A Complete Resource Book in Physics for JEE Main

Sanjeev Kumar

Chapter 18

Ray Optics and Wave Optics - all with Video Answers

Educators

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Chapter Questions

Problem 1

A thin lens of refractive index $1.5$ has a focal length of $15 \mathrm{~cm}$ in air. When lens is placed in a medium of refractive index ( $4 / 3$ ), focal length will be now
(A) $30 \mathrm{~cm}$
(B) $60 \mathrm{~cm}$
(C) $-60 \mathrm{~cm}$
(D) $-30 \mathrm{~cm}$

Prem Bijarniya

Prem Bijarniya

Numerade Educator

Problem 2

An object of mass $m$ is moving with velocity $\vec{u}$ towards a plane mirror kept on a stand as shown in the Fig. $18.43 .$ The mass of the mirror and stand system is $m$. A head-on elastic collision takes place between the object and the mirror stand, the velocity of image before and after the collision is
(A) $\vec{u}, 2 \vec{u}$
(B) $-\vec{u},-2 \vec{u}$
(C) $-\vec{u}, 2 \vec{u}$
(D) $\vec{u},-2 \vec{u}$

Mahendra Kumar

Numerade Educator

Problem 3

A concave mirror of focal length $f$ produces an image $n$ times the size of the object. If the image is real then the distance of the object from the mirror is
(A) $(n-1) f$
(B) $\frac{(n-1)}{n} f$
(C) $\frac{(n+1)}{f} f$
(D) $(n+1) f$

Mahendra Kumar

Numerade Educator

Problem 4

A spherical surface of radius of curvature $R$ separates air (refractive index $1.0$ ) from glass (refractive index 1.5). The centre of curvature is in the glass. A point object $P$ placed in air is found to have a real image $Q$ in the glass. The line $P Q$ cuts the surface at a point $O$, and $P O=O Q .$ The distance $P O$ is equal to
(A) $5 R$
(B) $3 R$
(C) $2 R$
(D) $1.5 R$

Prem Bijarniya

Numerade Educator

Problem 5

A ray of light falls normally on a refracting face of a prism of refractive index $1.5 .$ If the ray just fails to emerge from the prism. Then the angle of prism is
(A) $\sin ^{-1}\left(\frac{2}{3}\right)$
(B) $\cos ^{-1}\left(\frac{2}{3}\right)$
(C) $\sin ^{-1}\left(\frac{1}{2}\right)$
(D) $\sin ^{-1}\left(\frac{1}{3}\right)$

Prem Bijarniya

Numerade Educator

Problem 6

A ray of light passes through four transparent media with refractive indices $\mu_{1}, \mu_{2}, \mu_{3}$, and $\mu_{4}$ as shown in the Fig. 18.44. The surfaces of all media are parallel. If the emergent ray $C D$ is parallel to the incident ray $A B$, then
(A) $\mu_{1}=\mu_{2}$
(B) $\mu_{2}=\mu_{3}$
(C) $\mu_{3}=\mu_{4}$
(D) $\mu_{4}=\mu_{1}$

Prem Bijarniya

Numerade Educator

Problem 7

Two plane mirrors $A$ and $B$ are aligned parallel to each other as shown in Fig. 18.45. 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 Fig. 18.45. The maximum number of times the ray undergoes reflections (including the first one) before it emerges out is
(A) 28
(B) 30
(C) 32
(D) 34

Prem Bijarniya

Numerade Educator

Problem 8

An object $1 \mathrm{~cm}$ tall is placed in front of a mirror at a distance of $4 \mathrm{~cm} .$ In order to produce an upright image of $3 \mathrm{~cm}$ height, one needs a
(A) convex mirror of radius of curvature $12 \mathrm{~cm}$.
(B) concave mirror of radius of curvature $12 \mathrm{~cm} .$
(C) concave mirror of radius of curvature $4 \mathrm{~cm}$.
(D) plane mirror of height $12 \mathrm{~cm}$.

Prem Bijarniya

Numerade Educator

Problem 9

Light travels through a glass plate of thickness $t$ and having refractive index $\mu .$ If $c$ be the velocity of light in vacuum, the time taken by the light to travel this thickness of glass is
(A) $\frac{t}{\mu c}$
(B) $t \mu c$
(C) $\frac{\mu t}{c}$
(D) $\frac{t c}{\mu}$

Prem Bijarniya

Numerade Educator

Problem 10

The Young's double slits experiment is performed with blue and green light of wavelengths $4360 \AA$ and $5460 \AA$, respectively. If $x$ is the distance of fourth maximum from the central one, then
(A) $x$ (blue) $=x$ (green)
(B) $x$ (blue) $>x$ (green)
(C) $x$ (blue) $<x$ (green)
(D) $x$ (blue) $/ x$ (green) $=5460 / 4360$

