Q.1 Rainbow is formed due to :-

(1) Scattering \& refraction

(2) Total internal reflection \& dispersion

(3) Reflection only

(4) Diffraction and dispersion

[AIPMT 2000]

Q.2 For a plano convex lenx \((\mu=1.5)\) has radius of curvature \(10 \mathrm{~cm}\). It is silvered on its plane surface. Find focal length after silvering:-

(1) \(10 \mathrm{~cm}\)

(2) \(20 \mathrm{~cm}\)

(3) \(15 \mathrm{~cm}\)

(4) \(25 \mathrm{~cm}\)

[AIPMT 2000]

Q.3 A tall man of height 6 feet, want to see his full image. Then required minimum length of the mirror will be:-

(1) 12 feet

(2) 3 feet

(3) 6 feet

(4) Any length

[AIPMT 2000]

Q.4 A bubble in glass slab \((\mu=1.5)\) when viewed from one side appears at \(5 \mathrm{~cm}\) and \(2 \mathrm{~cm}\) from other side, then thickness of slab is:-

(1) \(3.75 \mathrm{~cm}\)

(2) \(3 \mathrm{~cm}\)

(3) \(10.5 \mathrm{~cm}\).

(4) \(2.5 \mathrm{~cm}\)

[AIPMT 2000]

Q.5 A ray of light travelling in air have wavelength \(\lambda\), frequency \(n\), velocity \(\mathrm{V}\) and intensity I. If this ray enters into water than these parameters are \(\lambda^{\prime}, \mathrm{n}^{\prime}, \mathrm{v}^{\prime}\) and \(\mathrm{I}^{\prime}\) respectively. Which relation is correct from following-

(1) \(\lambda=\lambda^{\prime}\)

\((2) n=n^{\prime}\)

(3) \(v=v^{\prime}\)

(4) \(I=I^{\prime}\)

[CPMT 2001]

Q.6 Optical fibre are based on -

(1) Total internal reflection

(2) Less scattering

(3) Refraction

(4) Less absorption coefficient

[CPMT 2001]

Q.7 Relation between critical angles of water and glass is

(1) \(\mathrm{C}_{\mathrm{w}}>\mathrm{C}_{\mathrm{g}}\)

(2) \(\mathrm{C}_{\mathrm{w}}<\mathrm{C}_{\mathrm{g}}\)

(3) \(\mathrm{C}_{\mathrm{w}}=\mathrm{C}_{\mathrm{g}}\)

(4) \(\mathrm{C}_{\mathrm{w}}=\mathrm{C}_{\mathrm{g}}=0\)

[AIPMT 2000, CPMT 2001]

Q.8 A plano convex lens is made of refractive index 1.6. The radius of curvature of the curved surface is 60 \(\mathrm{cm}\). The focal length of the lens is

[AIPMT 1999; Pb.PMT 1999; BHU 2001]

(1) \(50 \mathrm{~cm}\)

(2) \(100 \mathrm{~cm}\)

(3) \(200 \mathrm{~cm}\)

(4) \(400 \mathrm{~cm}\)

Q.9 A disc is placed on a surface of pond which has refractive index \(\frac{5}{3}\). A source of light is placed \(4 \mathrm{~m}\) below the surface of liquid. The minimum radius of disc will be so light is not coming out [AIPMT 2001]

(1) \(\infty\)

(2) \(3 \mathrm{~m}\).

(3) \(6 \mathrm{~m}\).

(4) \(4 \mathrm{~m}\).

Q.10 For the given incident ray as shown in figure, the condition of total internal refraction of this ray the minimum refractive index of prism will be :-

(1) \(\frac{\sqrt{3}+1}{2}\)

(2) \(\frac{\sqrt{2}+1}{2}\)

(3) \(\sqrt{\frac{3}{2}}\)

(4) \(\sqrt{\frac{7}{6}}\)

[AIPMT 2002] Q.11 A body is located on a wall. Its image of equal size is to be obtained on a parallel wall with the help of a convex lens. The lens is placed at a distance \(\mathrm{d}\) ahead of second wall, then the required focal length will be:

[AIPMT-2002]

