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Course: Geometrical Optics

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EXERCISE-I Part-I

(Single Correct type Questions)

Section-A

(Plane Mirror)

1. Figure shows a plane mirror on which a light ray is incident. If the incident

light ray is turned by 10º and the mirror by 20º, as shown, find the angle turned by the reflected ray.

(A) 30° clockwise (B) 30° anticlockwise (C) 10° clockwise (D) 10° anticlockwise

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

(A) θ = 45° (B) θ = 30° (C) θ = 60° (D) all three

3. A ray of light is incident on a plane mirror, along the direction given by,ˆ ˆ ˆ−A = 2i 3j+4k. Find the unit vector along the reflected ray. Take normal to

mirror along the direction of ˆ ˆ ˆ−B = 3i 6j+2k.

(A) ˆ ˆ ˆ− −94i 237j+68k

49 29 (B)

ˆ ˆ ˆ− −94i+68j 237k

49 29

(C) ˆ ˆ ˆ−3i+6j 2k

7 (D) None of these


4. An unnumbered wall clock shows time 04: 25: 37, where 1st term represents

hours, 2nd represents minutes and the last term represents seconds. What

time will its image in a plane mirror show.

(A) 08: 35: 23 (B) 07: 35: 23 (C) 07: 34: 23 (D) None

5. An object and a plane mirror are as shown in figure. Mirror is moved with velocity V as shown. The velocity of image is:

(A) 2V sin θ (B) 2V (C) 2V cos θ (D) None

6. A plane mirror is moving with velocity ˆ ˆ ˆ4i+5j+8k . A point object in front of the

mirror moves with a velocity ˆ ˆ ˆ− −3i 4j+5k . Here k̂ is along the normal to the

plane mirror and facing towards the object. The velocity of the image is:

(A) ˆ ˆ ˆ− −3i 4j+5k (B) ˆ ˆ ˆ3i+4j+11k (C) ˆ ˆ ˆ− −3i 4j+11k (D) ˆ ˆ ˆ7i+9j+11k

7. A man is walking under an inclined mirror at a constant velocity V m/s along X axis. If the mirror is inclined at an angle θ with the horizontal then what is

the velocity of the image ?

(A) ˆ ˆVsinθi+Vcosθ j (B) ˆ ˆVcosθi+Vsinθ j

(C) ˆ ˆVsin2θi+Vcos2θ j (D) ˆ ˆVcos2θi+Vsin2θ j

8. A particle is moving in a circle in froth of a plane mirror in situation as shown in figure. It is given that plane of motion of particle is perpendicular to the

plane of mirror. Then the motion of image w.r.t particle is

(A) in a circular path (B) Oscillating (C) in an elliptical path (D) no motion, image seems to be stationary


9. In the diagram shown, all the velocities are given with respect to earth. What is

the relative velocity of the image in mirror (1) with respect to the image in the

mirror (2)? The mirror (1) forms an angle β with the vertical.

(A) 2Vsin2β (B) 2V sin β (C) 2V /sin2 β (D) none

10. Two plane mirrors of length L are separated by distance L and a man M2 is standing at distance L from the connecting line of mirrors as shown in figure.

A man M1 is walking in a straight line at distance 2L parallel to mirrors at speed u, then man M2 at O will be able to see image of M1 for total time:

(A) 4L

u (B)

3L

u (C)

6L

u (D)

9L

u

11. Two plane mirrors are placed parallel to each other at a distance L apart. A point object O is placed between them, at a distance L/3 from one mirror. Both mirrors form multiple images. The distance between any two images cannot be

(A) 3L/2 (B) 2L/3 (C) 2L (D) None

12. A person is standing in a room of width 200 cm. A plane mirror of vertical

length 10 cm is fixed on a wall in front of the person. The person looks into the mirror from distance 50 cm. How much width (height) of the wall behind him

will he be able to see : (assume that he uses the full mirror)

(A) 30 cm (B) 40 cm (C) 50 cm (D) None


13. A boy of height 1.5 m with his eye level at 1.4 m stands before a plane mirror

of length 0.75 m fixed on the wall. The height of the lower edge of the mirror

above the floor is 0.8 m. then:

(A) the boy will see his full image (B) the boy cannot see his hair

(C) the boy cannot see his feet (D) the boy cannot see neither his hair nor his feet.

14. When a plane mirror AB is placed horizontally on level ground at a distance of 60 metres from the foot of a tower, the top of the tower and its image in the

mirror subtends, an angle of 90° at B. The height of the tower is :

(A) 30 metre (B) 60 metre (C) 90 metre (D) 120 metre

Section-B

(Spherical Mirror)

15. The circular boundary of the concave mirror subtends a cone of half angle θ at its centre of curvature. The minimum value of θ for which ray incident on this mirror parallel to the principle axis suffers reflection more than one is

(A) 30° (B) 45° (C) 60° (D) 75°


16. A ray of light is incident on a concave mirror. It is parallel to the principal axis

and its height from principal axis is equal to the focal length of the mirror. The

ratio of the distance of point B to the distance of the focus from the centre of curvature is (AB is the reflected by)

(A) 2

3 (B)

3

2 (C)

2

3 (D)

1

2

17. A convex mirror has a focal length = 20 cm. A convergent beam tending to converge to a point 20 cm behind convex mirror on principal axis falls on it. The image if formed at

(A) infinity (B) 40 cm (C) 20 cm (D) 10 cm

18. An object is placed in front of a convex mirror at a distance of 50 cm. A plane

mirror is introduced covering the lower half of the convex mirror. If the distance between the object and the plane mirror is 30 cm, it is found that there is no gap between the images formed by the two mirrors. The radius of the convex mirror is:

(A) 12.5 cm (B) 25 cm (C) 50 cm (D) 100 cm

19. The distance of an object from the focus of a convex mirror of radius of curvature 'a' is 'b'. Then the distance of the image from the focus is :

(A) 2b

4a (B)

2

a

b (C)

2a

4b (D) none of these

20. An infinitely long rod lies along the axis of a concave mirror of focal length f. The near end of the rod is at a distance u > f from the mirror. Its image will have a length

(A) f2 /(u – f) (B) uf /(u – f) (C) f2 /(u + f) (D) uf /(u + f)

21. A candle is kept at a distance equal to double the focal length from the pole of a convex mirror. Its magnification will be :

(A) –1/3 (B) 1/3 (C) 2/3 (D) –2/3

22. A boy 2 m tall stands 40 cm in front of a mirror. He sees an erect image, 1 m high. The mirror is : (A) Concave, f = 40 cm (B) Convex, f = 40 cm (C) Plane (D) Either convex or concave


23. A concave mirror gives an image three times as large as the object placed at a

distance of 20 cm from it. For the image to be real, the focal length should be:

(A) 10 cm (B) 15 cm (C) 20 cm (D) 30 cm

24. If an object is 30 cm away from a concave mirror of focal length 15 cm, the image will be

(A) erect (B) virtual (C) diminished (D) of same size

25. What is the distance of a needle from a concave mirror of focal length 10 cm

for which a virtual image of twice its height is formed ?

(A) 2.5 cm (B) 5 cm (C) 8 cm (D) 9.1 cm

26. A convex mirror has a focal length f. An object of height h is placed in front of it. If an erect image of height h/n is formed. The distance of the object from the

mirror is :

(A) n f (B) f /n (C) (n + 1) f (D) (n – 1) f

27. In the figure shown, the image of a real object is formed at point I. AB is the

principal axis of the mirror. The mirror must be:

(A) concave & placed towards right I (B) concave & placed towards left of I (C) convex and placed towards right of I

(D) convex & placed towards left of I.

28. A point object at 15 cm from a concave mirror of radius of curvature 20 cm is made to oscillate along the principal axis with amplitude 2 mm. The amplitude of its image will be

(A) 2mm (B) 4mm (C) 8mm (D) none of these

29. A luminous point object is moving along the principal axis of a concave mirror of focal length 12 cm towards it. When its distance from the mirror is 20 cm its

velocity is 4 cm/s. The velocity of the image in cm/s at that instant is

(A) 6, towards the mirror (B) 6, away from the mirror (C) 9, away from the mirror (D) 9, towards the mirror


30. A particle is moving towards a fixed spherical mirror. The image :

(A) must move away from the mirror

(B) must move towards the mirror. (C) may move towards the mirror. (D) will move towards the mirror, only if the mirror is convex.

31. A point object on the principal axis at a distance 15 cm in front of a concave mirror of radius of curvature 20 cm has velocity 2 mm/s perpendicular to the principal axis. The velocity of image at that instant will be :

(A) 2 mm/s (B) 4 mm/s (C) 8 mm/s (D) none of these

32. The origin of x and y coordinates is the pole of a concave mirror of focal length 20 cm. The x-axis is the optical axis with x > 0 being the real side of mirror. A point object at the point (25 cm, 1 cm) is moving with a velocity 10 cm/s in positive x -direction. The velocity of the image in cm/s is approximately

(A) –80i + 8 j (B) 160i + 8 j (C) –160i + 8 j (D) 160i – 4 j

33. In the figure shown find the total magnification after two successive reflections first on M1 & then on M2

(A) + 1 (B) – 2 (C) + 2 (D) – 1

34. In the figure shown if the object ‘O’ moves towards the plane mirror, then the image I (which is formed after successive reflections from M1 & M2 respectively)

(A) towards right (B) towards left (C) with zero velocity (D) cannot be determined


Section-C (Refraction at plane surface)

35. The wavelength of light in vacuum is 6000 Aº and in a medium it is 4000 Aº. The refractive index of the medium is:

(A) 2.4 (B) 1.5 (C) 1.2 (D) 0.67

36. A ray of light passes from vacuum into a medium of refractive index n. If the angle of incidence is twice the angle of refraction, then the angle of incidence is:

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

37. A ray incident at a point at an angle of incidence of 60° enters a glass sphere of

μ = 3 and it is reflected and refracted at the farther surface of the sphere. The

angle between reflected and refracted rays at this surface is

(A) 50° (B) 90° (C) 60° (D) 40°

38. The x-z plane separates two media A and B with refractive indices μ1 and μ2

respectively. A ray of light travels from A and B. Its directions in the two media

are given by the unit vectors, ˆ ˆ ˆ ˆBr = a i+b j & r = i+β j respectively where ˆ ˆi & j

unit are vectors in the x and y directions. Then

(A) µ1a = µ2α (B) µ1α = µ2a (C) µ1b = µ2β (D) µ1B = µ2b

39. A ray of light moving along the unit vector (–i – 2j) undergoes refraction at an interface of two media, which is the x-z plane. The refractive index for y > 0 is

2 while for y < 0, it is 5 /2. The unit vector along which the refracted ray

moves is:

(A) ˆ ˆ− −( 3i 5j)

34 (B)

ˆ ˆ− −( 4i 3j)

5 (C)

ˆ ˆ− −( 3i 4j)

5 (D) none of these

40. How much water should be filled in a container of 21 cm in height, so that it appears half filled (of total height of the container) when viewed from the top of the container ?(Assume near normal incidence and μw = 4/3)

(A) 8.0 cm (B) 10.5 cm (C) 12.0 cm (D) 14.0 cm

41. A mark at the bottom of a beaker containing liquid appears to rise by 0.1m. The depth of the liquid is 1m. the refractive index of liquid is :

(A) 1.33 (B) 9/10 (C) 10/9 (D) 1.5


42. A parallel sided block of glass of refractive index 1.5 which is 36 mm thick

rests on the floor of a tank which is filled with water (refractive index = 4/3.)

