Top of Pyramid - Test #59- Ray Optics

1.

One face of a prism of apex angle 30 $°$ is silvered and a ray of light is incident on the first face at an angle i such that it retraces its entire path after reflection from the silvered face. If the refractive index of prism material is 2, then the value of i must be -
1. 45 $°$
2. 60 $°$
3. 30 $°$
4. 90 $°$

2.

A ray of light incident on an equilateral prism at grazing incidence emerges from the prism at grazing emergence. The Refractive index of the prism is:

1.	$1.5$	2.	$1.8$
3.	$1.33$	4.	$2$

3.

The refractive index of the material of the prism for violet colour is 1.69 and that for red is 1.65. If the refractive index for mean colour is 1.66, the dispersive power of the material of the prism
1. 0.66
2. 0.06
3. 0.65
4. 0.69

4.

Two identical equiconvex thin lenses each of focal lengths $20$ cm, made of material of refractive index $1.5$ are placed coaxially in contact as shown. Now, the space between them is filled with a liquid with a refractive index of $1.5$. The equivalent power of this arrangement will be:

1.	$+5$ D	2.	zero
3.	$+2.5$ D	4.	$+0.5$ D

5.

In the situation shown, the incident monochromatic ray retraces its path after its incidence on the silvered surface. The speed of light inside the prism will be

1.   $3 x 10^{8} {ms}^{- 1}$
2.   $2 x 10^{8} {ms}^{- 1}$
3.   $1.41 x 10^{8} {ms}^{- 1}$
4.   $1.73 x 10^{8} {ms}^{- 1}$

6.

When a ray is refracted from one medium to another, the wavelength changes from 6000 $\overset{0}{A}$ to 4000 $\overset{0}{A}$ . The critical angle for the interface will be:
1.   $\cos^{- 1} (\frac{2}{3})$
2.   $\sin^{- 1} (\frac{2}{\sqrt{3}})$
3.   $\sin^{- 1} (\frac{2}{3})$
4.   $\cos^{- 1} (\frac{2}{\sqrt{3}})$

7. A ray of light falls on a transparent sphere as shown in the figure. If the final ray emerges from the sphere parallel to the horizontal diameter, then calculate the refractive index of the sphere. Consider that the sphere is kept in the air.

1.	$\sqrt{2}$	2.	$\sqrt{3}$
3.	$\sqrt{3 / 2}$	4.	$\sqrt{4 / 3}$

8.

Two plane mirrors, $A$ and $B$ are aligned parallel to each other, as shown in the figure. A light ray is incident at an angle of $30^\circ$ at a point just inside one end of $A.$ The plane of incidence coincides with the plane of the figure. The maximum number of times the ray undergoes reflections (excluding the first one) before it emerges out is:

1. $28$
2. $30$
3. $32$
4. $34$

9. A square of side $3$ cm is placed at a distance of $25$ cm from a concave mirror of focal length $10$ cm. The centre of the square is at the axis of the mirror and the plane is normal to the axis. The area enclosed by the image of the square is:

1.	$4~\text{cm}^2 $	2.	$6~\text{cm}^2 $
3.	$16~\text{cm}^2 $	4.	$36~\text{cm}^2 $

10.

One face of a rectangular glass plate 6 cm thick is silvered. An object held 8 cm in front of the first face, forms an image 10 cm behind the silvered face. The refractive index of the glass is [Consider that light ray returns back in the first medium]
1. 0.4
2. 0.8
3. 1.5
4. 1.6

11.

The image of point P when viewed from the top of the slabs will be

1. 2.0 cm above P
2. 1.5 cm above P
3. 2.0 cm below P
4. 1 cm above P

12. There is an equi-convex glass lens with a radius of each face as $R$ and $\mu_{ga}= \frac{3}{2}$ and $\mu_{wa} = \frac{4}{3}$. If there is water in the object space and air in the image space, then the focal length is:
1. $2R$

2. $R$
3. $\frac{3}{2}R$
4. $R^2$

13.