Prem Bijarniya

Numerade Educator

Problem 11

Monochromatic light from a narrow slit illuminates two parallel narrow slits producing an interference pattern on a screen. The separation between the two slits is now doubled and the distance between the screen and the slits is reduced to half. The fringe width
(A) Is doubled
(B) Becomes four times
(C) Becomes one-fourth
(D) Remains the same

Ranjeet Singh

Numerade Educator

Problem 12

A thin sheet of glass $(\mu=1.5)$ of thickness 6 microns introduced in the path of one of interfering beams of a double slit experiment shifts the central fringes to a position previously occupied by fifth bright fringe. Then the wavelength of the light used is
(A) $6000 \AA$
(B) $3000 \AA$
(C) $4500 \AA$
(D) $7500 \AA$

Ranjeet Singh

Numerade Educator

Problem 13

A concave lens of focal length $F$ produces an image equal to $1 / n$ of size of object, the distance of the image, from the lens is
(A) $(n+1) F$
(B) $(n-1) F$
(C) $\left(\frac{n+1}{n}\right) F$
(D) $\left(\frac{n-1}{n}\right) F$

Ranjeet Singh

Numerade Educator

Problem 14

A convex lens $A$ of focal length $20 \mathrm{~cm}$ and a concave lens $B$ of focal length $5 \mathrm{~cm}$ are kept along the same axis with a distance $d$ between them. If a parallel beam of light falling on $A$ leaves $B$ as a parallel beam, then the distance $d$ in $\mathrm{cm}$ will be
(A) 25
(B) 15
(C) 30
(D) 50

Ranjeet Singh

Numerade Educator

Problem 15

If $\varepsilon_{0}$ and $\mu_{0}$ represent the permittivity and permeability of vacuum, $\varepsilon$ and $\mu$ represent the permittivity and permeability of medium, then refractive index of the medium is given by
(A) $\sqrt{\frac{\mu_{0} \varepsilon_{0}}{\mu \varepsilon}}$
(B) $\sqrt{\frac{\mu \varepsilon}{\mu_{0} \varepsilon_{0}}}$
(C) $\sqrt{\frac{\varepsilon}{\mu_{0} \varepsilon_{0}}}$
(D) $\sqrt{\frac{\mu_{0} \varepsilon_{0}}{\mu}}$

Ranjeet Singh

Numerade Educator

Problem 16

A ray of light strikes a glass plate at an angle of $60^{\circ}$ with the vertical. If the reflected and refracted rays are perpendicular to each other, the refractive index of glass is
(A) $\frac{\sqrt{3}}{2}$
(B) $\frac{3}{2}$
(C) $\frac{1}{2}$
(D) $\sqrt{3}$

Ranjeet Singh

Numerade Educator

Problem 17

An optically active compound
(A) Rotates the plane polarized light
(B) Changes the direction of polarized light
(C) Do not allow plane polarized light to pass through
(D) None of the above

Ranjeet Singh

Numerade Educator

Problem 18

The principle of optical fibre is
(A) Diffraction
(B) Polarization
(C) Interference
(D) Total internal reflection

Ranjeet Singh

Numerade Educator

Problem 19

A beam of light starting from point $A$ reflects from a mirror $M$ and forms an image at $B$ as shown in the same horizontal plane as $A$. For small angle of incidence $i, A B$ is equal to
(A) $i D$
(B) $2 i D$
(C) $4 i D$
(D) $i D / 2$

Ranjeet Singh

Numerade Educator

Problem 20

In Young's double slit experiment, the width of one slit is double that of the other. The ratio of intensity of a bright band to that of a dark band in the interference pattern will be
(A) $2: 1$
(B) $3: 1$
(C) $6: 1$
(D) $9: 1$

Ranjeet Singh

Numerade Educator

Problem 21

The critical angle of a medium is $\sin ^{-1}(3 / 5)$. The polarizing angle of the medium will be
(A) $\sin ^{-1}(4 / 5)$
(B) $\tan ^{-1}(5 / 3)$
(C) $\tan ^{-1}(3 / 4)$
(D) $\tan ^{-1}(4 / 3)$

Ranjeet Singh

Numerade Educator

Problem 22

A glass prism of refractive index $1.5$ is immersed in water $(\mu=4 / 3)$. A light beam incident normally on the face $A B$ is totally reflected to reach the face $B \bar{C}$, if
(A) $\sin \theta \geq \frac{8}{9}$
(B) $\sin \theta \leq \frac{2}{3}$
(C) $\sin \theta=\frac{4}{5}$
(D) $\frac{2}{3}<\sin \theta<\frac{8}{9}$