The difference between apparent depth of floor at A & B when seen from vertically above is equal to

(A) 2 mm (B) 3mm (C) 4 mm (D) none

43. An under water swimmer is at a depth of 12 m below the surface of water. A bird is at a height of 18 m from the surface of water, directly above his eyes. For the swimmer, the bird appears to be at a distance X from the surface of water. (Refractive index of water is 4/3.) The value of X is

(A) 24 m (B) 12 m (C) 18 m (D) 9 m

44. A bird is flying 3 m above the surface of water. If the bird is diving vertically down with speed = 6 m/s, his apparent velocity as seen by a stationary fish

underwater is

(A) 8 m/s (B) 6 m/s (C) 12 m/s (D) 4 m/s

Section-D (Parallel slab and Composite slabs)

45. A ray of light is incident on a parallel slab of thickness t and refractive index n. If the angle of incidence θ is small, then the displacement in the incident and

emergent ray will be:

(A) −tθ(n 1)

n (B)

tθ

n (C)

−

tθ

n 1 (D) none of these

46. A ray of light passes through a plane glass slab of thickness t and refractive

index μ = 1.5. The angle between incident ray and emergent ray will be

(A) 0° (B) 30° (C) 45° (D) 60°


47. A beam of light is converging towards a point. A plane parallel plate of glass of

thickness t refractive index μ is introduced in the path of the beam. The

convergent point is shifted by (assume near normal incidence):

(A)

−

1t 1 away

μ (B)

1t 1+ away

μ

(C)

−

1t 1 nearer

μ (D)

1t 1+ nearer

μ

48. Given that, velocity of light in quartz = 1.5 × 108 m/s and velocity of light in

glycerin = 9

×4

108 m/s. Now a slab made of quartz is placed in glycerin as

shown. The shift of the object produced by slab is

(A) 6 cm (B) 3.55 cm (C) 9 cm (D) 2 cm

49. A ray of light is incident on one face of a transparent slab of thickness 15 cm. The angle of incidence is 60°. If the lateral displacement of the ray on emerging

from the parallel plane is 5 3 cm, the refractive index of the material of the

slab is

(A) 1.414 (B) 1.532 (C) 1.732 (D) none


50. A ray of light travelling in air is incident at grazing incidence on a slab with

variable refractive index, n(y) = [k y3/2 + 1]1/2 where k = 1 m–3/2 and follows

path as shown in the figure. What is the total deviation produced by slab when the ray comes out.

(A) 60º (B) 53º

(C) sin–1 (4/9) (D) no deviation at all

Section-E

(Total Internal Reflection)

51. Two transparent media A and B are separated by a plane boundary. The speed of light in medium A is 2.0 × 108 m s–1 and in medium B is 2.5 × 108 ms–1. The critical angle for which a ray of light going from A to B is totally internally

reflected is

(A) −

1 1sin

2 (B)

−

1 2sin

5 (C)

−

1 4sin

4 (D)

−

1 1sin

3

52. A ray of light from a denser medium strike a rarer medium. The angle of reflection is r and that of refraction is r’. The reflected and refracted rays make an angle of 90º with each other. The critical angle will be

(A) sin–1 (tan r) (B) tan–1 (sin r) (C) sin–1 (tan r’) (D) tan–1 (sin r’)

53. The critical angle of light going from medium A to medium B is θ. The speed of light in medium A is v. The speed of light in medium B is:

(A) v

sinθ (B) v sin θ (C) v cot θ (D) v tan θ

54. In the figure ABC is the cross section of a right angled prism and BCDE is the cross section of a glass slab. The value of θ so that light incident normally on the face AB does not cross the face BC is (given sin–1(3/5) = 37°)

(A) θ ≤ 37° (B) θ > 37° (C) θ ≤ 53° (D) θ < 53°


55. A small source of light is 4m below the surface of a liquid of refractive index

5/3. In order to cut off all the light coming out of liquid surface, minimum

diameter of the disc placed on the surface of liquid is

(A) 3m (B) 4m (C) 6m (D)

56. A cubical block of glass of refractive index n1 is in contact with the surface of water of refractive index n2. A beam of light is incident on vertical face of the block (see figure). After refraction, a total internal reflection at the base and refraction at the opposite vertical face, the ray emerges out at an angle θ. The value of θ is given by

(A) −2 21 2sinθ < n n (B) −2 2

1 2tanθ < n n

(C) −2 2

1 2

1sinθ <

n n (D)

−2 21 2

1tanθ <

n n

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

(A) 12×3× 5 (B) 4× 5 (C) 12×3× 7 (D) 12×3

7

58. A point source of light is placed at a distance h below the surface of a large deep lake. What is the percentage of light energy that escapes directly from the water surface ? µ of the water = 4/3 ? (neglect partial reflection)

(A) 50% (B) 25% (C) 20% (D) 17%


59. What should be i so that TIR occurs at the glass air interface

(A) sin–1 (2/3)

(B) sin–1 (3/4) (C) sin–1 (1/2) (D) TIR cannot occur in this situation

60. A light ray incident along vector ˆ ˆ ˆ2i+4 j+ 5 k strikes on the x-z plane from

medium-I of refractive index 2 and enters into medium-II of refractive index µ2. The value of µ2 for which the ray is just totally reflected from the boundary is

(A) 5

4 (B)

6

5 (C)

3 3

5 (D) 8

61. A triangular prism of glass is shown in figure. A ray incident normally on one face is totally reflected. If θ is 45°, the index of refraction of glass is:

(A) Less than 2 (B) Equal to 2

(C) Greater than 2 (D) None of the above

62. A vertical pencil of rays comes from bottom of a tank filled with a liquid. When it is accelerated horizontally with an accelerating of 7.5 m/s2 the ray is seen to

be totally reflected by liquid surface. What is minimum possible refractive index of liquid ?

(A) slightly greater than 4/3 (B) slightly greater than 5/3 (C) slightly greater than 1.5 (D) slightly greater than 1.75

Section-F (Prism)

63. A beam of monochromatic light is incident at i = 50° on one face of an equilateral prism, the angle of emergence is 40°, then the angle of minimum deviation is:

(A) 30° (B) < 30° (C) ≤ 30° (D) ≥ 30°


64. A ray incident at an angle 53° on a prism emerges at an angle at 37° as shown.

If the angle of incidence is made 50°, which of the following s is possible value

of the angle of emergence.

(A) 35° (B) 42° (C) 40° (D) 38°

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

(A) 45° (B) 49° (C) 40° (D) 55°

66. A thin prism of angle 5° is placed at a distance of 10 cm from object. What is the distance of the image from object ? (Given µ of prism = 1.5)

(A) π

cm8

(B) π

cm12

(C) 5π

cm36

(D) π

cm7

67. Light ray is incident on a prism of angle A = 60° and refractive index µ = 2 .

The angle of incidence at which the emergent ray grazes the surface is given by

(A) − −

1 3 1sin

2 (B) −

−

1 1 3sin

2 (C) −

1 3sin

2 (D) −

1 2sin

3

68. A ray of monochromatic light is incident on one refracting face of a prism of angle 75°. It passes through the prism and is incident on the other face at the

critical angle. If the refractive index of the material of the prism is 2 , the

angle of incidence on the first face of the prism is

(A) 30° (B) 45° (C) 60° (D) 0°

69. A prism having refractive index 2 and refracting angle 30°, has one of the

refracting surface polished. A beam of light incident on the other refracting surface will retrace its path if the angle of incidence is :

(A) 0° (B) 30° (C) 45° (D) 60°

70. A ray of light is incident at angle i on a surface of a prism of small angle A & emerges normally from the opposite surface. If the refractive index of the material of the prism is μ, the angle of incidence i is nearly equal to :

(A) A

μ (B)

A

(2μ) (C) µA (D)

Aμ

2


71. The angle of a prism is A and one of its refracting surfaces is silvered. Light

rays falling at an angle of incidence 2 A on the first surface return back

through the same path after suffering reflection at the second (silvered) surface. The refractive index of the material of the prism is

(A) 2 sin A (B) 2 cos A (C) 1/2 cos A (D) tan A

72. A prism has a refractive index 3

2 and refracting angle 90°. Find the minimum

deviation produced by prism.

(A) 40° (B) 45° (C) 30° (D) 49°

73. A prism is made up of material of refractive index 3 . The angle of prism is A.

If the angle of minimum deviation is equal to the angle of the prism, then the value of A is :

(A) 30° (B) 45° (C) 60° (D) 75°

74. A prism having an apex angle of 4° and refractive index of 1.50 is located in front of a vertical plane mirror as shown. A horizontal ray of light is incident

on the prism. The total angle through which the ray is deviated is

(A) 4° clockwise (B) 178° clockwise (C) 2° clockwise (D) 8° clockwise

Section-G

(Refraction of Spherical Surface)

75. A fish is near the centre of a spherical water filled fish bowl. A child stands in air at a distance 2R (R is radius of curvature of the sphere) from the centre of

the bowl. At what distance from the centre would the child's nose appear to

the fish situated at the centre (R.I. of water = 4/3)

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


76. The image for the converging beam after refraction through the curved surface

is formed at:

(A) x = 40 cm (B) 40

x = cm3

(C) −40

x = cm3

(D) 180

x = cm7

77. A Plano-concave lens is placed on a paper on which a flower is drawn. How far above its actual position does the flower appear to be ?

(A) 10 cm (B) 15 cm (C) 50 cm (D) none

78. A concave spherical surface of radius of curvature 10 cm separates two medium x & y of refractive index 4/3 & 3/2 respectively. If the object is placed along principal axis in medium X then

(A) image is always real

(B) image is real if the object distance is greater than 90cm

(C) image is always virtual

(D) image is virtual if the object distance is less than 90 cm

79. A spherical surface of radius of curvature 10 cm separates two media X and Y of refractive indices 3/2 and 4/3 respectively. Centre of the spherical surface lies in denser medium. An object is placed in medium X. For image to be real, the object distance must be

(A) greater than 90 cm (B) less than 90 cm

(C) greater than 80 cm (D) less than 80 cm


80. A beam of diameter ‘d’ is incident on a glass hemisphere as shown. If the

radius of curvature of the hemisphere is very large in comparison to d, then

the diameter of the beam at the base of the hemisphere will be

(A) 3/4 d (B) d (C) d/3 (D) 2/3 d

81. A concave spherical refracting surface separates two media glass and air (μglass = 1.5). If the image is to be real at what minimum distance u should the object be placed in glass if R is the radius of curvature ?

