Topic : 24 [Geometrical optics]

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1. A light wave travelling linearly in a medium of dielectric constant 4 , incidents on the horizontal
interface separating medium with air. The angle of incidence for which the total intensity of
incident wave will be reflected back into the same medium will be:
(Given: relative permeability of medium μr = 1 )
(A) 10∘ (B) 20∘ (C) 30∘ (D) 60∘
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2. The difference of speed of light in the two media A and B(vA − vB ) is 2.6 × 107 m/s. If the
refractive index of medium B is 1.47, then the ratio of refractive index of medium B to medium
A is: (Given: speed of light in vacuum C = 3 × 108 ms −1 )
(A) 1.303 (B) 1.318 (C) 1.13 (D) 0.12
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3. Consider a light ray travelling in air is incident into a medium of refractive index √2n. The
incident angle is twice that of refracting angle. Then, the angle of incidence will be : 2n
n n
(A) sin−1 (√n) (B) cos −1 (√2) (C) sin−1 (√2n) (D) 2cos −1 (√2)
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4. A convex lens has power P. It is cut into two halves along its principal axis. Further one piece
(out of the two halves) is cut into two halves perpendicular to the principal axis (as shown in
figure). Choose the incorrect option for the reported pieces.
(A) Power of L1 = P/2
(B) Power of L2 = P/2
(C) Power of L3 = P/2
(D) Power of L1 = P
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5. The refracting angle of a prism is A and refractive index of the material of the prism is cot(A/2).
Then the angle of minimum deviation will be –
(A) 180 − 2A (B) 90 − A (C) 180 + 2A (D) 180 − 3A
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6. The speed of light in media 'A' and 'B' are 2.0 × 1010 cm/s and 1.5 × 1010 chm/s respectively.
A ray of light enters from the medium B to A at an incident angle 'θ'. If the ray suffers total
internal reflection, then
3 2 3 3
(A) θ = sin−1 (4) (B) θ > sin−1 (3) (C) θ < sin−1 (4) (D) θ > sin−1 (4)
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7. Which of the following statement is correct?
(A) In primary rainbow, observer sees red colour on the top and violet on the bottom
(B) In primary rainbow, observer sees violet colour on the top and red on the bottom

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 (C) In primary rainbow, light wave suffers total internal reflection twice before coming out of
water drops
(D) Primary rainbow is less bright than secondary rainbow
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8. Time taken by light to travel in two different materials A and B of refractive indices μA and μB of
same thickness is t1 and t 2 respectively. If t 2 − t1 = 5 × 10−10 s and the ratio of μA to μB is
1: 2. Then the thickness of material, in meter is:
(Given vA and vB are velocities of light in A and B materials respectively).
(A) 5 × 10−10 va m (B) 5 × 10−10 m (C) 1.5 × 10−10 m (D) 5 × 10−10 vB m
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9. For an object placed at a distance 2.4 m from a lens, a sharp focused image is observed on a screen
placed at a distance 12 cm from the lens. A glass plate of refractive index 1.5 and thickness 1 cm
is introduced between lens and screen such that the glass plate plane faces parallel to the screen.
By what distance should the object be shifted so that a sharp focused image is observed again on
the screen?
(A) 0.8 m (B) 3.2 m (C) 1.2 m (D) 5.6 m
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10. Light travels in two media M1 and M2 with speeds 1.5 × 108 ms −1 and 2.0 × 108 ms −1
respectively. The critical angle between them is:
3 2 3 2
(A) tan−1 ( ) (B) tan−1 ( ) (C) cos −1 ( )(D) sin−1 ( )
√7 3 4 3
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11. As shown in the figure, after passing through the medium 1 . The speed of light v2 in medium 2
will be :
(Given c = 3 × 108 ms −1 )

(A) 1.0 × 108 ms −1

(B) 0.5 × 108 ms −1
(C) 1.5 × 108 ms −1
(D) 3.0 × 108 ms −1
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12. In normal adjustment, for a refracting telescope, the distance between objective and eye piece is
30 cm. The focal length of the objective, when the angular magnification of the telescope is 2,
will be:
(A) 20 cm (B) 30 cm (C) 10 cm (D) 15 cm
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13. Light enters from air into a given medium at an angle of 45∘ with interface of the air-medium
surface. After refraction, the light ray is deviated through an angle of 15∘ from its original
direction. The refractive index of the medium is :
(A) 1.732 (B) 1.333 (C) 1.414 (D) 2.732
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14. The power of a lens (biconvex) is 1.25 m−1 in particular medium. Refractive index of the lens is
1.5 and radii of curvature are 20 cm and 40 cm respectively. The refractive index of surrounding
medium:
(A) 1.0 (B) 9/7 (C) 3/2 (D) 4/3
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15. A convex lens of focal length 40 cm forms an image of an extended source of light on a
photoelectric cell. A current I is produced. The lens is replaced by another convex lens having the
same diameter but focal length 20 cm. The photoelectric current now is:
I
(A) I (B) 2I (C) 4I (D) 2
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A
16. If the refractive index of the material of a prism is cot⁡ ( 2 ), where A is the angle of prism then the
angle of minimum deviation will be:
π π
(A) 2 − 2 A (B) π − 2 A (C) 2 − A (D) π − A
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17. A convex mirror of radius of curvature 30 cm forms an image that is half the size of the object.
The object distance is :
(A) 45 cm (B) −15 cm (C) −45 cm (D) 15 cm
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18. A biconvex lens of refractive index 1.5 has a focal length of 20 cm in air. Its focal length when
immersed in a liquid of refractive index 1.6 will be:
(A) +16 cm (B) −160 cm (C) +160 cm (D) −16 cm
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19. If the distance between object and its two times magnified virtual image produced by a curved
mirror is 15 cm, the focal length of the mirror must be:
(A) −10 cm (B) 10/3 cm (C) 15 cm (D) −12 cm
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20. The refractive index of a prism with apex angle A is cot⁡ A/2. The angle of minimum deviation
is :