Ranjeet Singh

Numerade Educator

Problem 23

An object is placed at a distance of $3 f$ from a convex lens of focal length $f$. A slab of refractive index $\mu$ is placed in between lens and object. The image of the object will be formed nearest to the object if thickness of the slab is
(A) $f$
(B) $2 f$
(C) $\frac{f}{\mu-1}$
(D) $\frac{\mu f}{\mu-1}$

Hunza Gilgit

Numerade Educator

Problem 24

A liquid of refractive index $1.33$ is placed between two identical plano-convex lenses, with refractive index 1.50. Two possible arrangements, $P$ and $Q$, are shown. The system is
(A) divergent in $P$, convergent in $Q$.
(B) convergent in $P$, divergent in $Q$.
(C) convergent in both.
(D) divergent in both.

Ranjeet Singh

Numerade Educator

Problem 25

A concave lens of focal length $10 \mathrm{~cm}$ and a convex lens of focal length $20 \mathrm{~cm}$ are placed certain distance apart. If parallel rays incident on one lens become converging after passing through other lens, then the separation between the lenses must be greater than
(A) Zero
(B) $5 \mathrm{~cm}$
(C) $10 \mathrm{~cm}$
(D) $9 \mathrm{~cm}$

Ranjeet Singh

Numerade Educator

Problem 26

Light is incident normally on face $A B$ of a prism as shown in Fig. 18.46. A liquid of refractive index $\mu$ is placed on face $A C$ of the prism. The prism is made of glass of refractive index $3 / 2 .$ The limits of $\mu$ for which total internal reflection cannot takes place on face $A C$ is
Fig. $18.46$
(A) $\frac{3 \sqrt{3}}{4}>\mu>\frac{\sqrt{3}}{2}$
(B) $\mu<\frac{3 \sqrt{3}}{4}$
(C) $\mu>\sqrt{3}$
(D) $\mu<\frac{\sqrt{3}}{2}$

Ranjeet Singh

Numerade Educator

Problem 27

In a double slit experiment, instead of taking slits of equal widths, one slit is made twice as wide as the other. Then in the interference pattern
(A) The intensities of both the maximum and minimum increase
(B) The intensity of the maximum increases and the minimum has zero intensity
(C) The intensity of the maximum decreases and that of minimum increases
(D) The intensity of the maximum decreases and the minimum has zero intensity

Ranjeet Singh

Numerade Educator

Problem 28

A bulb is placed at a depth of $2 \sqrt{7} \mathrm{~m}$ in water and a floating opaque disc is placed over the bulb so that the bulb is not visible from the surface. The radius of the disc should be at least $\left(\mu_{\text {water }}=4 / 3\right.$ )
(A) $42 \mathrm{~m}$
(B) $6 \mathrm{~m}$
(C) $2 \sqrt{7} \mathrm{~m}$
(D) $12 \mathrm{~m}$

Ranjeet Singh

Numerade Educator

Problem 29

A ray of light falls on a prism $A B C(A B=B C)$ and travels as shown in Fig. $18.47$. The refractive index of the prism material should be greater than
(A) $4 / 3$
(B) $\sqrt{2}$
(C) $1.5$
(D) $\sqrt{3}$

Ranjeet Singh

Numerade Educator

Problem 30

On introducing a thin sheet of mica (thickness $12 \times$ $10^{-5} \mathrm{~cm}$ ) in path of one of the interfering beams in Young's double slit experiment, the central fringe is shifted through a distance equal to the spacing between successive bright fringes. The refractive index of mica is (wavelength of light used $\lambda=6 \times 10^{-5} \mathrm{~cm}$ )
(A) $1.33$
(B) $1.5$
(C) $2.5$
(D) $1.478$

Ranjeet Singh

Numerade Educator

Problem 31

A plane glass plate is kept on a paper on which letters are printed in various colours; colour of the letters which will be more close to upper surface is
(A) yellow
(B) red
(C) blue
(D) green

Ranjeet Singh

Numerade Educator

Problem 32

Focal length of an equiconvex lens is $20 \mathrm{~cm}$. If we cut it once perpendicular to principle axis, and then along principal axis, then focal length of each part will be
(A) $20 \mathrm{~cm}$
(B) $10 \mathrm{~cm}$
(C) $40 \mathrm{~cm}$
(D) $5 \mathrm{~cm}$

Ranjeet Singh

Numerade Educator

Problem 33

Rays are converging towards a convex mirror, final image will be
(A) Real
(B) Virtual
(C) May be real or virtual
(D) Image will not form