(A) u > 3R (B) u > 2R (C) u < 2R (D) u < R

Section-H

(Lens)

82. Two symmetric double convex lenses A and B have same focal length, but the radii of curvature differ so that RA = 0.9 RB. If nA = 1.63, find nB.

(A) 1.7 (B) 1.6 (C) 1.5 (D) 4/3

83. When a lens of power P (in air) made of material of refractive index μ is immersed in liquid of refractive index μ0. Then the power of lens is :

(A) −

− 0

μ 1P

μ μ (B)

−

−

0μ μP

μ 1 (C)

−

−

0

0

μ μ P.

μ 1 μ (D) none of these

84. A thin lens of focal length f and its aperture diameter d, forms a real image of intensity I. Now the central part of the aperture upto diameter (d/2) is blocked by an opaque paper. The focal length and image intensity would change to

(A) f l,

2 2 (B)

lf,

4 (C)

3f l,

4 2 (D)

3lf,

4

85. An object is placed at 10 cm from a lens and real image is formed with magnification of 0.5. Then the lens is :

(A) concave with focal length of 10/3 cm (B) convex with focal length of 10/3 cm (C) concave with focal length of 10 cm (D) convex with focal length of 10 cm


86. A thin symmetrical double convex lens of power P is cut into three part, as

shown in the figure. Power of A is :

(A) 2 P (B) P

2 (C)

P

3 (D) P

87. A thin linear object of size 1 mm is kept along the principal axis of a convex lens of focal length 10 cm. The object is at 15 cm from the lens. The length of the image is :

(A) 1 mm (B) 4 mm (C) 2 mm (D) 8 mm

88. A Plano convex lens has a curved surface of radius 100 cm. If μ = 1.5, then the focal length of the lens is :

(A) 50 cm (B) 100 cm (C) 200 cm (D) 500 cm

89. An object is placed at a distance of 15 cm from a convex lens of focal length 10 cm. On the other side of the lens, a convex mirror is placed at its focus such that the image formed by the combination coincides with the object itself. The focal length of the convex mirror is

(A) 20 cm (B) 10 cm (C) 15 cm (D) 30 cm

90. An object is placed in front of a thin convex lens of focal length 30 cm and a plane mirror is placed 15 cm behind the lens. If the final image of the object coincides with the object, the distance of the object from the lens is

(A) 60 cm (B) 30 cm (C) 15 cm (D) 25 cm

91. An object is placed in front of a symmetrical convex lens with refractive index 1.5 and radius of curvature 40 cm. The surface of the lens further away from the object is silvered. Under auto-collimation condition, the object distance is

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


92. A pin is placed 10 cm in front of convex lens of focal length 20 cm and

refractive index 1.5. The surface of the lens farther away from the pin is

silvered and has a radius of curvature of 22 cm. How far from the lens is the final image formed ?

(A) 10 cm (B) 11 cm (C) 12 cm (D) 13 cm

93. A planoconvex lens, when silvered at its plane surface is equivalent to a concave mirror of focal length 28cm. When its curved surface is silvered and the plane surface not silverted, it is equivalent to a concave mirror of focal length 10cm, then the refractive index of the material of the lens is :

(A) 9/14 (B) 14/9 (C) 17/9 (D) none

94. In the above question 93 the radius of curvature of the curved surface of Plano-convex lens is:

(A) 280

cm9

(B) 80

cm7

(C) 39

cm3

(D) 280

cm11

95. Consider the diagram shown. In the first diagram, the beam converges at F. What will be location of point of convergence in the second case ? The

refractive index of the lens is 2µ. In both the cases a parallel beam of light is incident from LHS.

(A) +F (B) –F (C) +2F (D) –2F

96. Parallel beam of light is incident on a system of two convex lenses of focal length f1 = 20 cm and f2 = 10 cm. What should be the distance between the two lenses so that rays after refraction from both the lenses pass parallel to

principal axis:

(A) 60 cm (B) 30 cm (C) 90 cm (D) 40 cm


97. A diverging lens of focal length 10 cm is placed 10 cm in front of a plane mirror

as shown in the figure. Light from a very far away source falls on the lens. The

final image is at a distance

(A) 20 cm behind the mirror (B) 7.5 cm in front of the mirror (C) 7.5 cm behind the mirror (D) 2.5 cm in front of the mirror

98. A thin lens of focal length f and its aperture has diameter d. It forms an image of intensity I. Now the central part of the aperture upto diameter (d/2) is blocked by an opaque paper. The focal length and image intensity would change to

(A) f/2, I/2 (B) f, I/4 (C) 3f/4, I/2 (D) f, 3I/4

99. An object is placed in front of a thin convex lens of focal length 30 cm and a plane mirror is placed 15 cm behind the lens. If the final image of the object

coincides with the object, the distance of the object from the lens is

(A) 60 cm (B) 30 cm (C) 15 cm (D) 25 cm

100. A converging lens of focal length 20 cm and diameter 5cm is cut along the line AB. The part of the lens shown shaded in the diagram is now used to form an image of a point P placed 30 cm away from it on the line XY. Which is perpendicular to the plane of the lens ? The image of P will be formed.

(A) 0.5 cm above XY (B) 1 cm below XY (C) on XY (D) 1.5 cm below XY

101. A screen is placed 90 cm from an object. The image of an object on the screen is formed by a convex lens at two different locations separated by 20 cm. The

focal length of the lens is

(A) 18 cm (B) 21.4 cm (C) 60 cm (D) 85.6 cm


102. In the above problem Qus 101, if the sizes of the images formed on the screen

are 6cm and 3 cm, then the height of the object is nearly:

(A) 4.2 cm (B) 4.5 cm (C) 5 cm (D) 9 cm

103. A point object is kept at the first focus of a convex lens. If the lens start moving towards right with a constant velocity, the image will

(A) always move towards right (B) always move towards left (C) first move towards right and then towards left (D) first move towards length and then towards right

104. Two Plano-convex lenses each of focal length 10 cm and refractive index 3/2 are placed as shown. In the space left, water (R.I = 4/3) is filled. The whole

arrangement is in air. The optical power of the system is (in diopters):

(A) 6.67 (B) –6.67 (C) 33.3 (D) 20

105. An object is placed in front of symmetrical convex lens with refractive index 1.5 and radius of curvature 40 cm. The surface of the lens further away from the object is silvered. Under auto-collimation condition, the object distance is

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

106. A Plano-convex lens, when silvered at its plane surface is equivalent to a

concave mirror of focal length 28 cm. when its curved surface is silvered and the plane surface not silvered it is equivalent to a concave mirror of focal length 10cm, then the refractive index of the material of the lens is :

(A) 9/14 (B) 14/9 (C) 17/9 (D) none


Section-I (Dispersion)

107. Two lenses in contact made of materials with dispersive powers in the ratio 2 : 1, behaves as an achromatic lens of focal length 10 cm. The individual focal lengths of the lenses are :

(A) 5 cm, –10 cm (B) –5 cm, 10 cm (C) 10 cm, –20 cm (D) –20 cm, 10 cm

108. A beam of consisting of red, green and blue is incident on a right angled prism.

The refractive index 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 part of the red color from the green and blue colors (B) separate part of the blue color from the red and green colours. (C) separate all the three colors from the other two colors (D) not separate even partially any color from the other two colors

109. It is desired to make an achromatic combination of two lenses (L1 and L2) made of material having dispersive power ω1 and ω2 (< ω1). If the combination of lenses is converging then

(A) L1 is converging (B) L2 is converging

(C) Power of L1 is greater than the power of L2 (D) None of these

110. The dispersion of light in a medium implies that: (A) lights of different wavelengths travels with different speeds in the medium (B) lights of different frequencies travel with different speeds in the medium (C) the refractive index of medium is different for different wavelengths

(D) all of the above.

111. Critical angle of light passing from glass to air is minimum for (A) red (B) green (C) yellow (D) violet

112. A plane glass slab is placed over various colored letters. The letter which appears to be raised the least is :

(A) violet (B) yellow (C) red (D) green


113. A medium has nv = 1.56, nr = 1.44. Then its dispersive power is :

(A) 3

50 (B)

6

25 (C) 0.03 (D) none

114. A thin prism P1 with angle 4° made of glass of refractive index 1.54 is combined with another thin prism P2 made of glass of refractive index 1.72 to produce dispersion without deviation. The angle of the prism P2 is :

(A) 3° (B) 2.6° (C) 4° (D) 5.33°

115. Light of wavelength 4000 Å is incident at small angle on a prism of apex angle

4°. The prism has nv = 1.5 & nr = 1.48. The angle of dispersion produced by the prism in this light is :

(A) 0.2° (B) 0.08° (C) 0.192° (D) none

Section-J

(Optical Instrument)

116. The figure shows a schematic diagram of a defective eye. What is this defect

called ?

(A) Myopia (B) Hypermetropia (C) Presbyopia (D) Astigmatism

117. The compound microscope is made from two lenses. Which statement is true concerning the operation of the compound microscope ?

(A) Both lenses form real images (B) Both lenses form virtual images

(C) The lens closest to the object forms a virtual image; the other lens forms a real image (D) The lens closest to the object forms a real image; the other lens forms a virtual image


118. Rama has a far point of 25 cm. Which statement here is true ?

(A) She may have normal vision

(B) She is myopic and requires diverging lenses to correct her vision (C) She is myopic and requires converging lenses to correct her vision (D) She is hyperopic and requires diverging lenses to correct her vision

119. A nearsighted person wears corrective lenses. One the focal points of the corrective lenses should be (A) at the cornea (B) at the retina

(C) at infinity (D) past the retina

120. An astronomical telescope has an angular magnification of 10. The length of the barrel is 33 cm. what are the focal lengths of the objective and the eyepiece, in that order respectively from the choices listed ?

(A) 3 cm, 30 cm (B) 30 cm, 3 cm (C) 20 cm, 13 cm (D) 0.3 m, 3 m

121. Consider the following four statement converging a compound microscope: 1. Each lens produces an image that is virtual and inverted 2. The objective lens has a very short focal length. 3. The eyepiece is used as a simple magnifying glass.

4. The objective lenses is convex and the eyepieces is concave.

Which two of the four statements are correct ?

