Arihant AIEEE Physics

D.B. Singh

Chapter 20

Refraction of Light - all with Video Answers

Educators

Chapter Questions

Problem 1

Due to increase of temperature of medium, refractive index will be:
(a) decreased
(b) increased
(c) unchanged
(d) none of these

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Problem 2

In the case of refraction:
(a) the frequency of light changes
(b) the phase changes
(c) the wave length changes
(d) all the above

Himanshu Kushwaha

Himanshu Kushwaha

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Problem 3

The rising and setting of sun appear red because of :
(a) refraction
(b) reflection
(c) diffraction
(d) scattering

Himanshu Kushwaha

Himanshu Kushwaha

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Problem 4

The electric permittivity and magnetic permeability of free space are $\varepsilon_{0}$ and $\mu_{0}$, respectively. The index of refraction of the medium, if $\varepsilon$ and $\mu$ are the electric permittivity and magnetic permeability in a medium is :
(a) $\frac{\varepsilon \mu}{\varepsilon_{0} \mu_{0}}$
(b) $\left(\frac{\varepsilon \mu}{\varepsilon_{0} \mu_{0}}\right)^{1 / 2}$
(c) $\frac{\varepsilon_{0} \mu_{0}}{\varepsilon \mu}$
(d) $\left(\frac{\varepsilon_{0} \mu_{0}}{\varepsilon \mu}\right)^{1 / 2}$

Himanshu Kushwaha

Himanshu Kushwaha

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Problem 5

Which of the following graphs represents the variation of longitudinal spherical aberration with the radius of the lens aperture for lenses of the same focal length and refractive index?

Himanshu Kushwaha

Himanshu Kushwaha

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Problem 6

The maximum possible deviation of the ray, when a ray of light travels from an optically denser to rarer medium and the critical angle for the two medium is $C$, is :
(a) $(\pi-C)$
(b) $(\pi-2 C)$
(c) $2 C$
(d) $\left(\frac{\pi}{2}+C\right)$

Himanshu Kushwaha

Himanshu Kushwaha

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Problem 7

A ray of light falls on a transparent glass slab of refractive index 1.62. What is the angle of incidence, if the reflected ray and refracted ray are mutually perpendicular?
(a) $\tan ^{-1}(1.62)$
(b) $\tan ^{-1}\left(\frac{1}{1.62}\right)$
(c) $\frac{1}{\tan ^{-1}(1.62)}$
(d) None of these

Himanshu Kushwaha

Himanshu Kushwaha

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Problem 8

A ray of light travelling in glass having refractive index ${ }_{a} \mu_{\mathrm{g}}=3 / 2$, is incident at a critical angle $\mathrm{C}$ on the glass-air interface. If a thin layer of water is poured on glass air interface, then what will be the angle of emergence of this ray in air when it emerges from water-air interface?
(a) $180^{\circ}$
(b) $0^{\circ}$
(c) $90^{\circ}$
(d) $45^{\circ}$

Himanshu Kushwaha

Himanshu Kushwaha

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Problem 9

The time required for the light to go from $A$ to $B$, when a ray of light goes from point $A$ in a medium where the speed of light is $v_{1}$ to a point $B$ in a medium where the speed of light is $v_{2}$ as shown in figure, is :(a) $t=\frac{a \sec i}{v_{1}}+\frac{b \sec r}{\partial_{2}}$
(b) $t=\frac{a \sec i}{v_{2}}+\frac{b \sec r}{v_{1}}$
(c) $t=\frac{a \sec i}{v_{1}}-\frac{b \sec r}{v_{2}}$
(d) $t=\frac{a \sec i}{v_{2}}-\frac{b \sec r}{v_{1}}$

Himanshu Kushwaha

Himanshu Kushwaha

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Problem 10

The time taken by the light to travel a distance of 500 metre in water of refractive index of $4 ;$ (Given: velocity of light in vacuum $=3 \times 10^{*}$ an $/$.(a) $3 \times 10^{-10} \mathrm{sec}$
(b) $2.22 \times 10^{-6} \mathrm{sec}$
(c) $4.3 \times 10^{-5} \mathrm{sec}$
(d) $3 \times 10^{-6} \mathrm{sec}$

Himanshu Kushwaha

Himanshu Kushwaha

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Problem 11

In a medium of refractive index $n_{1}$, a monochromatic light of wavelength $\lambda_{1}$ is travelling. When it enters in a denser medium of refractive index $n_{2}$, the wavelength of the light in the second medium is :
(a) $\lambda_{1}\left(\frac{n_{1}}{n_{2}}\right)$
(b) $\lambda_{1}\left(\frac{n_{2}}{n_{1}}\right)$
(c) $\frac{\lambda_{1}\left(n_{2}-n_{1}\right)}{n_{2}}$
(d) $\frac{\lambda_{1}\left(n_{2} \cdots n_{1}\right)}{n_{1}}$

Himanshu Kushwaha

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Problem 12

If ' $c^{\prime}$ is the velocity of light in vacuum, then the time taken by the light to travel through a glass plate of thickness ' $t^{\prime}$ and having refractive index $\mu$ is :
(a) $\left(\frac{t}{\mu c}\right)$
(b) $t \mu c$
(c) $\frac{\mu}{c}$
(d) $\frac{t c}{\mu}$