(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 \(\frac{d}{4}\)

Q.12 A bulb is located on a wall. Its image is to be obtained on a parallel wall with the help of convex lens. If the distance between parallel walls is ' \(\mathrm{d}\) ' then required focal length of lens placed in between the walls is :-

[AIPMT 2002]

(1) Only \(\frac{d}{4}\)

(2) Only \(\frac{d}{2}\)

(3) More than \(\frac{d}{4}\) but less than \(\frac{\mathrm{d}}{2}\)

(4) Less than or equal to \(\frac{d}{4}\)

Q.13 In the formation of a rainbow light from the sun on water droplets undergoes

(1) Dispersion only

[AIPMT 2000; Orissa JEE 2002; MP PET 2003]

(3) Dispersion and total internal reflection

(2) Only total internal reflection

(4) None of these

Q.14 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

[AIPMT 2003]

Q.15 An equiconvex lens is cut into two halves along (i) \(\mathrm{XOX}^{\prime}\) and (ii) \(\mathrm{YOY}^{\prime}\) as shown in the figure. Let \(\mathrm{f}, \mathrm{f}^{\prime}\), \(\mathrm{f}^{\prime \prime}\) be the focal lengths of the complete lens, of each half in case (i), and of each half in case (ii), respectively Choose the correct statement from the following :-

[AIPMT 2003]

(1) \(f^{\prime}=f, f^{\prime \prime}=2 f\)

(2) \(\mathrm{f}^{\prime}=2 \mathrm{f}, \mathrm{f}^{\prime \prime}=\mathrm{f}\)

(3) \(f^{\prime}=f, f^{\prime \prime}=f\)

(4) \(f^{\prime}=2 \mathrm{f}, \mathrm{f}^{\prime \prime}=2 \mathrm{f}\)

Q.16 A beam of light composed of red and green rays is incident obliquely at a point on the face of a rectangular glass slab. When coming out on the opposite parallel face, the red and green rays emerge from :-

(1) Two points propagating in two different parallel directions

[AIPMT 2004]

(2) One point propagating in two different directions

(3) One point propagating in the same direction

(4) Two points propagating in two different non parallel directions Q.17 The refractive index of the material of a prism is \(\sqrt{2}\) and its refracting angle is \(30^{\circ}\). One of the refracting surfaces of the prism is made a mirror inwards. A beam of monochromatic light entering the prism from the other face will retrace its path after reflection from the mirrored surface if its angle of incidence on the prism is :-

(1) \(60^{\circ}\)

(2) \(0^{\circ}\)

(3) \(30^{\circ}\)

(4) \(45^{\circ}\)

[AIPMT 2004]

Q.18 A telescope has an objective lens of \(10 \mathrm{~cm}\). diameter and is situated at a distance of one kilometer from two objects. The minimum distance between these two objects, which can be resolved by the telescope, when the mean wavelength of light is \(5000 \AA\), is of the order of :-

(1) \(5 \mathrm{~m}\).

(2) \(5 \mathrm{~mm}\).

(3) \(5 \mathrm{~cm}\).

(4) \(0.5 \mathrm{~m}\)

[AIPMT 2004]

Q.19 The angular resolution of a \(10 \mathrm{~cm}\) diameter telescope at a wavelength of \(5000 \AA\) is of the order of :

[AIPMT-2005]

(1) \(10^{6} \mathrm{rad}\)

(2) \(10^{-2} \mathrm{rad}\)

(3) \(10^{-4} \mathrm{rad}\)

(4) \(10^{-6} \mathrm{rad}\)

Q.20 A microscope is focussed on a mark on a piece of paper and then a slab of glass of thickness \(3 \mathrm{~cm}\) and refractive index 1.5 is placed over the mark. How should the microscope be moved to get the mark in focus again :-

[AIPMT 2006]

(1) \(1 \mathrm{~cm}\) upward

(2) \(4.5 \mathrm{~cm}\) downward

(3) \(1 \mathrm{~cm}\) downward

(4) \(2 \mathrm{~cm}\) upward

Q.21 The frequency of a light wave in a material is \(2 \times 10^{14} \mathrm{~Hz}\) and wavelength is \(5000 \AA\). The refractive index of material will be :

(1) 1.33

(2) 1.40

(3) 1.50

(4) 3.00

[AIPMT 2007]

Q.22 A small coin is resting on the bottom of a beaker filled with a liquid. A ray of light from the coin travels upto the surface of the liquid and moves along its surface (see figure).