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


Part-II Previous Year’s JEE Main Questions (2006-2020)

1. The refractive index of glass is 1.520 for red light and 1.525 for blue light. Let D1 and D2 be angles of minimum deviation for red and blue light respectively

in a prism of this glass. Then – (A) D1 can be less than or greater than D2 depending upon the angle of prism (B) D1 > D2 (C) D1 < D2 (D) D1 = D2

[AIEEE 2006]

2. Two lenses of power –15 D and +D are in contact with each other. The focal length of the combination is

(A) –20 cm (B) –10 cm (C) +20 cm (D) +10 cm

[AIEEE 2007]

3. An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distances are measures by-

(A) a standard laboratory scale (B) a meter scale provided on the microscope (C) a screw gauge provided on the microscope

(D) a vernier-scale provided on the microscope [AIEEE-2008]

4. A student measures the focal length of a convex lens by putting an object pin at a distance ‘u’ from the lens and measuring the distance ‘v’ of the image pin. The graph between ‘u’ and ‘v’ plotted by the student should look like –

(A) (B)

(C) (D) [AIEEE 2008]


5. A transparent solid cylindrical rod has a refractive index of 2

.3

It is

surrounded by air. A light ray is incident at the midpoint of one end of the rod

as shown in the figure.

The incident angle θ for which the light ray grazes along the wall of the rod is-

(A) −

1 1sin

2 (B) −

1 3sin

2 (C) −

1 2sin

3 (D) −

1 1sin

3

[AIEEE 2009]

6. A car is fitted with a convex side-view mirror of focal length 20 cm. A second car 2.8 m behind the first car is overtaking the first car at a relative speed of

15 m/s. The speed of the image of the second car as see in the mirror of the first one is

(A) 1

m/s10

(B) 1

m/s15

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

[AIEEE 2011]

7. Let the x-z plane be the boundary between two transparent media. Medium 1

in z ≥ 0 has a refractive index of 2 and medium 2 with z < 0 has a refractive

index of 3. A ray of light in medium 1 given by the vector

ˆ ˆ ˆ−A = 6 3 i+8 3 j 10k is incident on the plane of separation. The angle of

refraction in medium 2 is:

(A) 30° (B) 45° (C) 60° (D) 75°

[AIEEE 2011]

8. An object 2.4m in front of a lens forms a sharp image on a film 12 cm behind the lens. A glass plate 1 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?

(A) 3.2 m (B) 5.6 m (C) 7.2 m (D) 2.4 m [AIEEE 2012]


9. The graph between angle of deviation (δ) and angle of incidence (i) for a

triangular prism is represented by:

(A) (B)

(C) (D) [JEE Main 2013]

10. Diameter of a Plano–convex lens is 6 cm and thickness at the centre is 3 mm. If speed of light in material of lens is 2 × 108 m/s, the focal length of the lens is

(A) 20 cm (B) 30 cm (C) 10 cm (D) 15 cm

[JEE Main 2013]

11. A thin convex lens made from crown glass

3μ =

2 has focal length f. When it

is measured in two different liquids having refractive indices 4/3 and 5/3 it

has the focal lengths f1 and f2 respectively. The correct relation between the focal lengths is: (A) f1> f and f2 becomes negative (B) f2 > f and f1 becomes negative

(C) f1 and f2 both become negative (D) f1 = f2 < f

[JEE Main 2014]

12. A green light is incident from the water to the air-water interface at the critical angle (θ). Select the correct statement.

(A) The spectrum of visible light whose frequency is less than that of green light will come out to the air medium.

(B) The spectrum of visible light whose frequency is more than that of green light will come out to the air medium.

(C) The entire spectrum of visible light will come out of the water at various angles to the normal.

(D) The entire spectrum of visible light will come out of the water at an angle of 90o to the normal.

[JEE Main 2014]


13. Monochromatic light is incident on a glass prim of angle A. If the refractive

index of the material of the prism is μ, a ray, incident at an angle θ, on the

face AB would get transmitted through the face AC of the prism provided:

(A) − −

1 1 1θ >cos μsin A+sin

μ (B)

− −

1 1 1θ <cos μsin A+sin

μ

(C)− −

−

1 1 1θ >sin μsin A sin

μ (D)

− −

−

1 1 1θ <sin μsin A sin

μ

[JEE Main 2015]

14. In an experiment for determination of refractive index of glass of a prism by i – δ, plot, it was found that a ray incident at angle 35o, suffers a deviation of 40° and that it emerges at angle 79o. In that case which of the following is closest to the maximum possible value of the refractive index?

(A) 1.8 (B) 1.5 (C) 1.6 (D) 1.7 [JEE Main 2016]

15. A diverging lens with magnitude of focal length 25 cm is placed at a distance of

15 cm from a converging lens of magnitude of focal length 20 cm. A beam of

parallel light falls on the diverging lens. The final image formed is

(A) real and at a distance of 6 cm from the convergent lens (B) real and at a distance of 40 cm from the convergent lens (C) virtual and at a distance of 40 cm from convergent lens (D) real and at a distance of 40 cm from the divergent lens.

[JEE Main 2017]


16. A planoconvex lens becomes an optical system of 28 cm focal length when its

plane surface is silvered and illuminated from left to right as shown in Fig-A. If

the same lens is instead silvered on the curved surface and illuminated from other side as in Fig-B, it acts like an optical system of focal length 10 cm. The refractive index of the material of lens is:

(A) 1.75 (B) 1.51 (C) 1.55 (D) 1.50 [JEE Main 2018]

17. A particle is oscillating on the x-axis with an amplitude 2cm about the point

x0 = 10cm with a frequency ω. A concave mirror of focal length 5cm is placed at the origin (see figure). Identify the correct statements:

(1) The image executes periodic motion

(2) The image executes non-periodic motion (3) The turning points of the image are asymmetric w.r.t the image of the point at x =10cm (4) The distance between the turning points of the oscillation of the image

is 100

cm21

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

[JEE Main 2018]

18. A convergent doublet of separated lenses, corrected for spherical aberration, has resultant focal length of 10 cm. The separation between the two lenses is 2 cm. The focal lengths of the component lenses are

(A) 18 cm, 20 cm (B) 12 cm, 14 cm (C) 16 cm, 18 cm (D) 10 cm, 12 cm

[JEE Main 2018]

19. Two plane mirrors arc inclined to each other such that a ray of light incident on the first mirror (M1) and parallel to the second mirror (M2) is finally reflected from the second mirror (M2) parallel to the first mirror (M1). The angle between

the two mirrors will be :

(A) 90° (B) 45° (C) 75° (D) 60°

[JEE Main 2019]


20. The variation of refractive index of a crown glass thin prism with wavelength of

the incident light is shown. Which of the following, graph is the correct one, if

Dm is the angle of minimum deviation?

(A) (B)

(C) (D)

[JEE Main 2019]

21. A piano convex lens of refractive index μ1 and focal length f1 is kept in contact with another piano concave lens of refractive index μ2 and focal length f2. If the radius of curvature of their spherical faces is R each and f1 = 2f2, then μ1 and μ2 are related as :

(A) μ1 + μ2 = 3 (B) 2μ1 – μ2= = 1 (C) 2μ2 – μ1 = 1 (D) 3μ2 – 2μ1 = 1 [JEE Main 2019]

22. The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of cornea (7.8 mm). This surface separates two media of refractive indices 1 and 1.34. Calculate the distance from the refracting surface at which a parallel beam of light will come to focus.

(A) 2 cm (B) 1 cm (C) 3.1 cm (D) 4.0 cm [JEE Main 2019]


23. An object is at a distance of 20 m from a convex lens of focal length 0.3 m. The

lens forms an image of the object. If the object moves away from the lens at a

speed of 5 m/s, the speed and direction of the image will be:

(A) 2.26 × 10–3 m/s away from the lens (B) 0.92 × 10–3 m/s away from the lens (C) 3.22 × 10–3 m/s towards the lens

(D) 1.16 × 10–3 m/s towards the lens [JEE Main 2019]

24. A monochromatic light is incident at a certain angle on an equilateral

triangular prism and suffers minimum deviation. If the refractive index of the

material of the prism is 3 then the angle of incidence

(A) 90o (B) 30o (C) 60o (D) 45o

[JEE Main 2019]

25. What is the position and nature of image formed by lens combination shown in figure? (f1, f2 are focal lengths)

(A) 70 cm from point B at left; virtual (B) 40 cm from point B at right; real

(C) 20/3 cm from point B at right; real (D) 70 cm from point B at right ; real

[JEE Main 2019]

26. A Plano-convex lens (focal length f2, refractive index, radius of curvature R) fits

exactly into a Plano-concave lens (focal length f1, refractive index 1, radius of curvature R). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be :

(A) f1/ f2 (B) R / 1 – 2 (C) 2f1f2/ f1+f2 (D) f1+f2

[JEE Main 2019]


27. A point source of light, S is placed at a distance L in front of the centre of

plane mirror of width d which is hanging vertically on a wall. A man walks in

front of the mirror along a line parallel to the mirror, at a distance 2L as shown below. The distance over which the man can see the image of the light source in the mirror:

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

[JEE Main 2019]

28. Formation of real image using a biconvex lens is shown below:

If the whole set up is immersed in water without disturbing the object and the screen positions, what will one observe on the screen?

(A) Image disappears (B) Magnified image (C) Erect real image (D) No change

[JEE Main 2019]

29. In figure, the optical fiber is l = 2 m long and has a diameter of d = 20m. If a

ray of light is incident on one end of the fiber at angle 1 = 40°, the number of reflections it makes before emerging from the other end is close to : (refractive index of fiber is 1.31 and sin 40o = 0.64)

(A) 45000 (B) 55000 (C) 66000 (D) 57000

[JEE Main 2019]


30. A convex lens (of focal length 20 cm) and a concave mirror, having their

principal axes along the same lines, are kept 80 cm apart from each other. The

concave mirror is to the right of the convex lens. When an object is kept at a distance of 30 cm to the left of the convex lens, its image remains at the same position even if the concave mirror is removed. The maximum distance of the object for which this concave mirror, by itself would produce a virtual image would be

(A) 10 cm (B) 20 cm (C) 30 cm (D) 25 cm [JEE Main 2019]

31. A concave mirror for face viewing has focal length of 0.4 m. The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is:

(A) 0.24 m (B) 0.16 m (C) 1.60 m (D) 0.32 m [JEE Main 2019]

32. A convex lens of focal length 20 cm produces images of the same magnification 2 when an object is kept at two distance x1 and x2 (x1> x2) from the lens. The ratio of x1 and x2 is :

(A) 2 : 1 (B) 5 : 3 (C) 4 : 3 (D) 3 : 1 [JEE Main 2019]

33. A thin convex lens L (refractive index = 1.5) is placed on a plane mirror M. When a pin is placed at A, such that OA = 18 cm, its real inverted image is formed at A itself, as shown in figure. When a liquid of refractive index µ1 is put between the lens and the mirror, the pin has to be moved to A’, such that O’ = 27cm, to get its inverted real image at A’ itself. The value of µ1 will be:

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

[JEE Main 2019]


34. One Plano-convex and one plane of-concave lens of same radius of Curvature

‘R’ but of different materials are joined side by side as shown in the figure. If

refractive index of the material of 1 is 1 and that of 2 is 2, then the focal length of the combination is

(A) ( )− −1 2

R

2 μ μ (B)

−1 2

2R

μ μ (C)

( )1 2

R

μ +μ (D)

−1 2

R

μ μ

[JEE Main 2019]

35. A ray of light AO in vacuum is incident on a glass slab at angle 60° and refracted at angle 30° along OB as shown in the figure. The optical path length of light ray from A to B is:

(A) 2a + 2b (B) 2 3

+2ba

(C) 2b

2a +3

(D) 2b

2a +3

[JEE Main 2019]

36. The graph shows how the magnification m produced by a thin lens varies with image distance v. What is the focal length of the lens used?