Ranjeet Singh

Numerade Educator

Problem 34

In YDSE distance between the slits plane and screen is $1 \mathrm{~m}$ and distance between two slits is $5 \mathrm{~mm}$. If slabs of thickness $2 \mathrm{~mm}$ and $1.5 \mathrm{~mm}$ having refractive index $1.5$ and $1.4$ are placed in front of two slits, the shift of central maximum will be
(A) $2 \mathrm{~m}$
(B) $8 \mathrm{~cm}$
(C) $20 \mathrm{~cm}$
(D) $80 \mathrm{~cm}$

Ranjeet Singh

Numerade Educator

Problem 35

We have two equilateral prisms $A$ and $B$. They are made of materials having refractive index $1.5$ and $1.6 .$ For minimum deviation, incident angle will be
(A) Small for prism $A$
(B) Small for prism $B$
(C) Equal for both the prisms
(D) Can't be predicted

Ranjeet Singh

Numerade Educator

Problem 36

A light ray falls on a square slab at an angle $45^{\circ} .$ What must be the minimum index of refraction of glass, if total internal reflection takes place at the vertical face?
(A) $\frac{\sqrt{3}}{2}$
(B) $\sqrt{\frac{3}{2}}$
(C) $\frac{3}{2}$
(D) $\frac{3}{\sqrt{2}}$

Ranjeet Singh

Numerade Educator

Problem 37

A thin plano-convex glass lens $(\mu=1.5)$ has its plane surface silvered, and $R$ is the radius of curvature of curved part, then which of the following ray diagram is true for an object placed at $O$ ?

Ranjeet Singh

Numerade Educator

Problem 38

Interference fringes were produced in Young's double slit experiment using light of wavelength $5000 \AA$. When a film of thickness $2.5 \times 10^{-3} \mathrm{~cm}$ was placed in front of one of the slits, the fringe pattern shifted by a distance equal to 20 fringe-widths. The refractive index of the material of the film is
(A) $1.25$
(B) $1.35$
(C) $1.4$
(D) $1.5$

Ranjeet Singh

Numerade Educator

Problem 39

A thin convergent glass lens $\left(\mu_{g}=1.5\right)$ has a power of $+5.0 D .$ When this lens 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) $4 / 3$
(B) $5 / 3$
(C) $5 / 4$
(D) $6 / 5$

Himanshu Kushwaha

Himanshu Kushwaha

Numerade Educator

Problem 40

Two convex lenses placed in contact form the image of a distant object at $P$. If the lens $B$ is moved to the right, the image will
(A) move to the left.
(B) move to the right.
(C) remain at $P$.
(D) move either to the left or right, depending upon focal lengths of the lenses.

Ranjeet Singh

Numerade Educator

Problem 41

A thin film of thickness $t$ and index of refraction $1.33$ coats a glass with index of refraction $1.50 .$ Which of the following thickness $t$ will not reflect normally incident light with wavelength $640 \mathrm{~nm}$ in air?
(A) $120 \mathrm{~nm}$
(B) $240 \mathrm{~nm}$
(C) $300 \mathrm{~nm}$
(D) $480 \mathrm{~nm}$

Ranjeet Singh

Numerade Educator

Problem 42

For a concave mirror of focal length $20 \mathrm{~cm}$, if the object is at a distance of $30 \mathrm{~cm}$ from the pole, then the nature of the image and its magnification will be
(A) real and $-2$
(B) virtual and $-2$
(C) real and $+2$
(D) virtual and $+2$

Ranjeet Singh

Numerade Educator

Problem 43

The relation between lateral magnification $m$, object distance $u$, and focal length $f$ of a spherical mirror is
(A) $m=\frac{f-u}{f}$
(B) $m=\frac{f}{f+u}$
(C) $m=\frac{f+u}{f}$
(D) $m=\frac{f}{f-u}$

Ranjeet Singh

Numerade Educator

Problem 44

In a Young's double slit experiment, the fringe width is found to be $0.4 \mathrm{~mm}$. If the whole apparatus is immersed in water of refractive index $(4 / 3)$, without disturbing the geometrical arrangement, the new fringe width will be
(A) $0.30 \mathrm{~mm}$
(B) $0.40 \mathrm{~mm}$
(C) $0.53 \mathrm{~mm}$
(D) 450 microns

Prem Bijarniya

Numerade Educator

Problem 45

Light of wavelength $6328 \AA$ is incident normally on a slit having a width of $0.2 \mathrm{~mm}$. The width of the central maximum measured from minimum to minimum of diffraction pattern on a screen $9.0$ metres away will be about
(A) $0.36^{\circ}$
(B) $0.18^{\circ}$
(C) $0.72^{\circ}$
(D) $0.09^{\circ}$