[AIPMT 2007]

How fast is the light travelling in the liquid?

(1) \(1.2 \times 10^{8} \mathrm{~m} / \mathrm{s}\)

(2) \(1.8 \times 10^{8} \mathrm{~m} / \mathrm{s}\)

(3) \(2.4 \times 10^{8} \mathrm{~m} / \mathrm{s}\)

(4) \(3.0 \times 10^{8} \mathrm{~m} / \mathrm{s}\)

Q.23 A boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length \(10 \mathrm{~cm}\). The diameter of the sun is \(1.39 \times 10^{9} \mathrm{~m}\) and its mean distance from the earth is \(1.5 \times 10^{11}\) \(\mathrm{m}\). What is the diameter of the sun's image on the paper?

[AIPMT-2008]

(1) \(9.2 \times 10^{-4} \mathrm{~m}\)

(2) \(6.5 \times 10^{-4} \mathrm{~m}\)

(3) \(6.5 \times 10^{-5} \mathrm{~m}\)

(4) \(12.4 \times 10^{-4} \mathrm{~m}\)

Q.24 Two thin lenses of focal lengths \(f_{1}\) and \(f_{2}\) are in contact and coaxial.The power of the combination is:-

[AIPMT 2008]

(1) \(\frac{f_{1}+f_{2}}{2}\)


(3) \(\sqrt{\frac{f_{1}}{f_{2}}}\)

(4) \(\sqrt{\frac{f_{2}}{f_{1}}}\) Q.25 Alens having focal length f and aperture of diameter \(\mathrm{d}\) forms an image of intensity I. Aperture of diameter \(\frac{\mathrm{d}}{2}\) in central region of lens is covered by a black paper. Focal length of lens and intensity of image now will be respectively :-

[AIPMT 2010]

(1) \(\frac{\mathrm{f}}{2}\) and \(\frac{\mathrm{I}}{2}\)

(2) f and \(\frac{I}{4}\)

(3) \(\frac{3 \mathrm{f}}{4}\) and \(\frac{\mathrm{I}}{2}\)

(4) fand \(\frac{3 I}{4}\)

Q.26 A ray of light travelling in a transparent medium of refractive index \(\mu\), falls on a surface separating the medium from air at an angle of incidence of \(45^{\circ}\). For which of the following value of \(\mu\) the ray can undergo total internal reflection?

(1) \(\mu=1.25\)

(2) \(\mu=1.33\)

(3) \(\mu=1.40\)

(4) \(\mu=1.50\)

[AIPMT 2010]

Q.27 The speed of light in media \(\mathrm{M}_{1}\) and \(\mathrm{M}_{2}\) is \(1.5 \times 10^{8} \mathrm{~m} / \mathrm{s}\) and \(2.0 \times 10^{8} \mathrm{~m} / \mathrm{s}\) respectively. A ray of light enters from medium \(\mathrm{M}_{1}\) to \(\mathrm{M}_{2}\) at an incidence angle i. If the ray suffers total internal reflection, the value of \(i\) is :-

[AIPMT 2010]

(1) Equal to or less than \(\sin ^{-1}\left(\frac{3}{5}\right)\)

(2) Equal to or greater than \(\sin ^{-1}\left(\frac{3}{4}\right)\)

(3) Less than \(\sin ^{-1}\left(\frac{2}{3}\right)\)

(4) Equal to \(\sin ^{-1}\left(\frac{2}{3}\right)\)

Q.28 A ray of light is incident on a \(60^{\circ}\) prism at the minimum deviation position. The angle of refraction at the first face (i.e., incident face) of the prism is:-

(1) \(30^{\circ}\)

(2) \(45^{\circ}\)

(3) \(60^{\circ}\)

(4) Zero

[AIPMT 2010]

Q.29 Which of the following is not due to total internal reflection?