Himanshu Kushwaha

Himanshu Kushwaha

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Problem 13

The focal lengths of a thin convex lens for red and violet colours are $44.6 \mathrm{~cm}$ and $42.5 \mathrm{~cm}$. The focal length for the mean colour and dispersive power of the lens are respectively:
(a) focal length $=43.53 \mathrm{~cm}$
dispersive power $=0.048$
(b) focal length $=28.53$ dispersive power $=0.048$
(c) focal length $=63.53 \mathrm{~cm}$
dispersive power $=8.48$
(d) focal length $=30.43$ dispersive power $=4.8$

Himanshu Kushwaha

Himanshu Kushwaha

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Problem 14

A beam of parallel rays of width $6 \mathrm{~cm}$ propagates in glass at an angle $\theta$ to its plane face. What would the beam width $b_{1}$, be after it goes over to air through this face? (The refractive index of the glass is $\mu$.)
(a) b\mu
(b) $b \mu \cot \theta$
(c) $\frac{b\left(1-\mu^{2} \cos ^{2} \theta\right)^{1 / 2}}{\sin \theta}$
(d) $\frac{b\left(1-\mu^{2} \sin ^{2} \theta\right)^{1 / 2}}{\cos \theta}$

Himanshu Kushwaha

Himanshu Kushwaha

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Problem 15

Solar rays are incident at $45^{\circ}$ on the surface of water $(\mu=4 / 3) .$ What is the length of the shadow of a pole of length $1.2 \mathrm{~m}$ erected at the bottom of the pond, if the pole is vertical assuming that $0.2 \mathrm{~m}$ of the pole is above the water surface?
(a) $1 \mathrm{~m}$
(b) $0.75 \mathrm{~m}$
(c) $0.825 \mathrm{~m}$
(d) $1.2 \mathrm{~m}$

Himanshu Kushwaha

Himanshu Kushwaha

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Problem 16

$x-y$ plane separates two media. $z>0$ contains a medium of refractive index 1 and $z<0$ contains a medium of refractive index $2 .$ A ray of light is incident from first medium along a vector $\hat{i}+\hat{j}-\hat{k}$, the unit vector along refracted ray is :
(a) $\frac{1}{2 \sqrt{3}} \hat{\mathbf{i}}+\frac{1}{2 \sqrt{3}} \hat{\mathbf{j}}-\sqrt{\frac{5}{6}}^{-}$
(b) $\frac{1}{2 \sqrt{3}} \hat{\mathbf{i}}+\frac{1}{2 \sqrt{3}} \hat{\imath}-\frac{1}{2 \sqrt{3}} \hat{k}$
(c) $\hat{i}+\vec{j}-\hat{k}$
(d) none of the above

Himanshu Kushwaha

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Problem 17

A light ray strikes a flat glass plate, at a small angle ' $\theta^{\prime}$. The glass plate has thickness ' $t$ ' and refractive index ' $\mu^{\prime}$. What is the lateral displacement ' $d^{\prime}$ ?
(a) $\frac{t \theta(\mu+1)}{\mu}$
(b) $\frac{t \theta(\mu-1)}{\mu}$
(c) $\frac{t}{\theta \mu}(\mu-1)$
(d) $\frac{\mu}{t \theta}(\mu+1)$

Himanshu Kushwaha

Himanshu Kushwaha

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Problem 18

A glass slab has thickness ' $t^{\prime}$ and refractive index $\mu$. If a ray of light from air is incident on a glass slab, at an angle of incidence equal to the angle of total internal refraction of glass, then the displacement of the ray due to this slab in terms of thickness and refractive index of glass $\mu$ is:
(a) $\frac{t}{\mu}\left[1-\frac{1}{\sqrt{\mu^{2}-1}}\right]$
(b) $\frac{t}{\mu}\left[1+\frac{1}{\sqrt{\mu^{2}+1}}\right]$
(c) $\frac{t}{\mu}\left[1-\frac{1}{\sqrt{\mu^{2}+1}}\right]$
(d) $\frac{t}{\mu}\left[1+\frac{1}{\sqrt{\mu^{2}-1}}\right]$

Himanshu Kushwaha

Himanshu Kushwaha

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Problem 19

Considering normal incidence of ray, the equivalent refractive index of combination of two slabs shown in figure is:(a) $1.8$
(b) $1.43$
(c) 2
(d) none of these

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 20

A tank contains two different liquids which do not mix with each other. The lower and upper liquids are at depth $h_{2}$ and $h_{1}$ respectively and of refractive indices $\mu_{2}$ and
$\mu_{1}$. An object ' $O^{\prime}$ is located at the bottom, when seen vertically from above. Locate the position of image of the object $O$ as seen from above :
(a) $\frac{h_{1}}{\mu_{1}}-\frac{h_{2}}{\mu_{2}}$
(b) $\frac{h_{1}}{\mu_{1}}+\frac{h_{2}}{\mu_{2}}$
(c) $\frac{h_{1}}{\mu_{2}}+\frac{h_{2}}{\mu_{1}}$
(d) $\frac{h_{1}}{\mu_{2}}-\frac{h_{2}}{\mu_{1}}$

Himanshu Kushwaha

Himanshu Kushwaha

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Problem 21

A vessel contains a slab of glass $8 \mathrm{~cm}$ thick and of refractive index 1.6. Over the slab, the vessel is filled by oil of refractive index $\mu$ upto height $4.5 \mathrm{~cm}$ and also by another liquid i.e., water of refractive index $4 / 3$ and height $6 \mathrm{~cm}$ as shown in figure. An observer lookingdown from above, observes that, a mark at the bottom of the glass slab appears to be raised up to position $6 \mathrm{~cm}$ from the bottom of the slab. The refractive index of oil
$(\mu)$ is:
(a) $1.5$
(b) $2.5$
(c) $0.5$
(d) $1.2$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 22