(A) b2c/a (B) a/c (C) b2/ac (D) b/c

[JEE Main 2019]


37. A concave mirror has radius of curvature of 40 cm. It is at the bottom of a

glass that has water filled up to 5 cm (see figure). It a small particle is floating

on the surface of water, its image as seen, from directly above the glass, is at a distance d from the surface of water. The value of d is close to. (Refractive index of water = 1.33)

(A) 11.7 cm (B) 8.8 cm (C) 6.7 cm (D) 13.4 cm

[JEE Main 2019]

38. If we need a magnification of 375 from a compound microscope of tube length 150 mm and an objective of focal length 5 mm, the focal length of the eye-

piece, should be close to :

(A) 2 mm (B) 33 mm (C) 12 mm (D) 22 mm

[JEE Main 2020]

39. A thin lens made of glass (refractive index = 1.5) of focal length f = 16 cm is immersed in a liquid of refractive index 1.42. If its focal length in liquid is fl, then the ratio fl/f is closest to the integer:

(A) 1 (B) 5 (C) 17 (D) 9 [JEE Main 2020]

40. The magnifying power of a telescope with tube length 60 cm is 5. What is the focal length of its eye piece?

(A) 30 cm (B) 10 cm (C) 40 cm (D) 20 cm

[JEE Main 2020]

41. The critical angle of a medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability 4/3 for this wavelength, will be

(A) 15° (B) 30° (C) 60° (D) 45° [JEE Main 2020]

42. A point object in air is in front of the curved surface of a Plano-convex lens. The radius of curvature of the curved surface is 30 cm and the refractive index of the lens material is 1.5, then the focal length of the lens (in cm) is_______.

[JEE Main 2020]


43. An object is gradually moving away from the focal point of a concave mirror

along the axis of the mirror. The graphical representation of the magnitude of

linear magnification (m) versus distance of the object from the mirror (x) is correctly given by (Graphs are drawn schematically and are not to scale)

(A) (B)

(C) (D) [JEE Main 2020]

44. A vessel of depth 2h is half filled with a liquid of refractive index 2 2 and the

upper half with another liquid of refractive index 2 . The liquids are

immiscible. The apparent depth of the inner surface of the bottom of vessel will be :

(A) h

3 2 (B)

3h 2

4 (C)

h

2 (D)

h

2( 2+1)

[JEE Main 2020]

45. There is a small source of light at some depth below the surface of water

(refractive index = 4/3) in a tank of large cross sectional surface area. Neglecting any reflection from the bottom and absorption by water, percentage of light that emerges out of surface is (nearly) :

[Use the fact that surface area of a spherical cap of height h and radius of

curvature r is 2rh]

(A) 50% (B) 34% (C) 17% (D) 21% [JEE Main 2020]


EXERCISE-II Part-I

(Multiple Correct type Questions)

Section-A

1. A man of height 170 cm wants to see his complete image in a plane mirror (while standing). His eyes are at a height of 160 cm from the ground.

(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 or less (D) Bottom of the mirror should be at a height 85 cm

2. The reflecting surface is represented by the equation 2x = y2 as shown in figure. A ray travelling horizontal becomes vertical after reflection. The co-

ordinates of the point incidence can be

(A) (1/2, 1) (B) (1, 1/2) (C) (1/2, 1/2) (D) (1/2, –1)

3. A concave mirror cannot form

(A) virtual image of virtual object (B) virtual image of a real object

(C) real image of a real object (D) real image of a virtual object

4. Point A(0, 1) and B(12, 5) are object-image pair (one of the point acts as object and the other point as image) x-axis is the principal axis of the mirror. Then

this object image pair is:

(A) due to a convex mirror of focal length 2.5 cm

(B) due to a concave mirror having its pole at (2, 0) (C) real virtual pair (D) data is insufficient for options (A) and (B)


5. In the figure stick figure O stands in front of a thin, symmetric mirror that is

mounted within the boxed region; the central axis through the mirror is

shown. The four stick figures I1 to I4 suggest general locations and orientation for the images that might be produced by the mirror. (The figures are only sketched in; their height and their distance from the mirror is not drawn to scale.)

(A) I4 cannot be a possible image. (B) I1 cannot be a possible image. (C) If I2 is an image, mirror must be concave only. (D) If I3 is an image, mirror must be convex only.

6. A ray of light in a liquid of refractive index 1.4 approaches the boundary surface between the liquid and air at an angle of incidence whose sine is 0.8. which of the following statements is correct about the behavior of the light

(A) It is impossible to predict the behavior of the light ray of the basis of the information supplied

(B) The sine of the angle of refraction of the emergent ray will less than 0.8.

(C) The ray will be internally reflected

(D) The sine of the angle of refraction of the emergent ray will be greater than 0.8.

7. In the figure shown a point object O is placed in air on the principal axis. The radius of curvature of the spherical surface is 60 cm. If is the final image formed after all the refractions and reflections.

(A) If d1 = 120 cm, then the ‘If’ is formed on ‘O’ for any value of d2. (B) If d1 = 240 cm, then the ‘If’ is formed on ‘O’ only if d2 = 360 cm. (C) If d1 = 240 cm, then the ‘If’ is formed on ‘O’ for all value of d2. (D) If d1 = 240 cm, then the ‘If’ cannot be formed on O.


8. 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.

(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 μ2 > μ1 then there cannot be a real image of real object

9. A convex spherical surface of radius 10 cm is used to form the image of a point object as shown. What should be the object distance x so that the distance between object and the image is 1 m.

(A) 40 cm (B) 50 cm (C) 60 cm (D) 70 cm

10. A luminous point object is placed at O, whose image is formed at I as shown in the figure. AB is the optical axis. Which of the following statements are correct?

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

(B) If a mirror is used to obtain an image, the mirror must be a convex mirror

having a pole at the point of intersection of lines OI and AB.

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

(D) I is a real image.


11. A lens is placed in the XYZ coordinate system such that its optical center is at

the origin and principal axis is along the X axis. The focal length of the lens is

20 cm. A point object been placed at the point (–40 cm, +1 cm, –1 cm). Which of the following are correct about coordinates of the image ?

(A) x = 40 cm (B) y = +1 cm (C) z = +1 cm (D) z = –1 cm

12. 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

13. A concave spherical mirror has a radius of curvature of 50 cm. Find two position of an object for which the image is four times as large as the object.

(A) 75

cm4

from mirror (B) 125 cm from mirror

(C) 125

cm4

from mirror (D) 32 cm from mirror

14. Two value of d1 and d2 for final rays to be parallel to the principle axis are: (focal lengths of the lenses are written on the lenses)

(A) d1 = 10 cm, d2 = 15 cm (B) d1 = 20 cm, d2 = 15 cm (C) d1 = 30 cm, d2 = 15 cm (D) none of these

15. A man wanted to get a picture of a Zebra. He photographed a white donkey after fitting a glass with black streaks onto the objective of his camera.

(A) the image will look like a white donkey on the photograph

(B) the image will look like a Zebra on the photograph

(C) the image will be more intense compared to the case in which so such glass is used

(D) the image will be less intense compared to the case in which no such glass

is used.


16. A parallel beam of white light is made to fall on an equiconvex lens made of

glass. When the screen is kept at a distance of 10 cm, a spot of violet light is

observed at centre and outer ring of red colour of radius 1 mm. The radius of curvature of lens is 6 cm each and aperture diameter is 2 cm. Then :

(A) Refractive index of the glass for red light is 1.27

(B) Refractive index of the glass for red light is 1.3 (C) Dispersive power of lens is nearly 0.1 (D) Dispersive power of lens is nearly 0.2

17. A flat mirror M is arranged parallel to a wall W at a distance l from it. The light

produced by a point source S kept on the wall is reflected by the mirror and

produces a light spot on the wall. The mirror moves with velocity towards the wall.

(A) The spot of light will move with the speed v on the wall.

(B) The spot of light will not move on the wall.

(C) As the mirror comes closer, the spot of light will become larger and shift away from the wall with a speed larger than v

(D) The size of the light spot on the wall remains the same.


Section-B

(Comprehension type Questions)

Paragraph for Qus 1 to 3

All objects referred to, in the subsequent problems lie on the principal axis. The

light is incident from left. It gets refracted at surface-1, passes through water and gets refracted through surface-2.

1. The image formed after first refraction is definitely-

(A) Real for a real object (B) Virtual for a real object

(C) Real for a virtual object (D) Virtual for a virtual object

2. For a particular objet, it is seen that the rays pass through the second surface without any deviation. This implies that the image for 1st surface is formed at

(A) the pole of 1st surface

(B) the centre of curvature of 1st surface (C) the pole of second surface

(D) the centre of curvature of second surface

3. Taking refractive index for water as 4/3, and radii of curvature of both surfaces as 10 cm, where will a beam parallel to principal axis incident on surface-1 finally converge ?

(A) 150 cm from second surface (B) 35 cm from second surface

(C) 60 cm from second surface (D) none of these


The figure, shows a transparent sphere of radius R and refractive index µ. An object O is placed at a distance x from the pole of the first surface so that a real image is formed at the pole of the exactly opposite surface.

4. If x = 2R, then the value of µ is

(A) 1.5 (B) 2 (C) 3 (D) none of these


5. If x = , then the value of µ is


6. If an object is placed at a distance R from the pole of first surface, then the real image is formed at a distance R from the pole of the second surface. The refractive index µ of the sphere is given by



A turnip sits before a thing converging lens, outside the focal point of the lens.

The lens is filled with a transparent gel so that it is flexible; by squeezing its ends toward its center [as indicated in figure (a)], you can change the curvature of its front and rear sides.