A rectangular glass slab ABCD, of refractive index $n_{1}$ , is immersed in water of the refractive index $n_{2} (n_{1} > n_{2})$ . A ray of light is incident at the surface AB of the slab as shown. The maximum value of the angle of incidence $α_{m a x}$ , such that the ray comes out only from the other surface CD is given by

1.   $\sin^{- 1} [\frac{n_{1}}{n_{2}} \cos (\sin^{- 1} \frac{n_{2}}{n_{1}})]$
2.   $\sin^{- 1} [n_{1} \cos (\sin^{- 1} \frac{1}{n_{2}})]$
3.   $\sin^{- 1} (\frac{n_{1}}{n_{2}})$
4.   $\sin^{- 1} (\frac{n_{2}}{n_{1}})$

14.

The slab of a refractive index material equal to $2$ shown in the figure has a curved surface $APB$ of a radius of curvature of $10~\text{cm}$ and a plane surface $CD.$ On the left of $APB$ is air and on the right of $CD$ is water with refractive indices as given in the figure. An object $O$ is placed at a distance of $15~\text{cm}$ from the pole $P$ as shown. The distance of the final image of $O$ from $P$ as viewed from the left is:

1.	$20~\text{cm}$	2.	$30~\text{cm}$
3.	$40~\text{cm}$	4.	$50~\text{cm}$

15.

The focal length of the objective lens and the eye lens is 4 mm and 25 mm respectively in a compound microscope. The distance between objective and eyepiece lens is 16 cm. Find its magnifying power for relaxed eye position-
1. 32.75
2. 327.5
3. 0.3275
4. None of the above

16.

An air bubble in a sphere having 4 cm diameter that appears 1 cm from the surface nearest to the eye when looked along diameter. If ${}_{a}μ_{g}$ = 1.5, the distance of bubble from the refracting surface is
1. 1.2 cm
2. 3.2 cm
3. 2.8 cm
4. 1.6 cm

17.

Which one of the following spherical lenses does not exhibit dispersion? The radii of curvature of the surfaces of the lenses are as given in the diagrams

1.		2.
3.		4.

18.

A plano-convex lens when silvered in the plane side behaves like a concave mirror of
focal length 30 cm. However, when silvered on the convex side it behaves like a concave
mirror of focal length 10 cm. Then the refractive index of its material will be
1. 3.0
2. 2.0
3. 2.5
4. 1.5

19.

A telescope has an objective lens of 10 cm diameter and is situated at a distance of one kilometre from two objects. The minimum distance between these two objects, which can be resolved by the telescope, when the mean wavelength of light is 5000 Å, is of the order of
1. 0.5 m
2. 5 m
3. 5 mm
4. 5 cm

20.

A beam of light from a source L is incident normally on a plane mirror fixed at a certain distance x from the source. The beam is reflected back as a spot on a scale placed just above the source L. When the mirror is rotated through a small angle $θ$ , the spot of light is found to move through a distance y on the scale. The angle $θ$ is given by
1. $\frac{y}{2 x}$
2. $\frac{y}{x}$
3. $\frac{x}{2 y}$
4. $\frac{x}{y}$

21.

Two identical glass $(μ_{g} = 3 / 2)$ equi-convex lenses of focal length $f$ each are kept in contact. The space between the two lenses is filled with water $(μ_{w} = 4 / 3)$ . The focal length of the combination is
1. $f / 3$
2. $f$
3. $\frac{4 f}{3}$
4. $\frac{3 f}{4}$

22.

An air bubble in a glass slab with refractive index 1.5 (near normal incidence) is 5 cm deep when viewed from one surface and 3 cm deep when viewed from the opposite face. The thickness (in cm) of the slab is
1. 8
2. 10
3. 12
4. 16

23.

A person can see clearly objects only when they lie between 50 cm and 400 cm from his eyes. In order to increase the maximum distance of distinct vision to infinity, the type and power of the correcting lens, the person has to use will be-
1. convex, +2.25 diopter
2. concave, - 0.25 diopter
3. concave, - 0.2 diopter
4. convex, + 0.15 diopter

24.