(1) Working of optical fibre

(2) Difference between apparent and real depth of a pond

(3) Mirage on hot summer days

(4) Brilliance of diamond

[AIPMT(Pre) 2011]

Q.30 A conversing beam of rays is incident on a diverging lens. Having passed though the lens the rays intersect at a point \(15 \mathrm{~cm}\) from the lens on the opposite side. If the lens is removed the point where the rays meets will move \(5 \mathrm{~cm}\) closer to the lens. The focal length of the lens is :[AIPMT Mains 2011]

(1) \(-10 \mathrm{~cm}\)

(2) \(20 \mathrm{~cm}\)

(3) \(-30 \mathrm{~cm}\)

(4) \(5 \mathrm{~cm}\)

Q.31 A thin prism of angle \(15^{\circ}\) made of glass of refractive index \(\mu_{1}=1.5\) is combined with another prism of glass of refractive index \(\mu_{2}=1.75\). the combination of the prism produces dispersion without deviation . The angle of the second prism should be:

(1) \(7^{\circ}\)

(2) \(10^{\circ}\)

(3) \(12^{\circ}\)

(4) \(5^{0}\)

[AIPMT Mains 2011]

Q.32 A bioconvex lens has a radius of curvature of magnitude \(20 \mathrm{~cm}\). Which one of the following options describe best the image formed of an object of height \(2 \mathrm{~cm}\) placed \(30 \mathrm{~cm}\) from the lens?

(1) Virtual, upright, height \(=1 \mathrm{~cm}\)

(2) Virtual, upright, height \(=0.5 \mathrm{~cm}\)

(3) Real, inverted, height \(=4 \mathrm{~cm}\)

(4) Real, inverted, height \(=1 \mathrm{~cm}\)

Q.33 The dimensions of \(\left(\mu_{0} \in_{0}\right)^{-1 / 2}\) are :

(1) \(\left[\mathrm{L}^{1 / 2} \mathrm{~T}^{-1 / 2}\right]\)

(2) \(\left[\mathrm{L}^{-1} \mathrm{~T}\right]\)

(3) \(\left[\mathrm{L} \mathrm{T}^{-1}\right]\)

(4) \(\left[\mathrm{L}^{-1 / 2} \mathrm{~T}^{1 / 2}\right]\)

[AIPMT-2011] Q.34 The magnifying power of a telescope is 9 . When it is adjusted for parallel rays the distance between the objective and eyepiece is \(20 \mathrm{~cm}\). The focal length of lenses are :

(1) \(18 \mathrm{~cm}, 2 \mathrm{~cm}\)

(2) \(11 \mathrm{~cm}, 9 \mathrm{~cm}\)

(3) \(10 \mathrm{~cm}, 10 \mathrm{~cm}\)

(4) \(15 \mathrm{~cm}, 5 \mathrm{~cm}\)

Q.35 A ray of light is 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 oppositeface. If the refractive index of the prism is \(\mu\), the angle of incidence \(i\), is nearly equal to :

[AIPMT(Pre) 2012]

(1) \(\mathrm{A} / \mu\)

\((2) \mathrm{A} / 2 \mu\)

(3) \(\mu \mathrm{A}\)

(4) \(\frac{\mu \mathrm{A}}{2}\)

Q.36 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) \(f_{1}+f_{2}\)

\((2)-f_{1}+f_{2}\)

(3) \(2 \mathrm{f}_{1}+\mathrm{f}_{2}\)

(4) \(-2 f_{1}+f_{2}\)

[AIPMT Pre 2012]

Q.37 When a biconvex lens of glass having refractive index 1.47 is dipped in a liquid, it acts as a plane sheet of glass. This implies that the liquid must have refractive index.