Ranjeet Singh

Numerade Educator

Problem 46

Two polaroids are kept crossed to each other. Now one of them is rotated through an angle of $45^{\circ}$. The percentage of unpolarized incident light now transmitted through the system is
(A) $15 \%$
(B) $25 \%$
(C) $50 \%$
(D) $60 \%$

Ranjeet Singh

Numerade Educator

Problem 47

A ray incident at a point at an angle of incidence of $60^{\circ}$ enters a glass sphere of R.1. $n=\sqrt{3}$ and gets reflected and refracted at the farther surface of the sphere. The angle between the reflected and refracted rays at this surface is
(A) $50^{\circ}$
(B) $60^{\circ}$
(C) $90^{\circ}$
(D) $40^{\circ}$

Ranjeet Singh

Numerade Educator

Problem 48

A microscope has an objective of focal length $1.5 \mathrm{~cm}$ and an eye-piece of focal length $2.5 \mathrm{~cm}$. If the distance between objective and eye-piece is $25 \mathrm{~cm}$, what is the approximate value of magnification produced for relaxed eye?
(A) 75
(B) 110
(C) 140
(D) 25

Ranjeet Singh

Numerade Educator

Problem 49

A circular beam of light of diameter $d=2 \mathrm{~cm}$ falls on a plane surface of glass. The angle of incidence is $60^{\circ}$ and refractive index of glass is $\mu=3 / 2$. The diameter of the refracted beam is
(A) $4.0 \mathrm{~cm}$
(B) $3.0 \mathrm{~cm}$
(C) $3.26 \mathrm{~cm}$
(D) $2.52 \mathrm{~cm}$

Ranjeet Singh

Numerade Educator

Problem 50

The maximum intensity in Young's double slit experiment is $I_{0}$. Distance between the slits is $d=5 \lambda$, where $\lambda$ is the wavelength of monochromatic light used in the experiment. What will be the intensity of light in front of one of the slits on a screen at a distance $D=10 d$ ?
(A) $\frac{I_{0}}{2}$
(B) $\frac{3 I_{0}}{4}$
(C) $I_{0}$
(D) $\frac{I_{0}}{4}$

Ranjeet Singh

Numerade Educator

Problem 51

Light wave enters from medium 1 to medium $2 .$ Its velocity in second medium is double from first. For total internal reflection, the angle of incidence must be greater than
(A) $30^{\circ}$
(B) $60^{\circ}$
(C) $45^{\circ}$
(D) $90^{\circ}$

Ranjeet Singh

Numerade Educator

Problem 52

A light ray is incident upon a prism in minimum deviation position and suffers a deviation of $34^{\circ}$. If the shaded half of the prism is knocked off, the ray will
(A) suffer a deviation of $34^{\circ}$.
(B) suffer a deviation of $68^{\circ}$.
(C) suffer a deviation of $17^{\circ}$.
(D) not come out of the prism.

Ranjeet Singh

Numerade Educator

Problem 53

The light ray is incident at angle of $60^{\circ}$ on a prism of angle $45^{\circ}$. When the light ray falls on the other surface at $90^{\circ}$, the refractive index of the material of prism $\mu$ and the angle of deviation $\delta$ are given by
(A) $\mu=\sqrt{\frac{3}{2}}, \delta=30^{\circ}$
(B) $\mu=1.5, \delta=15^{\circ}$
(C) $\mu=\frac{\sqrt{3}}{2}, \delta=30^{\circ}$
(D) $\mu=\sqrt{\frac{3}{2}}, \delta=15^{\circ}$

Ranjeet Singh

Numerade Educator

Problem 54

In a Young's experiment, two coherent sources are placed $0.90 \mathrm{~mm}$ apart and the fringes are observed 1 $\mathrm{m}$ away. If it produces the second dark fringe at a distance of $1 \mathrm{~mm}$ from the central fringe, the wavelength of monochromatic light used would be
(A) $60 \times 10^{-4} \mathrm{~cm}$
(B) $10 \times 10^{-4} \mathrm{~cm}$
(C) $10 \times 10^{-5} \mathrm{~cm}$
(D) $6 \times 10^{-5} \mathrm{~cm}$

Ranjeet Singh

Numerade Educator

Problem 55

If two lenses of power $+5$ diopters are mounted at some distance apart, the combination will always behave like a diverging lens if the distance between them is
(A) Greater than $40 \mathrm{~cm}$
(B) Equal than $40 \mathrm{~cm}$
(C) Equal to $10 \mathrm{~cm}$
(D) Less than $10 \mathrm{~cm}$