Match the corresponding entries of Column 1 with Column 2. [Where m is the magnification produced by the mirror]
Column 1 Column 2
A. m=-2 a. Convex mirror
B. m=-1/2 b. Concave mirror
C. m=+2 c. Real image
D. m=+1/2 d. Virtual Image
1. A->a and c;B->a and d; C->a and b; D->c and d
2. A->a and d; B->b and c; C->b and d; D-> b and c
3. A->c and d; B->b and d;C->b and c;D->a and d
4. A->b and c; B->b and c; C->b and d; D->a and d

25.

A beam of light consisting of red, green and blue colours 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
1. separate the blue colour part from the red and green colours
2. separate all the three colours from one another
3. not separate the three colours at all
4. separate the red colour part from the green and blue colours

26.

If the focal length of the objective lens is increased, then magnifying power of :
1. microscope will increase but that of telescope decrease
2. microscope and telescope both will increase
3. microscope and telescope both will decrease
4. microscope will decrease but that of telescope will increase

27.

The angle of a prism is A. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2A on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index μ of the prism is
1. 2sinA

2. 2cosA

3. 1/2cosA

4. tanA

28.

For a normal eye, the cornea of eye provides a converging power of 40 D and the least converging power of the eye lens behind the cornea is 20 D. Using this information, the distance between the retina and the cornea-eye lens can be estimated to be
1. 5 cm
2. 25 cm
3. 1.67 cm
4. 1.5 cm

29.

The magnifying power of a telescope is 9. When it is adjusted for parallel rays the distance between the objective and eyepiece is 20cm. The focal length of lenses are
1. 10cm,10cm
2. 15cm,5cm
3. 18cm,2cm
4. 11cm,9cm

30. A rod of length $10$ cm lies along the principal axis of a concave mirror of focal length $10$ cm in such a way that its end closer to the pole is $20$ cm away from the mirror. The length of the image is:

1.	$10$ cm	2.	$15$ cm
3.	$2.5$ cm	4.	$5$ cm

31.

Which of the following is not due to total internal reflection?
(1) Difference between apparent and real depth of a pond
(2) Mirage on hot summer days
(3) Brilliance of diamond
(4) Working of optical fibre

32.

A ray of light traveling in a transparent medium of refractive index $μ$ falls, on a surface separating the medium from the air at an angle of incidence of 45 $°$ . For which of the following values of $μ$ the ray can undergo total internal reflection?
1. $μ = 1.33$
2. $μ = 1.40$
3. $μ = 1.50$
4. $μ = 1.25$

33.

The speed of light in media $M_{1}$ and $M_{2}$ is $1.5 \times 10^{8} m / s$ and $2.0 \times 10^{8} m / s$ respectively. A ray of light enters from medium $M_{1}$ to $M_{2}$ at an incidence angle i. If the ray suffers total internal reflection, the value of i is
1. equal to $\sin^{- 1} (\frac{2}{3})$
2. equal to or less than $\sin^{- 1} (\frac{3}{5})$
3. equal to or greater than $\sin^{- 1} (\frac{3}{4})$
4. less than $\sin^{- 1} (\frac{2}{3})$

34.

A convex lens of focal length 15 cm forms three times magnified real image of an object placed in front of it. Distance of object from the lens is
1. 10 cm
2. 20 cm
3. 25 cm
4. 17.5 cm

35.

A luminous object is placed at a distance of 30 cm from the convex lens of focal length 20 cm. On the other side of the lens, at what distance from the lens, a convex mirror of radius of curvature 10 cm, be placed in order to have an upright image of the object coincident with it?
1. 12 cm
2. 30cm
3. 50 cm
4. 60cm

36.

A plano-convex lens is made of material of refractive index 1.6. The radius of curvature of the curved surface is 60 cm. The focal length of the lens is
1. 50 cm
2. 100cm
3. 200 cm
4. 400 cm

37.