[AIPMT(Pre) 2012]

(1) greater than that of glass

(2) less than that of glass

(3) equal to that of glass

(4) less than one

Q.38 A rod of length \(10 \mathrm{~cm}\) lies along the principal axis of a concave mirror of focal length \(10 \mathrm{~cm}\) in such a way that its end closer to the pole is \(20 \mathrm{~cm}\) away from the mirror. The length of the image is :-

[AIPMT(Mains) 2012]

(1) \(2.5 \mathrm{~cm}\)

(2) \(5 \mathrm{~cm}\)

(3) \(10 \mathrm{~cm}\)

(4) \(15 \mathrm{~cm}\)

Q.39 For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index :-

(1) is less than 1

(2) is greater than 2

(3) lies between \(\sqrt{2}\) and 1

(4) lies between 2 and \(\sqrt{2}\)

[AIPMT(Mains) 2012]

Q.40 A plano convex lens fits exactly into a plano concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices \(\mu_{1}\) and \(\mu_{2}\) and \(\mathrm{R}\) is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is : [NEET 2013]

(1) \(\frac{R}{2\left(\mu_{1}-\mu_{2}\right)}\)

(2) \(\frac{\mathrm{R}}{\left(\mu_{1}-\mu_{2}\right)}\)

(3) \(\frac{2 R}{\left(\mu_{2}-\mu_{1}\right)}\)

(4) \(\frac{R}{2\left(\mu_{1}+\mu_{2}\right)}\)

Q.41 For a normal eye, the cornea of eye provides a converging power of \(40 \mathrm{D}\) and the least converging power of the eye lens behind the cornea is \(20 \mathrm{D}\). Using this information, the distance between the retina and the cornea - eye lens can be estimated to be :

(1) \(2.5 \mathrm{~cm}\)

(2) \(1.67 \mathrm{~cm}\)

(3) \(1.5 \mathrm{~cm}\)

(4) \(5 \mathrm{~cm}\)

[NEET 2013]

Q.42 The angle of a prism is 'A'. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence \(2 \mathrm{~A}\) on the first surface returns hack through the same path after suffering reflection at the silvered surface. The refractive index \(\mu\), of the prism is :

[AIPMT 2014]

(1) \(2 \sin \mathrm{A}\)

(2) \(2 \cos \mathrm{A}\)

(3) \(\frac{1}{2} \cos A\)

(4) \(\tan \mathrm{A}\) Q.43 If the focal length of objective lens is increased then magnefying power of:

GEOMETRICAL OPTICS [AIPMT 2014]

(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 increase

Q.44 Two identical thin plano-convex glass lenses (refractive index 1.5) each having radius of curvature of 20 \(\mathrm{cm}\) are placed with their convex surfaces in contact at the centre. The intervening spaces is filled with oil of refractive index 1.7. The focal length of the combination is

(1) \(-25 \mathrm{~cm}\)

(2) \(-50 \mathrm{~cm}\)

(3) \(50 \mathrm{~cm}\)

(4) \(-20 \mathrm{~cm}\)

[AIPMT 2015]

Q.45 The refracting angle of a prism is ' \(\mathrm{A}\) ', and refractive index of the material of the prism is \(\cot (\mathrm{A} / 2)\). The angle of minimum deviation is :

(1) \(180^{\circ}-2 \mathrm{~A}\)

(2) \(90^{\circ}-\mathrm{A}\)

(3) \(180^{\circ}+2 \mathrm{~A}\)

(4) \(180^{\circ}-3 \mathrm{~A}\)

[AIPMT 2015]

Q.46 A beam of light consisting of red, green and blue colours is incident on a right angled prism. The refractive index of he 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 all the three colours from one another

(2) not separate the three colours at all

(3) separate the red colour part from the green and blue colours

(4) separate the blue colour part from the red and green colours

[AIPMT 2015]

Q.47 In an astronomical telescope in normal adjustment a straight black line of length \(\mathrm{L}\) is drawn on inside part of objective lens. The eye-piece forms a real image of this line. The length of this image is \(l\). The magnification of the telescope is :

[AIPMT 2015]

(1) \(\frac{L}{\mathrm{I}}-1\)

(2) \(\frac{L+I}{L-I}\)

(3) \(\frac{L}{I}\)

(4) \(\frac{L}{\mathrm{I}}+1\)

Q.48 Match the corresponding entries of column-1 with column-2 (Where \(m\) is the magnification produced by the mirror) :

Column-1

(P) \(\mathrm{m}=-2\)

(Q) \(\mathrm{m}=-\frac{1}{2}\)

(R) \(\mathrm{m}=+2\)

(S) \(\mathrm{m}=+\frac{1}{2}\)

(1) \(\mathrm{P} \rightarrow \mathrm{B}\) and \(\mathrm{C}, \mathrm{Q} \rightarrow \mathrm{B}\) and \(\mathrm{C}, \mathrm{R} \rightarrow \mathrm{B}\) and \(\mathrm{D}, \mathrm{S} \rightarrow \mathrm{A}\) and \(\mathrm{D}\).