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 (A) δm = 180∘ − 2A (B) δm = 180∘ − 3A
(C) δm = 180∘ − A (D) δm = 180∘ − 4A
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21. A 2 meter long scale with least count of 0.2 cm is used to measure the locations of objects on an
optical bench. While measuring the focal length of a convex lens, the object pin and the convex
lens are placed at 80 cm mark and 1 m mark, respectively. The image of the object pin on the
other side of lens coincides with image pin that is kept at 180 cm mark. The % error in the
estimation of focal length is:
(1) 1.02 (2) 0.85 (3) 1.70 (4) 0.51
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22. When one light ray is reflected from a plane mirror with 30∘ angle of reflection, the angle of
deviation of the ray after reflection is:
(1) 140∘ (2) 120∘ (3) 110∘ (4) 130∘
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23. An ice cube has a bubble inside. When viewed from one side the apparent distance of the bubble
is 12 cm. when viewed from the opposite side, the apparent distance of the bubble is observed as
4 cm. If the side of the ice cube is 24 cm, the refractive index of the ice cube is
4 3 2 6
(1) 3 (2) 2 (3) 3 (4) 5
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24. A vessel of depth ' d ' is half filled with oil of refractive index n1 and the other half is filled with
water of refractive index n2 . The apparent depth of this vessel when viewed from above will be-
dn1 n2 d(n1 +n2 ) dn n 2 d(n1 +n2 )
(1) (n (2) (3) 2(n 1+n2 ) (4)
1 +n2 ) 2n1 n2 1 2 n 1 n2
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25. A monochromatic light wave with wavelength λ1 and frequency v1 in air enters another medium.
If the angle of incidence and angle of refraction at the interface are 45∘ and 30∘ respectively, then
the wavelength λ2 and frequency v2 of the refracted wave are :
1
(1) λ2 = λ1 , v2 = √2v1 (2) λ2 = λ ,v = v1
√2 1 2
1
(3) λ2 = √2λ1 , v2 = v1 (4) λ2 = λ1 , v2 = v
√2 1
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26. A thin prism P1 with an angle 6∘ and made of glass of refractive index 1.54 is combined with
another prism P2 made from glass of refractive index 1.72 to produce dispersion without average
deviation. The angle of prism P2 is :
(1) 6∘ (2) 1.3∘ (3) 7.8∘ (4) 4.5∘
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27. As shown in the figure, a combination of a thin plano concave lens and a thin plano convex lens
is used to image an object placed at infinity. The radius of curvature of both the lenses is 30 cm
and refraction index of the material for both the lenses is 1.75. Both the lenses are placed at
distance of 40 cm from each other.
Due to the combination, the image of the object is formed at distance x = cm, from concave
lens.

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28. When a beam of white light is allowed to pass through convex lens parallel to principal axis, the
different colours of light converge at different point on the principle axis after refraction. This is
called :
(1) Scattering (2) Chromatic aberration
(3) Spherical aberration (4) Polarisation
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29. A scientist is observing a bacteria through a compound microscope. For better analysis and to
improve its resolving power he should. (Select the best option)
(1) Increase the wave length of the light
(2) Increase the refractive index of the medium between the object and objective lens
(3) Decrease the focal length of the eye piece
(4) Decrease the diameter of the objective lens
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30. A thin cylindrical rod of length 10 cm is placed horizontally on the principle axis of a concave
mirror of focal length 20 cm. The rod is placed in a such a way that mid point of the rod is at
x
40 cm from the pole of mirror. The length of the image formed by the mirror will be 3 cm. The
value of x is _____ .
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 ANSWER KEY
Ques. Ans Ques. Ans Ques. Ans Ques. Ans Ques. Ans Ques. Ans Ques. Ans
1 D 2 C 3 C 4 A 5 A 6 D 7 A
8 A 9 B 10 A 11 A 12 A 13 C 14 B
15 A 16 B 17 B 18 B 19 A 20 A 21 C
22 B 23 B 24 B 25 B 26 D 27 120 28 B
29 B 30 32

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