$n$ transparent slabs of refractive index $1.5$ each having thickness $1 \mathrm{~cm}, 2 \mathrm{~cm}, \ldots$ to $n \mathrm{~cm}$ are arranged one over another. A point object is seen through this combination with near perpendicular light. If the shift of object by the combination is $1 \mathrm{~cm}$ then the value of $n$ is:
(a) either 2 or 3
(b) 2
(c) 3
(d) $0.3$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 23

In the figure, a point source $' P^{\prime}$ is placed at a height $h$ above the plane mirror in a medium of refractive index $\mu$. An observer $O$, vertically above $P$, outside the liquid, sees $P$ and its image in the mirror. The apparent distance between these two is:
(a) $2 \mu h$
(b) $\frac{2 h}{\mu}$
(c) $\frac{2 h}{\mu-1}$
(d) $h\left(1+\frac{1}{\mu}\right)$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 24

In a lake, a fish rising vertically to the surface of water uniformly at the rate of $3 \mathrm{~m} / \mathrm{s}$, observes a bird diving vertically towards the water at a rate of $9 \mathrm{~m} / \mathrm{s}$ vertically above it. The actual velocity of the dive of the bird is:
(Given: refractive index of water $=4 / 3$ )
(a) $9.2 \mathrm{~m} / \mathrm{s}$
(b) $4.5 \mathrm{~m} / \mathrm{s}$
(c) $9.0 \mathrm{~m} / \mathrm{s}$
(d) $3.2 \mathrm{~m} / \mathrm{s}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 25

An object $O$ is placed at $8 \mathrm{~cm}$ infront of a glass slab, whose one face is silvered as shown in the figure. The thickness of the slab is $6 \mathrm{~cm}$. If the image formed $10 \mathrm{~cm}$ behind the silvered face, the refractive index of glass is :
(a) $\mu=1.8$
(b) $\mu=1.2$
(c) $\mu=1.5$
(d) $\mu=1.3$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 26

A concave mirror with its optic axis vertical and mirror facing upward is placed at the bottom of the water tank. The radius of curvature of mirror is $40 \mathrm{~cm}$ and refractive index for water $\mu=4 / 3$. The tank is $20 \mathrm{~cm}$ deep and if a bird is flying over the tank at a height $60 \mathrm{~cm}$ above the surface of water, the position of image of a bird is:
(a) $3.75 \mathrm{~cm}$
(b) $4.23 \mathrm{~cm}$
(c) $5.2 \mathrm{~cm}$
(d) $3.2 \mathrm{~cm}$

Himanshu Kushwaha

Himanshu Kushwaha

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Problem 27

Word 'Newton' is printed on a paper and is placed on a horizontal surface below a cubical glass. The minimum value of refractive index of a cubical glass for whichletters are not visible from any of vertical faces of the glass, is:
(a) $\sqrt{3}$
(b) $0.5$
(c) 1
(d) $\sqrt{2}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 28

In a tank filled with water of refractive index $5 / 3$, a point source of light is placed $4 \mathrm{~m}$ below the surface of water. To cut-off all light coming out of water from the source, what should be the minimum diameter of a disc, which should be placed over the source on the surface of water ?
(a) $1 \mathrm{~m}$
(b) $4 \mathrm{~m}$
(c) $3 \mathrm{~m}$
(d) $6 \mathrm{~m}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 29

A person is looking into a cubical vessel with opaque wall. It is so placed that the eye of an observer cannot see its bottom but can see the entire wall $C D$ as shown in the figure. At a distance $b=10 \mathrm{~cm}$ from corner $D, \mathrm{a}$
small object is placed at $O$. Upto how much height should the vessel must be filled with water $(\mu=4 / 3)$, so the observer can see the object?
(a) $x=2.67 \mathrm{~cm}$
(b) $x=267 \mathrm{~cm}$
(c) $x=26.7 \mathrm{~cm}$
(d) $x=0.267 \mathrm{~cm}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 30

You stand at one end of a long airport runway. A vertical temperature gradient in the air has resulted in the index of refraction of the air above the runway to vary with the height $y$ according to $n=n_{0}(1+a y)$ where $n_{0}$ is
refractive index at the runway surface and $a=1.5 \times 10^{-6} \mathrm{~m}^{-1}$. Your eyes
are at a height $h=1.7 \mathrm{~m}$ above the runway. Beyond what horizontal distance ' $d^{\prime}$ can you not see the runway (shown in figure)?
(a) $652 \mathrm{~m}$
(b) $752 \mathrm{~m}$
(c) $460 \mathrm{~m}$
(d) $370 \mathrm{~m}$

Mishal Gul

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Problem 31

In a prism a ray deviates towards:
(a) base of prism
(b) refracting edge of a prism
(c) normal to the base
(d) second phase of the prism

Himanshu Kushwaha

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Problem 32

In the condition of minimum deviation position, a ray travels within the prism :
(a) symmetrically
(b) assymmetrically
(c) normally
(d) transversally

Himanshu Kushwaha

Himanshu Kushwaha

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Problem 33

The maximum refractive index of a prism which permits the passage of light through it, when the refracting angle of the prism is $90^{\circ}$, is:
(a) $\sqrt{3}$
(b) $\sqrt{2}$
(c) $\sqrt{\frac{3}{2}}$
(d) $\frac{3}{2}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 34