7. When you squeeze the lens, the image.

(A) moves towards the lens (B) moves away from the lens (C) shifts up (D) remains as it is

8. When you squeeze the lens, the lateral height of image

(A) increases (B) decreases

(C) remains same (D) data insufficient

9. Suppose that a sharp image must be formed on a card which is at a certain distance behind the lens [figure (b)], while your move the turnip away from the

lens, then you should

(A) decrease the squeeze of the lens (B) increase the squeeze of the lens (C) keep the card and lens as it is (D) move the card away from the lens


Section-C

[MATRIX TYPE]

1. A bird in air is diving vertically over a tan k with speed 6 cm/s. Base of the tank is silvered. A fish in the tank is rising upward along the same line with speed 4 cm/s. [Take: µwater = 4/3]

Column-I Column-II (in cm/s)

(A) Speed of the image of fish as seen by

the bird directly (P) 12

(B)

Speed of the image of fish formed

after reflection from the mirror as seen by the bird

(Q) 4

(C) Speed of image of bird relative to the fish looking upwards

(R) 9

(D) Speed of image of bird relative to the fish looking downwards in the mirror

(S) 3


PART-II

(Subjective type Questions)

1. Two flat mirrors have their reflecting surfaces facing each other, with an edge of one mirror in contact with an edge of the other, so that the angle between the mirrors is 60°. Find all the angular positions of the image with respect to x-axis. Take the case when a point object is between the mirror at (1, 1). Point of intersection is (0, 0) and 1st mirror is along x axis.

2. A point object is moving with a speed of 5 m/s infront of a mirror moving with a speed of 2.5 m/s as shown in figure. The velocity of image of the object with

respect to ground is 10x m/s , then x is

3. In figure shown AB is a plane mirror of length 40 cm placed at a height 40 cm from ground. There is a light source S at a point on the ground. Find the minimum and maximum height of a man (eye height) required to see the image of the source if he is standing at a point P on ground and shown in figure.

4. The angle between two flat mirror is changed by rotating one of the mirrors around the edge of another with a constant angular velocity ω = 1.5 deg/sec. Source of light S is located as shown in Figure, t distance h = 10 cm. At the initial moment mirrors were in the same plane (φ = 180°).

After what minimum time (in second) 3 images will be formed by the mirrors.


5. A fluorescent lamp of length 1 m is placed horizontally at a depth of 1.2 m

below a ceiling. A plane mirror of length 0.6 m is placed below the lamp

parallel to and symmetric to the lamp at a distance 2.4 m from it as shown in figure. Find the length in meters (distance between the extreme points of the visible region along x-axis) of the reflected patch of light on the ceiling.

6. A light ray I is incident on a plane mirror M. The mirror is rotated in the direction as shown in the figure by an arrow at frequency 9/π rps. The light reflected by the mirror is received on the wall W at a distance 10m from the axis of rotation. When the angle of incidence becomes 37º the speed of the spot (a point) on the wall is V × 102 m/s. Find the value of V

7. The diagram shows a mirror system. If after two reflection the image and the object O coincide with each other, then find the value of radius of curvature of the concave mirror in meter. Take a = 3m.


8. A concave mirror of focal length 20 cm is cut into two parts from the middle

and the two parts are moved perpendicularly by a distance 1 cm from the

previous principal axis AB. Find the distance between the images formed by the two parts ?

9. A point object is placed 33 cm from a convex mirror of curvature radius = 40 cm. A glass plate of thickness 6 cm and index 2.0 is placed between the object and mirror, close to the mirror. Find the distance of final image from the object?

10. A vessel, whose bottom is flat and perfectly reflecting, is filled with water (index = 4/3) upto a height = 40 cm. A point object in air above is moving towards the water surface with a constant speed = 4 m/s. What is the relative

speed of its final image (in m/s), as seed by the object itself, at a moment when the object is 30 cm above the water surface ?

11. An insect at point ‘P’ sees its two images in the water mirror system as shown in the figure. One image is formed due to direct partial reflection from water

surface and the other image is formed due to refraction, reflection and again refraction by water mirror system in order. Find the separation (in cm) between the two images. Mirror M has focal length 60 cm. [Take µw = 4/3]

12. A concave mirror forms the real image of a point source lying on the optical axis at a distance of 50 cm from the mirror. The focal length of the mirror is

25 cm. The mirror is cut into two halves and its halves are drawn a distance of

1 cm apart (from each other) in a direction perpendicular to the optical axis. Find the distance (in cm) between the two images formed by the two halves of the mirror.


13. A convex mirror and a concave mirror each of focal length 10 cm are placed

coaxially. They are separated by 40cm and their reflecting surfaces face each

other. A point object is kept on the principle axis at a distance x cm from the concave mirror such that final image after two reflections, first on the concave mirror, is on the object itself. Find the integer next to x.

14. Mirror in the arrangement shown in figure is moving up with speed 4 cm/sec. Find the speed of final image of object O (in cm/s) formed after two refraction and one reflection.

15. A point object is placed on principal axis of a concave mirror of radius of curvature 20 cm at a distance 31 cm from poll of the mirror. A glass slab of

thickness 3 cm and refractive index 1.5 is placed between object and mirror as shown in the figure.

Find the distance (in cm) of final image formed by the system from the mirror.

16. An opaque cylindrical tank with an open top has a diameter of 3.00 m and is completely filled with water. When the setting Sun reaches an angle of 37°

above the horizon, sunlight ceases to illuminate any part of the bottom of the tank. How deep is the tank ?


17. 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 (see

fig). The point of incidence is the origin A(0, 0), The medium has a variable index of refraction n(y) given by:

n(y) = [ky3/2 + 1]1/2 Where k=1.0(m)–3/2 , The refractive index of air is 1.0.

(i) Obtain a relation between the slope (dy/dx) of the trajectory of ray at point

B(x, y) in the medium and the incident angle (i) at the point.

(ii) Find the value of n sin i.

(iii) Obtain an equation for the trajectory y (x) of the ray in the medium.

(iv) Determine the coordinates (x1, y1) of the point P, where the ray intersects the upper surface of the slab-air boundary.

(v) Indicated the path of the ray subsequently.

18. A rod made of glass (µ = 1.5) and of square cross-section is bent into the shape shown in figure. A parallel beam light falls perpendicularly on the plane flat surface A. Referring to the diagram, d is the width of a side and R is the radius of inner semicircle. Find the maximum value of ratio d/R so that all light entering the glass through surface A emerge from the glass through surface B.


19. Light is incident from glass to air. The variation of the angle of deviation δ with

the angle of incidence i for 0 < i < 90° is shown. The refractive index of glass is

2

3. If the value of (x + y + z) is

nπ

6 then find value of n.

20. A prism of refractive index 2 has a refracting angle of 30°. One of the

refracting surfaces of the prism is polished. For the beam of monochromatic light to retrace its path, find the angle of incidence on the refracting surface.

21. An thin glass prism (µ = 1.5) has one of its equal faces coated with silver. A ray is normally incident on the other face after reflection from face BC, the ray

reenters air through face AB. What is the angle (in degree) made by emerging ray with normal.

22. An equilateral prism deviates a ray through 23° for two angles of incidence differing by 23°. Find µ of the prism ?

23. Figure shows the path of a light beam in an isosceles prism with apex angle δ = 60° (inside the prism beam is parallel to the base). Find the angle of deflection in degrees. The refractive index of prism material is 1.732.


24. In the figure shown a point object O is placed in air. A spherical boundary of

radius of curvature1.0 m separates two media. AB is principal axis. The

refractive index above AB is 1.6 and below AB is 2.0. Find the separation between the images (in m) formed due to refraction at spherical surface.

25. A glass hemisphere of refractive index 4/3 and of radius 4 cm is placed on a plane mirror. A point object is placed on axis of this sphere at a distance 'd ' from O as shown in the figure. If the final image is formed at infinity, then find the value of 'd ' in mm.

26. A thick biconvex lens of thickness 6 cm and refractive index 1.5 appears to be of thickness 5 cm when viewed from one side and 4.8 cm when viewed from the other side. Calculate the radii of curvature of two sides of the lens.

27. A point object is placed at a distance of 25 cm from a convex lens of focal length 20 cm. If a glass slab of thickness t and refractive index 1.5 is inserted

between the lens and object. The image is formed at infinity. Find the thickness t ?

28. A point source of light is kept at a distance of 15 cm from a converging lens, on its optical axis. The focal length of the lens is 10 cm and its diameter is 3 cm. A screen is placed on the other side of the lens, perpendicular to the axis of lens, at a distance 20 cm from it. Then find the area of the illuminated parted of the screen ?

29. A plano convex lens (µ = 1.5) has a maximum thickness of 1 mm. If diameter of its aperture is 4 cm. Find

(i) Radius of curvature of curved surface (ii) its focal length in air


30. A thin equiconvex lens of glass of refractive index µ = 3/2 and of focal length

0.3 m in air is sealed into an opening at one end of a tank filled with water

(µ = 4/3). On the opposite side of the lens, a mirror is placed inside the tank on the tank wall perpendicular to the lens axis, as shown in figure. The separation between the lens and the mirror is 0.8 m. A small object is placed outside the tank in front of the 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.

31. A quarter beam cylinder of radius R and refractive index 1.5 is placed on a table. A point object P is kept at a distance of mR from it. Find the value of m

for which a ray from P will emerge parallel to the table as shown in the figure.

32. A uniform, horizontal beam of light is incident upon a quarter cylinder of

radius R = 5 cm, and has refractive index 2

3. A patch on the table for a

distance ‘x’ from the cylinder is unilluminated. Find the value of ‘x’ ?


33. A prism of refractive index n1 and another prism of refractive index n2 are

struck together without a gap as shown, n1 and n2 depend upon λ the wave

length of light according to n1 = 4

2

10.8+101.20+

λ and

4

2 2

1.80+10n =1.45+

λ

where λ is in nanometer.

(a) Calculate the wave length λ0 for which rays incident at any angle on the

interface BC pass through without bending a the interface.

(b) For light of wave length λ0 for which rays incident on the face AC such that the deviated produced by the combination of the prism is minimum.


EXERCISE-III

JEE ADVANCED Previous Year’s Questions

1. A point object is placed at a distance of 20 cm from a thin Plano-convex lens of focal length 15 cm, if the plane surface is silvered. The image will form at

(A) 60 cm left of AB (B) 30 cm left of AB (C) 12 cm left of AB (D) 60 cm right of AB

[JEE 2006]

2. Parallel rays of light from Sun falls on a biconvex lens of focal length f and the circular image of radius r is formed on the focal plane of the lens. Then which of the following statement is correct?

(A) Area of image πr2 directly proportional to f (B) Area of image πr2 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 of image will become half.

[JEE 2006]

3. A ray of light travelling in water is incident on its surface open to air. The angle of incidence is θ, which is less than the critical angle. Then there will be (A) only a reflected ray and no refracted ray (B) only a refracted ray and no reflected ray (C) a reflected ray and a refracted ray and the angle between them would be less than 180° – 2θ

(D) a reflected ray and a refracted ray and the angle between them would be

greater than 180° – 2θ [JEE 2007]


4. STATEMENT-1: The formula connecting u, v and f for a spherical mirror is

valid only for mirror whose sizes are very small compared to their radii of

curvature because STATEMENT-2 : Laws of reflection are strictly valid for plane surfaces, 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 [JEE 2007]

5. Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is 60°). In the position of minimum deviation, the angle of refraction will be:

(A) 30° for both the colours (B) greater for the violet colour

(C) greater for the red colour

(D) equal but not 30° for both the colours [JEE 2008]

6. A light beam is traveling from Region I to Region IV (Refer Figure). The

refractive index in Regions I, II, III and IV are 0 00

n nn , ,

2 6 and 0n

,8

respectively.