Ranjeet Singh

Numerade Educator

Problem 56

When the angle of incidence on a material is $60^{\circ}$, the reflected light is completely polarized. The velocity of the refracted ray inside the material is (in $\mathrm{m} / \mathrm{s}$ )
(A) $3 \times 10^{8}$
(B) $\left(\frac{3}{\sqrt{2}}\right) \times 10^{8}$
(C) $\sqrt{3} \times 10^{8}$
(D) $0.5 \times 10^{8}$

Ranjeet Singh

Numerade Educator

Problem 57

An object is placed at $20 \mathrm{~cm}$ from a convex mirror of focal length $10 \mathrm{~cm}$. The image formed by the mirror is
(A) real and at $20 \mathrm{~cm}$ from the mirror.
(B) virtual and at $20 \mathrm{~cm}$ from the mirror.
(C) virtual and at $(20 / 3) \mathrm{cm}$ from the mirror.
(D) real and at ( $20 / 3) \mathrm{cm}$ from the mirror.

Ranjeet Singh

Numerade Educator

Problem 58

A convex lens of focal length $12 \mathrm{~cm}$ is made of glass of $\mu=\frac{3}{2} .$ What will be its focal length when immersed in liquid of $\mu=\frac{5}{4}$
(A) $6 \mathrm{~cm}$
(B) $12 \mathrm{~cm}$
(C) $24 \mathrm{~cm}$
(D) $30 \mathrm{~cm}$

Ranjeet Singh

Numerade Educator

Problem 59

For a material, the refractive indices for red, violet, and yellow colour light are, respectively, $1.52,1.64$, and 1.60. The dispersive power of the material is
(A) 2
(B) $0.45$
(C) $0.2$
(D) $0.045$

Ranjeet Singh

Numerade Educator

Problem 60

The refractive index of water is $4 / 3$ and that of glass is $5 / 3$. Then the critical angle for a ray of light entering in water from glass will be
(A) $\sin ^{-1}\left(\frac{4}{5}\right)$
(B) $\sin ^{-1}\left(\frac{5}{4}\right)$
(C) $\sin ^{-1}\left(\frac{20}{9}\right)$
(D) $\sin ^{-1}\left(\frac{9}{20}\right)$

Ranjeet Singh

Numerade Educator

Problem 61

In Young's double slit experiment, when sodium light of wavelength $5893 \AA$ is used, then 62 fringes are seen in the field of view. Instead of sodium light, if violet light of wavelength $4358 \AA$ is used, then the number of fringes that will be seen in the field of view will be
(A) 54
(B) 64
(C) 74
(D) 84

Ranjeet Singh

Numerade Educator

Problem 62

A prism $(\mu=1.5)$ has a refracting angle of $30^{\circ}$. The deviation of a monochromatic ray incident normally on its one surface will be $\left(\sin 48^{\circ} 36^{\prime}=0.75\right)$
(A) $18^{\circ} 36^{\prime}$
(B) $22^{\circ} 38^{\prime}$
(C) $18^{\circ}$
(D) $22^{\circ} 1$

Ranjeet Singh

Numerade Educator

Problem 63

The length of a vertical pole above the surface of a lake of water $(n=4 / 3)$ is $24 \mathrm{~cm} .$ To an underwater fish, just below the water surface, the tip of the pole appears to be
(A) $18 \mathrm{~cm}$ above the surface.
(B) $24 \mathrm{~cm}$ above the surface.
(C) $32 \mathrm{~cm}$ above the surface.
(D) $36 \mathrm{~cm}$ above the surface.

Ranjeet Singh

Numerade Educator

Problem 64

An object is placed in front of a convex mirror at a distance of $50 \mathrm{~cm}$. A plane mirror is introduced covering the lower half of the convex mirror. If the distance between the object and the plane mirror is $30 \mathrm{~cm}$, there is no parallax between the images formed by the two mirrors. The radius of curvature of the convex mirror (in $\mathrm{cm}$ ) is
(A) 60
(B) 50
(C) 30
(D) 25

Ranjeet Singh

Numerade Educator

Problem 65

A plano-convex lens has a thickness of $4 \mathrm{~cm}$. When placed on a horizontal table with curved surface in contact with it, the apparent depth of the bottom-most point of the lens is found to be $3 \mathrm{~cm}$. If the lens is inverted such that the plane face is in contact with the table, the apparent depth of the centre of plane face is found to be $25 / 8 \mathrm{~cm}$. The focal length of the lens is
(A) $50 \mathrm{~cm}$
(B) $75 \mathrm{~cm}$
(C) $100 \mathrm{~cm}$
(D) $150 \mathrm{~cm}$

Ranjeet Singh

Numerade Educator

Problem 66

A lens of power $+2$ diopters is placed in contact with a lens of power $-1$ diopter. The combination will behave like
(A) a convergent lens of focal length $50 \mathrm{~cm}$.
(B) a divergent lens of focal length $100 \mathrm{~cm}$.
(C) a convergent lens of focal length $100 \mathrm{~cm}$.
(D) a convergent lens of focal length $200 \mathrm{~cm}$.