A glass prism of refractive index $8 / 5$ is immersed in a liquid of refractive index $4 / 3 .$ A ray of light incident at grazing angle on one face emerges at grazing angle on the other face of the prism. The angle of the prism is :
(a) $30^{\circ}$
(b) $60^{\circ}$
(c) $37^{\circ}$
(d) none of these

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 35

An equilateral prism deviates a ray through $45^{\circ}$ for the two angle of incidence differing by $20^{\circ}$. The angle of incidence is:
(a) $60^{\circ}$
(b) $40^{\circ}$
(c) $120^{\circ}$
(d) none of these

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 36

There is a glass prism of refractive index $\mu$ and angle of prism is $A$. A ray of light enter the side $A B$ face of the prism at an angle of incidence $i$. The value of angle of incidence $i$ so, that no ray emerges from the face $A C$ of the prism, is:
(a) $\sin ^{-1}\left[\sqrt{\mu^{2}-1} \sin A-\cos A\right]$
(b) $\sin ^{-1}\left[\sqrt{\mu^{2}+1} \sin A-\cos A\right]$
(c) $\sin ^{-1}\left[\sqrt{\mu^{2}+1} \sin A+\cos A\right]$
(d) none of the above

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 37

On one face $M L$ of a prism of refractive index ' $\mu^{\prime}$ and refracting angle ${ }^{\prime} A^{\prime}$, a ray of light $P Q$ is incident at an angle $i$, and refracted along
QR, as shown in figure. If after refraction from MN, this ray travels along $R N$ at grazing emergence, then choose the correct option :
(a) $\mu=\left[1+\left(\frac{\sin A+\cos i}{\sin A}\right)^{2}\right]^{1 / 2}$
(b) $\mu=\left[1+\left(\frac{\sin i+\cos A}{\sin A}\right)^{2}\right]^{1 / 2}$
(c) $\mu:=\left[1-\left(\frac{\sin t+\cos A}{\sin A}\right)^{2}\right]^{1 / 2}$
(d) $\mu=\left[1+\left(\frac{\sin i-\cos A}{\sin i}\right)^{2}\right]^{1 / 2}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 38

The refractive index of the material of prism, if a thin prism of angle $A=6^{\circ}$, produces a deviation $\delta=3^{\circ}$, is:
(a) $1.5$
(b) $1.2$
(c) $1.1$
(d) $1.25$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 39

Figure shows, a glass prism. $A B C$ (refractive index 1.5), immersed in water (refractive index $4 / 3$ ). A ray of light incident normally on face $A B$. If it is totally reflected at face AC then :(a) $\sin \theta>\frac{8}{9}$
(b) $\sin \theta>\frac{\hat{2}}{3}$
(c) $\sin \theta=\frac{\sqrt{3}}{2}$
(d) $\frac{2}{3}<\sin \theta<\frac{8}{9}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 40

The refractive index of the material, if a prism having an angle $A=60^{\circ}$ which produces a minimum deviation of $30^{\circ} ?$
(a) $\sqrt{3}$
(b) $\sqrt{2}$
(c) $\sqrt{5}$
(d) $1 / \sqrt{2}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 41

Which of the following graphs will represent the angle of deviation $\delta$ by a prism versus angle of incidence $i$ for a monochromatic light?

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 42

A drop of liquid is spread on the hypotenuse of $30^{\circ}-60^{\circ}-90^{\circ}$ prism as shown and a ray of light incident normally on face $A B$ of the prism. If the refractive index
B
of liquid is $1.3$, then the refractive index of prism, so that total internal reflection take place, is:
(a) $1.2$
(b) $1.4$
(c) $1.3$
(d) $1.5$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 43

One face $A C$ of the glass prism is silvered as shown and the principal section of a glass prism is an isosceles triangle $A B C$ with $A B=A C$. The $\angle B A C$, if the ray incident normally on face $A B$ and after two reflections, it emerges from the base $B C$, perpendicular to it, is :
(a) $70^{\circ}$
(b) $36^{\circ}$
(c) $72^{\circ}$
(d) $44^{\circ}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 44

The prism shown in the figure has one side silvered. The angle of the prism is $30^{\circ}$ and $\mu=\sqrt{2}$. What should be angle of incidence, if the incident ray retraces its initial path ?
(a) $50^{\circ}$
(b) $45^{\circ}$
(c) $60^{\circ}$
(d) $75^{\circ}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 45

A beam of light consisting of red, green and blue colour is incident on a right angled prism as shown in the figure. Light of red, green and blue colour travel in prism with velocities respectively $5 / 7$ $20 / 29$ and $2 / 3$ times that in the air. The prism will:
(a) separate all three colours from one another
(b) not separate even partially any colour from the other two colours
(c) separate the blue colour partially by transmission fror: red and green colours
(d) separate the part of the red colour from the green and the blue colour

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 46

In a glass prism, spectrum is produced due to:
(a) refraction
(b) dispersion
(c) scattering
(d) diffraction

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 47

If a crown glass prism of refracting angle $10^{\circ}$ have refractive indices for red and violet rays $1.514$ and $1.523$ respectively, then the dispersion caused by a crown glass prism is :
(a) $0.07^{\circ}$
(b) $0.08^{\circ}$
(c) $0.09^{\circ}$
(d) $0.10^{\circ}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 48

A thin prism of angle $7^{\circ}$ made of glass of refractive index $1.5$ is combined with another prism made of glass of $\mu=1.75$ to produce dispersion without deviation. The angle of second prism is:
(a) $7^{\circ}$
(b) $4.67^{\circ}$
(c) $9^{\circ}$
(d) $5^{\circ}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 49