The angle of incidence q for which the beam just misses entering Region IV is

(A) −

1 3sin

4 (B) −

1 1sin

8 (C) −

1 1sin

4 (D) −

1 1sin

3

[JEE 2008]


7. An optical component and an object S placed along its optic axis are given in

Column I. The distance between the object and the component can be varied.

The properties of images are given in Column II. Match all the properties of images from Column II with the appropriate components given in Column I.

[JEE 2008]

8. A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive index of water is 4/3. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At an instant, when the ball is 12.8 m above the

water surface, the fish sees the speed of ball as [Take g = 10 m/s2.]

(A) 9 m/s (B) 12 m/s (C) 16 m/s (D) 21.33 m/s

[JEE 2009]

9. A student performed the experiment of determination of focal length of a concave mirror by u-v method using an optical bench of length 1.5 meter. The focal length of the mirror used is 24 cm. The maximum error in the location of the image can be 0.2 cm. The 5 sets of (u, v) values recorded by the student (in cm) are: (42, 56), (48, 48), (60, 40), (66, 33), (78, 39). The data set(s) that

cannot come from experiment and is (are) incorrectly recorded, is (are)

(A) (42, 56) (B) (48, 48) (C) (66, 33) (D) (78, 39) [JEE 2009]


10. A ray OP of monochromatic light is incident on the face AB of prism ABCD

near vertex B at an incident angle of 60° (see figure). If the refractive index of

the material of the prism is 3, which of the following is (are) correct?

(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

[JEE 2010]

11. The focal length of a thin biconvex less is 20 cm. When an object is moved

from a distance of 25 cm in front of it to 50 cm, the magnification of its image

changes from m25 to m50. The ratio 25

50

m

m is

[JEE 2010]

12. A biconvex lens of focal length 15 cm is in front of a plane mirror. The distance between the lens and the mirror is 10 cm. A small object is kept at a distance of 30 cm from the lens. The final image is

(A) virtual and at a distance of 16 cm from the mirror

(B) real and at a distance of 16 cm from the mirror (C) virtual and at a distance of 20 cm from the mirror

(D) real and at a distance of 20 cm from the mirror [JEE 2010]

13. Image of an object approaching a convex mirror of radius of curvature 20 m

along its optical axis is observed to move from 25

m3

to 50

m7

in 30 seconds.

What is the speed of the object in km per hour?

[JEE 2010]


14. Two transparent media of refractive indices μ2 and μ3 have solid lens shaped

transparent material refractive index m2 between then as shown in figures in

Column II. A ray traversing these media is also shown in the figures. In Column I different relationship between μ1, μ2 are given. Match them to the ray diagrams shown in Column II.

[JEE 2010]

15. A large glass slab (μ = 5/3) of thickness 8 cm is placed over a point source of

light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius R cm. What is the value of R?

[JEE 2010]


16. A light ray traveling in glass medium is incident on glass-air interface at an

angle of incidence θ. The reflected (R) and transmitted (T) intensities, both as

function of θ, are plotted. The correct sketch is

(A) (B)

(C) (D)

[JEE 2011]

17. Water (with refractive index = 4/3) in a tank is 18 cm deep. Oil of refractive index 7/4 lies on water making a convex surface of radius of curvature ‘R = 6 cm’ as shown. Consider oil to act as a thin lens. An object ‘S’ is placed 24 cm above water surface. The location of its image is at ‘x’ cm above the bottom of

the tank. Then ‘x’ is

[JEE 2011]


18. A bi-convex lens is formed with two thin plano-convex lenses as shown in the

figure. Refractive index n of the first lens is 1.5 and that of the second lens is

1.2. Both the curved surfaces are of the same radius of curvature R = 14 cm. For this bi-convex lens, for an object distance of 40 cm, the image distance will be

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

[JEE 2012]

Paragraph for Questions 19 and 20

Most materials have the refractive index, n > 1. So, when a light ray from air

enters a naturally occurring material, then by Shell’s law, 21

2 1

nsinθ= ,

sinθ n it is

understood that the refracted ray bends towards the normal. But it never emerges on the same side of the normal as the incident ray. According to electromagnetism, the refractive index of the medium is given by the relation,

r r

cn= ± ε u ,

v where c is the speed of electromagnetic waves in vacuum, v its

speed in the medium, εr and μr are the relative permittivity and permeability of the medium respectively.

In normal materials, both εr and μr are positive, implying positive n for the medium. When both εr and μr are negative, one must choose the negative root

of n. Such negative refractive index materials can now be artificially prepared and are called meta-materials. They exhibit significantly different optical

behavior, without violating any physical laws. Since n is negative, it results in a change in the direction of propagation of the refracted light. However, similar to normal materials, the frequency of light remains unchanged upon refraction even in meta-materials.

19. Choose the correct statement

(A) The speed of light in the meta-material is v = c |n|

(B) The speed of light in the meta-material is c

v =|n|

(C) The speed of light in the meta-material is v = c

(D) The wavelength of the light in the meta-material (λm) is given by λm = λair|n|, where λair is the wavelength of the light in air

[JEE 2012]


20. For light incident from air on a meta-material, the appropriate ray diagram is

(A) (B)

(C) (D) [JEE 2012]

21. The image of an object, formed by a plano-convex lens at distance of 8 m behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is 2/3 times the wavelength in free space. The radius of the curved surface of the lens is

(A) 1 m (B) 2 m (C) 3 m (D) 6 m [JEE 2013]

22. A ray of light travelling in the direction ( )ˆ ˆ1i+ 3 j

2 is incident on a plane

mirror. After reflection, it travels along the direction ( )ˆ ˆ−1

i 3 j .2

The angle of

incidence is

(A) 30° (B) 45° (C) 60° (D) 75° [JEE 2013]


23. A right angled prism of refractive index μ1 is placed in a rectangular block of

refractive index μ2, which is surrounded by a medium of refractive index μ3, as

shown in the figure, A ray of light ‘e’ enters the rectangular block at normal incidence. Depending upon the relationships between μ1, μ2 and μ3 it takes one of the four possible paths ‘ef’, ‘eg’, ‘eh’ or ‘ei’.

Match the paths in List I with conditions of refractive indices in List II and

select the correct answer using the codes given below the lists:

List I List II

P. e → f 1. 1 2μ > 2μ

Q. e → g 2. 2 1 2 3μ > μ and μ > μ

R. e → h 3. 1 2μ = μ

S. e → i 4. 2 1 2 2 3μ < μ < 2μ and μ > μ

Codes:

P Q R S P Q R S

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

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

[JEE 2013]

24. A transparent thin film of uniform thickness and refractive index n1 = 1.4 is coated on the convex spherical surface of radius R at one end of a long solid glass cylinder of refractive index n2 = 1.5, as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance f1 from the film, while rays of light traversing from glass to air get focused at distance f2 from the film. Then

(A) |f1| = 3R (B) |f1| = 2.8R (C) |f2| = 2R (D) |f2| = 1.4R

[JEE 2014]


25. A point source S is placed at the bottom of a transparent block of height

10 mm and refractive index 2.72. It is immersed in a lower refractive index

liquid as shown in the figure. It is found that the light emerging from the block to the liquid forms a circular bright spot of diameter 11.54 mm on the top of the block. The refractive index of the liquid is

(A) 1.21 (B) 1.30 (C) 1.36 (D) 1.42

[JEE 2014]

26. Four combinations of two thin lenses are given in List-I. The radius of curvature of all curved surfaces is r and the refractive index of all the lenses is 1.5. Match lens combinations in List-I with their focal length in List-II and select the correct answer using the code given below the lists.

(A) P-1, Q-2, R-3, S-4 (B) P-2, Q-4, R-3, S-1 (C) P-4, Q-1, R-2, S-3 (D) P-2, Q-1, R-3, S-4

[JEE 2014]

27. Consider a concave mirror and a convex lens (refractive index = 1.5) of focal length 10 cm each, separated by a distance of 50 cm in air (refractive index = 1) as shown in the figure. An object is placed at a distance of 15 cm from the mirror. Its erect images formed by this combination has magnification M1. When the set-up is kept in a medium of refractive index 7/6, the magnification

becomes M2. The magnitude 2

1

M

M is

[JEE 2015]


28. Two identical glass rods S1 and S2 (refractive index = 1.5) have one convex end

of radius of curvature 10cm. They are placed with the curved surfaces at a

distance d as shown in the figure, with their axes (shown by the dashed line) aligned. When a point source of light P is placed inside rod S1 on its axis at a distance of 50 cm from the curved face, the light rays emanating from it are found to be parallel to the axis inside S2. The distance d is

(A) 60 cm (B) 70 cm (C) 80 cm (D) 90 cm [JEE 2015]

29. For photo-electric effect with incident photon wavelength λ, the stopping potential is V0. Identify the correct variation(s) of V0 with l and 1/λ.

(A) (B) (C) (D) [JEE 2015]

30. A monochromatic beam of light is incident at 60° on one face of an equilateral prism of refractive index n and emerges from the opposite face making angle

θ(n) with the normal (see the figure). For n = 3 the value of θ is 60° and

dθ= m.

dn The value of m is

[JEE 2015]


31. A parallel beam of light is incident from air at an angle α on the side PQ of a

right angled triangular prism of refractive index n = 2 . Light undergoes total

internal reflection in the prism at the face PR when α has minimum value

of 45°. The angle θ of the prism is:

(A) 15° (B) 22.5° (C) 30° (D) 45°

[JEE 2016]

32. A small object is placed 50 cm to the left of a thin convex lens of focal length 30 cm. A convex spherical mirror of radius of curvature 100 cm is placed to the right of the lens at a distance of 50 cm. The mirror is titled such

that the axis of the mirror is at an angle θ = 30° to the axis of the lens, as shown in the figure.

If the origin of the coordinate system is taken to be at the centre of the lens, the coordinates (in cm) of the point (x, y) at which the image is formed are:

(A) (25, 25 3) (B) (0, 0)

(C) (125/3, 25/ 3) (D) −(50 25 3, 25)

[JEE 2016]


33. A transparent slab of thickness d has a refractive index n(z) that increases

with z. Here z is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices n1

and n2(> n1), as shown in the figure. A ray of light incident with angle θi from medium 1 and emerges in medium 2 with refraction angle θf with lateral displacement l.

Which of the following statement(s) is (are) true?