Ranjeet Singh

Numerade Educator

Problem 67

In a Young's double slit experiment, the slit separation is $1 \mathrm{~mm}$ and the screen is $1 \mathrm{~m}$ from the slit. For a monochromatic light of wavelength $500 \mathrm{~nm}$, the distance of third minimum from the central maximum is
(A) $0.50 \mathrm{~mm}$
(B) $1.25 \mathrm{~mm}$
(C) $1.50 \mathrm{~mm}$
(D) $1.75 \mathrm{~mm}$

Ranjeet Singh

Numerade Educator

Problem 68

An insect of negligible mass is sitting on a block of mass $M$, tied with a spring of force constant $k$. The block performs simple harmonic motion with amplitude $A$ in front of a plane mirror placed as shown. The maximum speed of insect relative to its image will be
(A) $A \sqrt{\frac{k}{M}}$
(B) $\frac{A \sqrt{3}}{2} \sqrt{\frac{k}{M}}$
(C) $A \sqrt{3} \sqrt{\frac{k}{M}}$
(D) $\frac{A}{2} \frac{k}{\sqrt{M}}$

Ranjeet Singh

Numerade Educator

Problem 69

In Young's double slit experiment, double slit of separation $0.1 \mathrm{~cm}$ is illuminated by white light. A coloured interference pattern is formed on a screen $100 \mathrm{~cm}$ away. If a pinhole is located on this screen at a distance of $2 \mathrm{~mm}$ from the central fringe, the wavelength in the visible spectrum which will be absent in the light transmitted through the pin hole are
(A) $5714 \AA$ and $4444 \AA$
(B) $6000 \AA$ and $5000 \AA$
(C) $5500 \AA$ and $4500 \AA$
(D) $5200 \AA$ and $4200 \AA$

Ranjeet Singh

Numerade Educator

Problem 70

In the diagram shown, the object is performing SHM according to the equation $y=2 A \sin (\omega t)$ and the plane mirror is performing SHM according to the equation $Y=-A \sin \left(\omega t-\frac{\pi}{3}\right)$. The diagram shows the state of the object and the mirror at time $t=0 \mathrm{~s}$. The minimum time from $t=0 \mathrm{~s}$ after which the velocity of the image becomes equal to zero is
(A) $\frac{\pi}{3 \omega}$
(B) $\frac{3 \pi}{\omega}$
(C) $\frac{\pi}{6 \omega}$
(D) $\frac{2 \pi}{3 \omega}$

Ranjeet Singh

Numerade Educator

Problem 71

In a converging lens of focal length $f$ and the distance between real object and its real image is $4 f$. If the object moves $x_{1}$ distance towards lens, its image moves $x_{2}$ distance away from the lens and when object moves $y_{1}$ distance away from the lens its image moves $y_{2}$ distance towards the lens, then choose the correct option
(A) $x_{1}>x_{2}$ and $y_{1}>y_{2}$
(B) $x_{1}<x_{2}$ and $y_{1}<y_{2}$
(C) $x_{1}<x_{2}$ and $y_{1}>y_{2}$
(D) $x_{1}>x_{2}$ and $y_{2}>y_{1}$

Ranjeet Singh

Numerade Educator

Problem 72

A thin film of thickness $t$ and index of refraction $1.33$ coats a glass with index of refraction 1.50. Which of the following thickness $t$ will not reflect normally incident light with wavelength $640 \mathrm{~nm}$ in air?
(A) $120 \mathrm{~nm}$
(B) $240 \mathrm{~nm}$
(C) $300 \mathrm{~nm}$
(D) $480 \mathrm{~nm}$

Ranjeet Singh

Numerade Educator

Problem 73

When a thin transparent sheet of refractive index $\mu=\frac{3}{2}$ is placed near one of the slits in Young's double slits experiment, the intensity at the centre of the screen reduces to half of the maximum intensity. The minimum thickness of the sheet should be
(A) $\frac{\lambda}{4}$
(B) $\frac{\lambda}{8}$
(C) $\frac{\lambda}{2}$
(D) $\frac{\lambda}{3}$