Four similar prisms of same material having same angle of prism are arranged. Which of the following arrangements give no net angular deviation ?
(a)
(b)
(c)
(d)

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 50

In $n$ simillar thin prisms of same material and refractive index are arranged in series as shown :
(a) if $n$ is even number, no net deviation and no net dispersion
(b) if $n$ is odd, no net deviation and no net dispersion
(c) it depends upon angle of prism
(d) no sufficient information

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 51

A small object is enclosed in a sphere of solid glass $8 \mathrm{~cm}$ in radius. It is situated $2 \mathrm{~cm}$ from the centre and is viewed from the side to which it is nearer. Where will it appear to be if $\mu$ of glass $=1.5$ ?
(a) $6 \mathrm{~cm}$ from the centre

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 52

The human eye can be regarded as a single spherical refractive surface of curvature of cornea $7.8 \mathrm{~mm}$. If a parallel beam of light comes to focus at $3.075 \mathrm{~cm}$ behind the refractive surface, the refractive index of the eye is:
(a) $1.34$
(b) 1
(c) $1.5$
(d) $1.33$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 53

In a glass sphere, there is a small bubble $2 \times 10^{-2} \mathrm{~m}$ from its centre. If the bubble is viewed along a diameter of the sphere, from the side on which it lies, how far from the surface will it appear? The radius of glass sphere is $5 \times 10^{-2} \mathrm{~m}$ and refractive index of glass is $1.5:$
(a) $2.5 \times 10^{-2} \mathrm{~m}$
(b) $3.2 \times 10^{-2} \mathrm{~m}$
(c) $6.5 \times 10^{-2} \mathrm{~m}$
(d) $0.2 \times 10^{-2} \mathrm{~m}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 54

Where would an object be placed in a medium of refractive index $\mu_{1}$, so that its real image is formed at equidistant from the sphere of radius $R$ and refractive index $\mu_{2}$, which is also placed in the medium of refractive index $\mu_{1}$ as shown in figure?
(a) $\left(\frac{\mu_{2}-\mu_{1}}{\mu_{2}+\mu_{1}}\right) R$
(b) $\left(\frac{\mu_{2}}{\mu_{2}-\mu_{1}}\right) R$
(c) $\left(\frac{\mu_{1}}{\mu_{2}-\mu_{1}}\right) R$
(d) None of these

Mahendra Kumar

Numerade Educator

Problem 55

A ray incident at a point at an angle of incidence $60^{\circ}$ enters a glass sphere of $\mu=\sqrt{3}$ and is reflected and refracted at the further surface of the sphere. The angle between the reflected and the refracted rays at this surface is :
(a) $50^{\circ}$
(b) $90^{\circ}$
(c) $60^{\circ}$
(d) $40^{\circ}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 56

Which of the following statements is/are correct?
(a) The lens has two principal foci, but may have one focal length
(b) A single lens can never bring a beam of white light to a point focus
(c) A burning glass brings light rays to same focus as heat radiation
(d) Both (a) and (b) are correct

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 57

Consider three converging lenses $L_{1}, L_{2}$ and $L_{3}$ having identical geometrical construction. The index of refraction of $L_{1}$ and $L_{2}$ are $\mu_{1}$ and $\mu_{2}$ respectively. Theupper half of the lens $L_{3}$ has a refractive index $\mu_{1}$ and the lower half has (shown). A point object has an image at $O_{1}$ by lens $L_{1}$ and at $O_{2}$ by the
$L_{2}$ placed in the same position. If $L_{3}$ is placed at the same place:
(a) there will be an image at $O_{1}$
(b) there will be an image at $\mathrm{O}_{2}$
(c) the only image will forms somewhere between $\mathrm{O}_{1}^{\prime}$ and $\mathrm{O}_{2}$
(d) (a) and (b) are correct

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 58

A point source is placed on the axis of a symmetrical convex lens of focal length $20 \mathrm{~cm}$ at a distance $40 \mathrm{~cm}$. If lens is raised by $1 \mathrm{~cm}$, by how much will the image be lifted relative to the previous axis?(a) 1 cru
(b) $3 \mathrm{~cm}$
(c) $2 \mathrm{~cm}$
(d) $4 \mathrm{~cm}$

Mishal Gul

Numerade Educator

Problem 59

A thin convex lens is used to form a real image of a bright point object. The aperture of the lens is small. A graph shown is obtained by plotting, a suitable parameter $y$ against another suitable parameter $x$.
If $f=$ the focal length of the lens $u=$ the object distance $v=$ image distance
(a) $(u v) \rightarrow x,(u+v) \rightarrow y$
(b) $u+v \rightarrow x, u v \rightarrow y$
(c) $u \rightarrow x, \frac{u}{v}:$
(d) $\frac{1}{u} \rightarrow x, \frac{1}{v} \rightarrow y$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 60

If the resolution limit of the eye is 1 minute and at a distance $x \mathrm{~km}$ from the eye, two persons stand with a leteral separation of 3 metre, then the value of $x$ for which the positions of the two persons can be just resolved by the nacked eye, is:
(a) $10 \mathrm{~km}$
(b) $15 \mathrm{~km}$
(c) $20 \mathrm{~km}$
(d) $30 \mathrm{~km}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 61

Which of the following best represents object distance $u$ versus image distance $v$ -graph for a convex lens?