(2) \(\mathrm{P} \rightarrow \mathrm{A}\) and \(\mathrm{C}, \mathrm{Q} \rightarrow \mathrm{A}\) and \(\mathrm{D}, \mathrm{R} \rightarrow \mathrm{A}\) and \(\mathrm{B}, \mathrm{S} \rightarrow \mathrm{C}\) and \(\mathrm{D}\)

(3) \(\mathrm{P} \rightarrow \mathrm{A}\) and \(\mathrm{D}, \mathrm{Q} \rightarrow \mathrm{B}\) and \(\mathrm{C}, \mathrm{R} \rightarrow \mathrm{B}\) and \(\mathrm{D}, \mathrm{S} \rightarrow \mathrm{B}\) and \(\mathrm{C}\)

(4) \(\mathrm{P} \rightarrow \mathrm{C}\) and \(\mathrm{D}, \mathrm{Q} \rightarrow \mathrm{B}\) and \(\mathrm{D}, \mathrm{R} \rightarrow \mathrm{B}\) and \(\mathrm{C}, \mathrm{S} \rightarrow \mathrm{A}\) and \(\mathrm{D}\)

(A) Convex mirror

(B) Concave mirror

(C) Real image

(D) Virtual image

[NEET 2016] 

\section{GEOMETRICAL OPTICS}

Q.49 The angle of incidence for a ray of light at a refracting surface of a prism is \(45^{\circ}\). The angle of prism is \(60^{\circ}\). If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are:

[NEET 2016]

(1) \(45^{\circ}, \frac{1}{\sqrt{2}}\)

(2) \(30^{\circ}, \sqrt{2}\)

(3) \(45^{\circ}, \sqrt{2}\)

(4) \(30^{\circ}, \frac{1}{\sqrt{2}}\)

Q.50 A astronomical telescope has objective and eyepiece of focal lengths \(40 \mathrm{~cm}\) and \(4 \mathrm{~cm}\) respectively. To view an object \(200 \mathrm{~cm}\) away from the objective, the lenses must be separated by distance :

[NEET 2016]

(1) \(37.3 \mathrm{~cm}\)

(2) \(46.0 \mathrm{~cm}\)

(3) \(50.0 \mathrm{~cm}\)

(4) \(54.0 \mathrm{~cm}\)

Q.51 A beam of light from a source \(\mathrm{L}\) is incident normally on a plane mirror fixed at a certain distance \(\mathrm{x}\) from the source. The beam is reflected back as a spot on a scale placed just above the source1. When the mirror is rotated through a small angle \(\theta\), the spot of the light is found to move through a distance y on the scale. The angle \(\theta\) is given by

[NEET 2017]

(1) \(\frac{y}{x}\)

(2) \(\frac{x}{2 y}\)

(3) \(\frac{x}{y}\)

(4) \(\frac{y}{2 x}\)

Q.52 A thin prism having refracting an angle \(10^{\circ}\) is made of glass of refractive index 1.42. The prism is combined with another thin prism of glass of refractive index 1.7. This combination produces dispersion without deviation. The refractive angle of second prism should be

(1) \(6^{\circ}\)

(2) \(8^{\circ}\)

(3) \(10^{\circ}\)

(4) \(4^{\circ}\)

[NEET 2017]

Q.53 The refractive index of the material of a prism is \(\sqrt{2}\) and the angle of the prism is \(30^{\circ}\). One of the two refracting surfaces of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is

(1) \(30^{\circ}\)

(2) \(45^{\circ}\)

(3) \(60^{\circ}\)

(4) zero

[NEET 2018]