(A) l is independent of n2 (B) n1sinθi = n2 sinθf

(C) l is independent of n(z) (D) n1sinθi = (n2 – n1) sinθf

[JEE 2016]

34. A plano-convex lens is made of a material of refractive index n. When a small object is placed 30 cm away in front of the curved surface of the lens, an image of double the size of the object is produced. Due to reflection from the convex

surface of the lens, another faint image is observed at a distance of 10 cm away from the lens. Which of the following statement (s) is (are) true?

(A) The refractive index of the lens is 2.5

(B) The radius of curvature of the convex surface is 45 cm (C) The faint image is erect and real (D) the focal length of the lens is 20 cm

[JEE 2016]


35. A monochromatic light is travelling in a medium of refractive index n = 1.6. It

enters a stack of glass layers from the bottom side at an angle θ = 30o. The

interface of the glass layers are parallel to each other. The refractive indices of different glass layers are monotonically decreasing as nm = n– m∆n, where nm is the refractive index of the mth slab and ∆n = 0.1 (see the figure). The ray is refracted out parallel to the interface between the (m – 1)th and mth slabs from the right side of the stack. What is the value of m?

[JEE 2017]

36. For an isosceles prism of angle A and refractive index μ, it is found that the angle of minimum deviation δm= A. Which of the following options is/are correct?

(A) For the angle of incidence i1 = A, the ray inside the prism is parallel to the base of the prism

(B) For this prism, the refractive index μ and the angle of prism A are related

as A = −

11 μcos

2 2

(C) At minimum deviation, the incident angle i1 and the refracting angle r1 at the first refracting surface are related by r1 = (i1/2) (D) For this prism, the emergent ray at the second surface will be tangential to the surface when the angle of incidence at the first surface is

−

− −

1 21

Ai =sin sinA 4cos 1 cosA

2

[JEE 2017]


37. Two coherent monochromatic point sources S1 and S2 of wavelength λ = 600

nm are place symmetrically on either side of the center of the circle as shown.

The sources are separated by a distance d = 1.8mm. This arrangement produces interference fringes visible as alternate bright and dark spots on the circumference of the circle. The angular separation between two consecutive bright spots is Δθ. Which of the following options is/are correct?

(A) The angular separation between two consecutive bright spots decreases as

we move from P1 to P2 along the first quadrant.

(B) At P2 the order of the fringe will be maximum.

(C) A dark spot will be formed at the point P2.

(D) The total number of fringes produced between P1 and P2 in the first quadrant is close to 3000.

[JEE 2017]

38. A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length f, as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of

the bent wire ? (These figures are not to scale.)?

(A) (B)


(C) (D) [JEE 2018]

39. Sunlight of intensity 1.3kWm–2 is incident normally on a thin convex lens of

focal length 20cm. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal length. The average intensity of light, in kWm–2, at a distance 22cm from the lens on the other side is _________.

[JEE 2018]

40. A thin convex lens is made of two materials with refractive indices n1 and n2, as shown in figure. The radius of curvature of the left and right spherical surfaces are equal. f is the focal length of the lens when n1 = n2 = n. The focal

length is f + Δf when n1 = n and n2 = n + Δn. Assuming Δn << (n – 1) and

1 < n < 2, the correct statement(s) is/are:

(A) If Δn Δ

<0 then >0n

f

f

(B) For n = 1.5, Δn = 10–3 and f = 20 cm, the value of |Δf | will be 0.02 cm (round off to 2nd decimal place).

(C) Δ Δn

<n

f

f

(D) The relation between Δ Δn

andn

f

fremains unchanged if both the convex

surfaces are replaced by concave surfaces of the same radius of curvature [JEE 2019]


41. A planar structure of length L and width W is made of two different optical

media of refractive indices n1 = 1.5 and n2 = 1.44 as shown in figure. If L >> W,

a ray entering from end AB will emerge from end CD only if the total internal reflection condition is met inside the structure, For L = 9.6 m, if the incident angle θ is varied, the maximum time taken by a ray to exit the plane CD is t × 10–9 s, where t is_____. [Speed of light c = 3 × 108 m/s]

[JEE 2019]

42. In a Young's double slit experiment, the slit separation d is 0.3 mm and the screen distance D is 1m. A parallel beam of light of wavelength 600 nm is incident on the slits at angle α as shown in figure. On the screen, the point O

is equidistant from the slits and distance PO is 11.0mm. Which of the following statement (s) is/are correct ?

(A) For α = 0, there will be constructive interference at point P. (B) For α = 0.36/π degree, there will be destructive interference at point P.

(C) For α = 0.36/π degree, there will be destructive interference at point O. (D) Fringe spacing depends on α.

[JEE 2019]


43. Three glass cylinders of equal height H = 30 cm and same refractive index

n = 1.5 are placed on a horizontal surface as shown in figure. Cylinder I has a

flat top, cylinder II has a convex top and cylinder III has a concave top. The radii of curvature of the two curved tops are same (R = 3 m). If H1, H2, and H3 are the apparent depths of a point X on the bottom of the three cylinders, respectively, the correct statement(s) is/are:

(A) 0.8 cm < (H2 – H1) < 0.9 cm (B) H2 > H3

(C) H3 > H1 (D) H2 > H1 [JEE 2019]

44. A monochromatic light is incident from air on a refracting surface of a prism of angle 75° and refractive index n0 = √3. The other refracting surface of the prism is coated by a thin film of material of refractive index n as shown in figure. The light suffers total internal reflection at the coated prism surface for an

incidence angle of θ ≤ 60°. The value of n2 is _______.

[JEE 2019]

45. An optical bench has 1.5 m long scale having four equal divisions in each cm. While measuring the focal length of a convex lens, the lens is kept at 75 cm mark of the scale and the object pin is kept at 45 cm mark. The image of the

object pin on the other side of the lens overlaps with image pin that is kept at 135 cm mark. In this experiment, the percentage error in the measurement of the focal length of the lens is ____.

[JEE 2019]


46. A large square container with thin transparent vertical walls and filled with

water (refractive index 4/3) is kept on a horizontal table. A student holds a

thin straight wire vertically inside the water 12 cm from one of its corners, as shown schematically in the figure. Looking at the wire from this corner, another student sees two images of the wire, located symmetrically on each side of the line of sight as shown. The separation (in cm) between these images is ____________.

[JEE 2020]

47. A beaker of radius 𝑟 is filled with water (refractive index 4/3) up to a height 𝐻 as shown in the figure on the left. The beaker is kept on a horizontal table rotating with angular speed ω. This makes the water surface curved so that the difference in the height of water level at the center and at the circumference of

the beaker is h (h << H, h << r), as shown in the figure on the right. Take this

surface to be approximately spherical with a radius of curvature 𝑅. Which of the following is/are correct?

(g is the acceleration due to gravity)

(A) 2 2h +r

R =2h

(B) 23r

R =2h

(C) Apparent depth of the bottom of the beaker is close to

−

123H ω H

1+2 2g

(D) Apparent depth of the bottom of the beaker is close to 4

−

123H ω H

1+4g

[JEE 2020]


ANSWER KEY

EXERCISE-I

Part-I Section-A to J

1. A 2. B 3. A 4. C 5. A 6. B 7. D 8. B 9. B 10. C

11. A 12. C 13. C 14. B 15. B 16. A 17. A 18. B 19. C 20. A

21. B 22. B 23. B 24. D 25. B 26. D 27. B 28. C 29. C 30. C

31. B 32. C 33. C 34. A 35. B 36. C 37. B 38. A 39. B 40. D

41. C 42. B 43. A 44. A 45. A 46. A 47. A 48. A 49. C 50. D

51. C 52. A 53. A 54. A 55. C 56. A 57. D 58. D 59. D 60. B

61. C 62. B 63. B 64. D 65. B 66. C 67. A 68. B 69. C 70. C

71. B 72. C 73. C 74. B 75. C 76. A 77. A 78. C 79. A 80. D

81. A 82. A 83. C 84. D 85. B 86. D 87. B 88. C 89. B 90. B

91. A 92. B 93. B 94. A 95. B 96. B 97. D 98. D 99. B 100. D

101. B 102. A 103. D 104. A 105. A 106. B 107. A 108. A 109. B 110. D

111. D 112. C 113. B 114. A 115. D 116. A 117. D 118. B 119. D 120. B

121. D

Part-II Previous Year’s Question (2006-2020)

1. C 2. B 3. D 4. B 5. D 6. B 7. B 8. B 9. B 10. B

11. A 12. A 13. C 14. B 15. B 16. C 17. C 18. A 19. D 20. B

21. B 22. C 23. D 24. C 25. D 26. B 27. C 28. A 29. D 30. A

31. A 32. D 33. C 34. D 35. A 36. D 37. B 38. D 39. D 40. B

41. B 42. 60 43. A 44. B 45. C

EXERCISE-II

PART-I

Section-A

1. BC 2. AD 3. A 4. ABC 5. ACD 6. C 7. AB 8. AC 9. AB

10. AD 11. AC 12. BD 13. AC 14. ABC 15. AD 16. AC 17. BD

Section-B

1. B 2. D 3. C 4. C 5. B 6. B 7. A 8. B 9. A


Section-C

1. (A)-R; (B)-S; (C)-P; (D)-Q

PART-II

1. (i) 75° (ii) 165° (iii) 195° (iv) 285° (v) 315°

2. 9 3. 160 cm; 320 cm 4. 30 5. 3

6. 10 7. 8 8. 2 cm 9. 42cm 10. 8

11. 24 cm 12. 2 13. 12 14. 6 15. 16

16. 4m

17. (i) dy

tanθ = =cot = i;dx

(ii) 1; (iii) y = k2(x/4)4; (iv) 4.0, 1;

(v) It will become parallel to x-axis

18. max

d 1=

R 2 19. 5 20. 45° 21. 9 22.

43

5

23. 60 24. 12 25. 30 26. 12 cm, 10 cm 27. 15 cm 28. (π/4) cm2 29. (i) 0.2 m, (ii) 0.4 m

30. 90 cm from the lens towards right 31. m = 4/3

32. 5 cm 33. (i) λ0 = 600 nm, n = 1.5 (ii) i = sin–1 (0.75) = 48.59°

EXERCISE-III

JEE ADVANCED Previous Year’s Questions

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

7. (A) - p,q,r,s (B)-q, (C)-p,q,r,s (D)-p,q,r,s 8. C 9. C 10. ABC 11. 6

12. B 13. 3 14. (a)-p,r; (b)-q,s,t; (c)-p,r,t; (d)-q, s 15. 6 16. C 17. 2

18. B 19. B 20. C 21. C 22. A 23. D 24. A 25. C 26. B 27. 7

28. B 29. A 30. 2 31. A 32. A 33. ABC 34. AD 35. 8 36. ACD

37. BD 38. D 39. 130.00 40. ABD 41. 50 42. B 43. BD

44. 1.5 45. 0.69 46. 2 47. AD

presented by kailash sharma

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