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 62

Mark correct option or options:
(a) The minimum distance between a real image and the real object in concave mirror is zero
(b) The minimum distance between a real object and real image in concave mirror is greater than $4 f$, where $f$ is focal length of the lens
(c) The focal length of concave mirror depends upon the wavelength of light incident on it
(d) The focal length of mirror depends upon medium infront of the mirror

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 63

Select the correct alternative(s):
(a) A convex lens may form a real image
(b) $R=2 f$ formula is applicable to only paraxial ray
(c) A convex lens becomes less convergent when it is immersed in water
(d) All of the above

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 64

From an air craft flying at an altitude of $2000 \mathrm{~m}$, photograph of the ground are taken from a camera, whose size of the film is $18 \mathrm{~cm} \times 18 \mathrm{~cm}$ and the focal length of camera is $50 \mathrm{~cm}$. The area of the ground can be photographed by the camera is :
(a) $648910 \mathrm{~m}^{2}$
(b) $721879 \mathrm{~m}^{2}$
(c) $518400 \mathrm{~m}^{2}$
(d) $482529 \mathrm{~m}^{2}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 65

The distance between the object and screen is $x$ and a convex lens is placed somewhere in between an object and a screen. The focal length $(f)$ of the lens, if the numerical value of magnification produced by the lens is $m$ is :
(a) $\frac{m x}{(m+1)^{2}}$
(b) $\frac{m x}{(m-1)^{2}}$
(c) $\frac{(m+1)^{2}}{m} \cdot x$
(d) $\frac{(m-1)^{2}}{m} \cdot x$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 66

On the axis of a spherical mirror of focal length $f$, a short linear object of length $L$ lies on the axis at a distance $u$ from the mirror. Its image has an axial length $L^{\prime}$ equal to:
(a) $L\left[\frac{f}{(u-f)}\right]^{1 / 2}$
(b) $L\left[\frac{(u+f)}{f}\right]^{1 / 2}$
(c) $L\left[\frac{(u-f)}{f}\right]^{2}$
(d) $L\left[\frac{f}{(u-f)}\right]^{2}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 67

A light source is placed at a distance $b$ from a screen. The power of the lens required to obtain $k$ -fold magnified image is:
(a) $\frac{k+1}{k b}$
(b) $\frac{(k+1)^{2}}{k b}$
(c) $\frac{k b}{k+1}$
(d) $\frac{k b}{(k-1)^{2}}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 68

In the given arrangement, a lens of refractive index $1.5$ is placed havin $\overrightarrow{6}$ media of refractive indices $\mu_{1}$ and $\mu_{2}$ in either sides. Then the value of $\mu_{1}$ and $\because$ with respect to lens
are:
(a) $1.5$ and $1.5$
(b) less than $1.5$
(c) greater than $1.5$ and less than $1.5$
(d) 1 and 1

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 69

The refractive index of a lens material is $\mu$ and focal length $f$. Due to some chemical changes in the material, its refractive index has increased by $2 \%$. The percentage decrease, in focal length for $\mu=1.5$ will be :
(a) $4 \%$
(b) $2 \%$
(c) $6 \%$
(d) $8 \%$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 70

The focal length of a convex lens when placed in air and then in water will:
(a) increase in water with respect to air
(b) increase in air with respect to water
(c) decrease in water with respect to air
(d) remain the same

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 71

A lens forms a sharp image of a real object on a screen. On inserting a parallel slide between the lens and the screen with its thickness along the principal axis of the lens, it is found necessary to shift the screen parallel to itself distance $d$ away from the lens for getting image sharply focussed on it. If the refractive index of the glass relative to air is $\mu$, the thickness of the slab is:
(a) $\frac{d}{\mu}$
(b) $\mu d$
(c) $\frac{r d}{\mu-1}$
(d) $(\mu-1) \frac{d}{\mu}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 72

The radius of curvature of the face of planoconvex lens is $12 \mathrm{~cm}$ and its refractive index is $1.5$. If the plane surface of the lens is now silvered, then the focal length of the lens is :
(a) $26 \mathrm{~cm}$
(b) $22 \mathrm{~cm}$
(c) $24 \mathrm{~cm}$
(d) $20 \mathrm{~cm}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 73

When a thin convergent glass lens $\left(\mu_{\mathrm{g}}=1.5\right)$ and has power of $+5.0 \mathrm{D}$, is immersed in a liquid of refractive index $\mu_{l}$, it acts as a divergent lens of focal length $100 \mathrm{~cm}$. The value of $\mu_{l}$ is:
(a) $\frac{4}{3}$
(b) $\frac{5}{3}$
(c) $\frac{5}{4}$
(d) $\frac{6}{5}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 74

The change in the focal length of the lens, if a convex lens of focal length $20 \mathrm{~cm}$ and refractive index $1.5$, is immersed in water having refractive index $1.33$, is :
(a) $62.2 \mathrm{~cm}$
(b) $5.82 \mathrm{~cm}$
(c) $58.2 \mathrm{~cm}$
(d) $6.22 \mathrm{~cm}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 75

A converging lens is used to form an image on a screen. When the upper half of the lens is covered by an opaque screen:
(a) the complete image will be formed
(b) the intensity of image will increase
(c) the intensity of image will decrease
(d) both (a) and (c) are correct

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 76

A layered lens is made of materials indicated by shades in the figure. The number of images formed is :
(a) 1
(b) 2
(c) 3
(d) 4

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 77

Two plano-convex lens each of focal length $f$ are placed as shown in figure. The ratio of their focal lengths is:(a) $1: 2: 3$
(b) $1: 1: 1$
(c) $1: 2: 1$
(d) $3: 2: 1$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 78

The number of images formed by the lens, if an object is placed on the axis of the lens is:
(a) one
(b) two
(c) three
(d) four

