 4000Å, 5 × 1014 Hz 46. 6047. 30 cm to the right of P. Image will be virtual 48. –1.5 49. zero 50. smaller

PHYSICS

111

51. 00me

em52. 5 / 1014, 4000 53. 0.125, 0.5 54. 15°

True/False

55. T 56. F 57. T 58. T

59. (a)-(Q), (b)-(P, S), (c)-(R), (d)-(Q) 60. A - p, q, r, s B - q C - p, q, r, s D - p, q, r, s

61. A-pr, B-qst, C-prt, D-qs 62. 6 63. B 64. ABC

65. D 66. B 67. A 68. A 69. D

Exercise - 10

1. (i) 15 cm, (ii) 13.84 cm 2. 75 cm 4. (i) 2 , (ii) No 5. (i) – 6 mm, – 5mm

6. (a) b = 8 × 105 (Å)2, (b) d4000Å = 37°, d5000Å = 27.13

7. 2 9. (a) slope = cot i, (b) 4y1/4 = x, (c) (4m, 1m)

10. (i) i1 = sin–1 2 2

1 11 ( n n n2

é ù- -ê úë û (ii) 73º 11. 0.4m, 0.6m

12. 0.9 m from the lens (rightwards) or 0.1 m behind the mirror

13. (a) 600 nm, (b) sin–1(3/4) 14. )k5j4i3(25

1-+ 15. 4/3 16. 15 cm, –3/2

17. (i) 4°, (ii) –0.04° 18.1.6 19. 13

3Rm-m

m 20. (a) zero

21. 6.06 m 22. 0.09 m/s, 0.3 per second 23. 60° 24. (a) 60°, (b) 60°

Exercise - 11Q.1 2 Q.2 8 Q.3 3 Q.4 5Q.5 1 Q.6 8 Q.7 3 Q.8 2Q.9 1 Q.10 8