A plane convex lens is made of a material of refractive index $μ = 1.5$ . The radius of curvature of curved surface of the lens is 20 cm. If its plane surface is silvered, the focal length of the silvered lens will be
1. 10cm
2. 20cm
3. 40cm
4. 80cm

38.

A bulb is located on a wall. Its image is to be obtained on a parallel wall with the help of a convex lens. If the distance between parallel walls is 'd', then the required focal length of the lens placed i between the walls is
1. only $\frac{d}{4}$
2. only $\frac{d}{2}$
3. more than $\frac{d}{4}$ but less than $\frac{d}{2}$
4. less than or equal to $\frac{d}{4}$

39.

A convex lens is dipped in a liquid whose refractive index is equal to the refractive index of the lens. Then its focal length will
1. become zero
2. become infinite
3. become small, but non-zero
4. remain unchanged

40.

An equiconvex lens is cut into two halves along (a) XOX' and (b) YOY' as shown in the figure. Let f, f' and f'' be the focal lengths of the complete lens, of each half in case (a) and of each half in case (b), respectively. Choose the correct statement from the following

1. f'=f, f''=2f
2. f'=2f, f''=f
3. f'=f, f''=f
4. f'=2f, f''=2f

41.

A thin prism of angle $15 °$ made of glass of refractive index $μ_{1} = 1.5$ is combined with another prism of glass of refractive index $μ_{2} = 1.75$ . The combination of the prisms produces dispersion without deviation. The angle of the second prism should be
1. $5 °$
2. $7 °$
3. $10 °$
4. $12 °$

42.

A converging beam of rays is incident on a diverging lens. Having passed through the lens ,the rays intersect at a point 15cm from the lens on the opposite side. If the lens is removed ,the point where the rays meet will move 5 cm closer to the lens. The focal length of the lens is
1. 5cm
2. -10cm
3. 20cm
4. -30cm

43.

A concave mirror of focal length $f_{1}$ is placed at a distance of d from a convex lens of focal length $f_{2}$ . A beam of light coming from infinity and falling on this convex lens-concave mirror combination returns to infinity. The distance d must equal.
1. $2 f_{1} + f_{2}$
2. $- 2 f_{1} + f_{2}$
3. $f_{1} + f_{2}$
4. $- f_{1} + f_{2}$

44.

A ray of light incident at an angle of incidence, i, on one face of a prism of angle A(assumed to be small) and emerges normally from the opposite face. If the refractive index of the prism is $μ$ , the angle of the incidence i, is nearly equal to
1. $\frac{A}{μ}$
2. $\frac{A}{2 μ}$
3. $μA$
4. $\frac{μA}{2}$

45.

A plano-convex lens fits exactly into a plane-concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices $μ_{1} and μ_{2}$ and R is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is
1. $\frac{R}{2 (μ_{1} + μ_{2})}$
2. $\frac{R}{2 (μ_{1} - μ_{2})}$
3. $\frac{R}{(μ_{1} - μ_{2})}$
4. $\frac{2 R}{(μ_{2} - μ_{1})}$

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1.	\(\sqrt{2}\)	2.	\(\sqrt{3}\)
3.	\(\sqrt{3 / 2}\)	4.	\(\sqrt{4 / 3}\)

1.	\(4~\text{cm}^2 \)	2.	\(6~\text{cm}^2 \)
3.	\(16~\text{cm}^2 \)	4.	\(36~\text{cm}^2 \)

1.	\(20~\text{cm}\)	2.	\(30~\text{cm}\)
3.	\(40~\text{cm}\)	4.	\(50~\text{cm}\)

1.	\(1.5\)	2.	\(1.8\)
3.	\(1.33\)	4.	\(2\)

1.	\(+5\) D	2.	zero
3.	\(+2.5\) D	4.	\(+0.5\) D

1.	\(10\) cm	2.	\(15\) cm
3.	\(2.5\) cm	4.	\(5\) cm

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