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 79

How many images are formed by the lens shown, if an object is kept on its axis?
(a) One
(b) Two
(c) Three
(d) Four

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 80

The focal length of each half, if the symmetrical lens of focal length $f$ cut along $A B$ is:
(a) $f$
(b) $\left(\frac{1}{2}\right) f$
c
(c) $2 f$
(d) zero

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 81

A symmetric double convex lens is cut in two equal parts along its diameter. If the power of the original lens was 4 D, the power of a divided lens will be:
(a) $2 \mathrm{D}$
(b) $3 \mathrm{D}$
(c) $4 \mathrm{D}$
(d) $5 \mathrm{D}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 82

If an equiconvex lens of focal length $30 \mathrm{~cm}$ is cut into two equal parts by a horizontal plane, then:
(a) the light transmitting area of each part becomes half of the initial
(b) the intensity will reduce to half
(c) the aperture becomes $\frac{1}{\sqrt{2}}$ times of tis initial value
(d) all the above

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 83

If an equiconvex lens of focal length $20 \mathrm{~cm}$ is cut into two equal parts by a vertical plane, the focal length of each part will become:
(a) $40 \mathrm{~cm}$
(b) $10 \mathrm{~cm}$
(c) $20 \mathrm{~cm}$
(d) $5 \mathrm{~cm}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 84

A convex lens of focal length $0.2 \mathrm{~m}$, is cut into two halves each of which is displaced by $0.0005 \mathrm{~m}$ and a point object is placed at a distance of $0.3 \mathrm{~m}$ from the lens, as shown in figure. The position of the image is :
(a) $0.2 \mathrm{~m}$
(b) $0.3 \mathrm{~m}$
(c) $0.6 \mathrm{~m}$
(d) $0.5 \mathrm{~m}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 85

Two similar plano convex lenses are placed with their convex surfaces in contact and the space between them is filled with a liquid of refractive index $1.7$, as shown in figure. The focal length of plano convex lens is $25 \mathrm{~cm}$ and radius of curvature of the curved surface is $12.5 \mathrm{~cm}$ and is made of glass of refractive index 1.5. The focal length of the combination is :
(a) $-31.25 \mathrm{~cm}$
(b) $-42.05 \mathrm{~cm}$
(c) $-37.73 \mathrm{~cm}$
(d) $-52.65 \mathrm{~cm}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 86

Mark correct option or options:
(a) The image formed by a convex lens may coincide with object
(b) The image formed by a plane mirror is always virtual
(c) If one surface of convex lens is silvered, then the image may coincide with the object
(d) Both (a) and (b) are correct

Mishal Gul

Numerade Educator

Problem 87

A convex lens forms real image at a point $P$. A plane mirror is placed at $45^{\circ}$ to the line joining pole $O$ of mirror and before point $P$ at distance $10 \mathrm{~cm}$, then :
(a) the final image is virtual
(b) the final image is on line the $P O$ produced
(c) the final image is above the $P O$ produced at distance $10 \mathrm{~cm}$
(d) the final image is below the PO produced at distance $10 \mathrm{~cm}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 88

The object distance $u$ for a concave mirror:
(a) must be positive
(b) must be negative
(c) must not be negative
(d) may be negative

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 89

Two thin convex lenses of focal lengths $f_{1}$ and $f_{2}$ are separated by a horizontal distance $d$ (where $d<f_{1}, d<f_{2}$ ) and their centres are displaced by a vertical separation \Delta. Taking the origin of co-ordinates $O$ at the centre of the first lens, the $x$ and $y$ co-ordinates of the focal point of this lens system for a parallel beam of rays coming from the left, are given by:
(a) $x=\frac{f_{1} f_{2}}{f_{1}+f_{2}}, y=\Delta$
(b) $x=\frac{f_{1}\left(f_{2}+d\right)}{f_{1}+f_{2}-d}-\frac{\Delta^{2}}{f_{1}+f_{2}}$
(c) $x-\frac{f_{1} f_{2}+d\left(f_{1}-d\right)}{f_{1}+f_{2}-d}, y=\frac{\Delta\left(f_{1}-d\right)}{f_{1}+f_{2}-d}$
(d) $x=\frac{f_{1} f_{2}+d\left(f_{1}-d\right)}{f_{1}+f_{2}-d}, y=0$

Mishal Gul

Numerade Educator

Problem 90

Two thin convex lenses of focal lengths $f_{1}$ and $f_{2}$ are separated by a horizontal distance $d$ (where $d<f_{1}, d<f_{2}$ ) and their centres are displaced by a vertical separation \Delta. Taking the origin of co-ordinates $O$ at the centre of the first lens, the $x$ and $y$ co-ordinates of the focal point of this lens system for a parallel beam of rays coming from the left, are given by:
(a) $x=\frac{f_{1} f_{2}}{f_{1}+f_{2}}, y=\Delta$
(b) $x=\frac{f_{1}\left(f_{2}+d\right)}{f_{1}+f_{2}-d}-\frac{\Delta^{2}}{f_{1}+f_{2}}$
(c) $x-\frac{f_{1} f_{2}+d\left(f_{1}-d\right)}{f_{1}+f_{2}-d}, y=\frac{\Delta\left(f_{1}-d\right)}{f_{1}+f_{2}-d}$
(d) $x=\frac{f_{1} f_{2}+d\left(f_{1}-d\right)}{f_{1}+f_{2}-d}, y=0$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 91

An arrangement of an object, a lens with a focal length of $f=30 \mathrm{~cm}$, a flat mirror and a tray is shown in figure. A flat mirror is turned through $45^{\circ}$ with respect to the optic axis of the lens. At what height ' $h$ ' from the optic axis should the bottom of a tray filled with water up to depth $d=20 \mathrm{~cm}$ be placed to obtain a sharp image of the object at the bottom?

Mishal Gul

Numerade Educator

Problem 92

The focal length of plano-convex lens, the convex surface of which is silvered is $0.3 \mathrm{~m}$. If $\mu$ of the lens is $7 / 4$, the radius of curvature of the convex surface is :
(a) $0.45 \mathrm{~m}$
(b) $1.05 \mathrm{~m}$
(c) $3 \mathrm{~m}$
(d) $0.9 \mathrm{~m}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 93

On a horizontal plane mirror, a thin equi-convex lens of glass is placed and when the space between the lens and mirror is filled with a liquid, an object held at a distance $D$ vertically above the lens is found to coincide with its own image as shown in figure. If equi-convex lens of glass has refractive index $\mu=1.5$ and radius of curvature

Mishal Gul

Numerade Educator

Problem 94

The focal length of the objective of a compound microscope is $f_{o}$ and its distance from the eye piece is $L$. The object is placed at a distance $u$ from the objective. For proper working of the instrument:
(a) $L>u$
(b) $L<u$
(c) $f_{0}<L<2 f_{o}$
(d) $L>2 f_{o}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 95

The magnification of a compound microscope is 30 and the focal length of its eye piece is $5 \mathrm{~cm}$. The magnification produced by the objective, when the image is to be formed at least distance of distinct vision $(25 \mathrm{~cm})$, is:
(a) 5
(b) 6
(c) 8
(d) 10

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 96

A convergent doublet of separated lens, corrected for spherical aberration, are separated by $2 \mathrm{~cm}$, and has an equivalent focal length of $10 \mathrm{~cm}$. The focal length of its component lenses are:
(a) $f_{1}=18 \mathrm{~cm}$
(b) $f_{i}=20 \mathrm{~cm}$
$f_{2}=10 \mathrm{~cm}$
$f_{2}=28 \mathrm{~cm}$
(c) $f_{1}=20 \mathrm{~cm}$
(d) $f_{1}=24 \mathrm{~cm}$
$f_{2}=18 \mathrm{~cm}$
$f_{2}=18 \mathrm{~cm}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 97

A compound microscope has an eye piece of focal length $10 \mathrm{~cm}$ and an objective of focal length $4 \mathrm{~cm}$. The magnification, if an object is kept at a distance of $5 \mathrm{~cm}$ from the objective and final image is formed at the least distance of distinct vision $(20 \mathrm{~cm})$, is :
(a) 10
(b) 11
(c) 12
(d) 13

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 98

A compound microscope has an eye piece of focal length $10 \mathrm{~cm}$ and an objective of focal length $4 \mathrm{~cm}$. The magnification, if an object is kept at a distance of $5 \mathrm{~cm}$ from the objective and final image is formed at the least distance of distinct vision $(20 \mathrm{~cm})$, is :
(a) 10
(b) 11
(c) 12
(d) 13

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 99

An astronomical telescope has an angular magnification of magnitude 5 for distant object. The separation between the objective and the eye piece is $36 \mathrm{~cm}$ and final image is formed at infinity. The focal length of the objective and focal length of eye-piece respectively are :
(a) $f_{o}=45 \mathrm{~cm}$ and $f_{e}=-9 \mathrm{~cm}$
(b) $f_{o}=50 \mathrm{~cm}$ and $f_{e}=10 \mathrm{~cm}$
(c) $f_{o}=7.2 \mathrm{~cm}$ and $f_{e}=5 \mathrm{~cm}$
(d) $f_{o}=30 \mathrm{~cm}$ and $f_{e}=6 \mathrm{~cm}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 100

A planet is observed by an astronomical refracting telescope having an objective of focal length $16 \mathrm{~cm}$ and eye-piece of focal length $20 \mathrm{~cm}$. Then :
(a) the distance between objective and eye-piece is $16.02 \mathrm{~m}$
(b) the angular magnification of the planet is 800
(c) the image of the planet is inverted
(d) both (a) and (b) are correct

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 101

A planet is observed by an astronomical refracting telescope having an objective of focal length $16 \mathrm{~cm}$ and eye-piece of focal length $20 \mathrm{~cm}$. Then :
(a) the distance between objective and eye-piece is $16.02 \mathrm{~m}$
(b) the angular magnification of the planet is 800
(c) the image of the planet is inverted
(d) both (a) and (b) are correct

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 102

What is the power of the lens, if the far point of a short sighted eye is $200 \mathrm{~cm}$ ?

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 103

The limit of resolution of microscope, if the numerical aperture of microscope is $0.12$, and the wavelength of light used is $600 \mathrm{~nm}$, is :
(a) $0.3 \mu \mathrm{m}$
(b) $1.2 \mu \mathrm{m}$
(c) $2.3 \mu \mathrm{m}$
(d) $3 \mu \mathrm{m}$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 104

The power and type of the lens by which a person can see clearly the distant objects, if a person cannot see objects beyond $40 \mathrm{~cm}$, are :
(a) $-2.5 \mathrm{D}$ and concave lens
(b) $-2.5 \mathrm{D}$ and convex lens
(c) $-3.5 \mathrm{D}$ and concave lens
(d) $-3.5 \mathrm{D}$ and convex lens

Mishal Gul

Numerade Educator