Ranjeet Singh

Numerade Educator

Problem 74

A thin equiconvex lens of glass has radii of curvature of its surfaces $30 \mathrm{~cm}$ each. This lens has different medium on its two sides as shown in the Fig. $18.48$. The refractive indices of the mediums on the two sides of the lens are $1.2$ and $1.6$, and refractive index of the glass is $1.5$. The focal length of the lens in the shown Fig. $18.48$ is
(A) $30 \mathrm{~cm}$
(B) $60 \mathrm{~cm}$
(C) $120 \mathrm{~cm}$
(D) $240 \mathrm{~cm}$

Ranjeet Singh

Numerade Educator

Problem 75

In an usual Young's double slit experiment with $\lambda=5000 \AA, d=2 \mathrm{~mm}$, and $D=1 \mathrm{~m}$, the number of
maximum obtained on the screen if it is large enough to receive any number of fringes
(A) 8001
(B) 6001
(C) 4001
(D) 2001

Ranjeet Singh

Numerade Educator

Problem 76

In YDSE, one of the slits is covered by a thin sheet of variable refractive index, whose variation with time is represented by graph as shown. The variation of intensity ( $I$ ) at a point on the screen with time, where first minimum is obtained at $t=0$ will be best represented by

Ranjeet Singh

Numerade Educator

Problem 77

A ray of light from a liquid $(\mu=\sqrt{3})$ is incident on a system of two right-angled prisms of refractive indices $\sqrt{3}$ and $\sqrt{2}$ as shown. The ray suffers zero deviation when emerges into air from $C D .$ The angle of incidence $i$ is
(A) $45^{\circ}$
(B) $35^{\circ}$
(C) $20^{\circ}$
(D) $10^{\circ}$

Ranjeet Singh

Numerade Educator

Problem 78

A thin isosceles prism with angle $4^{\circ}$ and refractive index $1.5$ is placed inside a transparent tube with water $\left(\right.$ refractive index $\left.=\frac{5}{4}\right)$ as shown. The deviation of light due to prism will be
(A) $0.8^{\circ}$ upward
(B) $0.8^{\circ}$ downward
(C) $0.67^{\circ}$ upward
(D) $0.67^{\circ}$ downward

Ranjeet Singh

Numerade Educator

Problem 79

A ray of light is incident on the plane mirror at rest. The mirror starts turning at a uniform angular acceler- ation of $2 \pi \mathrm{rad} \mathrm{s}^{-2}$. The reflected ray, at the end of $\frac{1}{4}$ s. must have turned through
(A) $90^{\circ}$
(B) $45^{\circ}$
(C) $22.5^{\circ}$
(D) $11.25^{\circ}$

Ranjeet Singh

Numerade Educator

Problem 80

A thin rod of length $f / 3$ is placed along the optic axis of a concave mirror of focal length $f$ such that its image, which is real and elongated, just touches the rod. The magnification is
(A) 2
(B) 4
(C) $2.4$
(D) $1.5$

Ranjeet Singh

Numerade Educator

Problem 81

The plane face of plano-convex lens of focal length 20 $\mathrm{cm}$ is silvered. This combination is equivalent to the type of mirror and its focal length is
(A) convex, $f=20 \mathrm{~cm}$
(B) concave, $f=20 \mathrm{~cm}$
(C) convex, $f=10 \mathrm{~cm}$
(D) concave, $f=10 \mathrm{~cm}$

Ranjeet Singh

Numerade Educator

Problem 82

The magnifying power of an astronomical telescope in normal adjustment is 8 and the distance between the two lenses is $54 \mathrm{~cm}$. The focal length of eye lens and objective lens will be, respectively.
(A) $6 \mathrm{~cm}$ and $48 \mathrm{~cm}$
(B) $48 \mathrm{~cm}$ and $6 \mathrm{~cm}$
(C) $8 \mathrm{~cm}$ and $64 \mathrm{~cm}$
(D) $64 \mathrm{~cm}$ and $8 \mathrm{~cm}$

Ranjeet Singh

Numerade Educator

Problem 83

An astronomical telescope has magnifying power 10 . The focal length of the eyepiece is $20 \mathrm{~cm}$. The focal length of the objective is
(A) $\frac{1}{200} \mathrm{~cm}$
(B) $\frac{1}{2} \mathrm{~cm}$
(C) $2 \mathrm{~cm}$
(D) $200 \mathrm{~cm}$

Ranjeet Singh

Numerade Educator

Problem 84

In a displacement method using convex lens, two images are obtained for a separation of $d$ between the positions of the lens. One image is magnified and the other is diminished. If $m$ is the magnification of one image, the focal length of the lens is $(m>1)$
(A) $d /(m-1)$
(B) $m d /\left(m^{2}-1\right)$
(C) $d /\left(m^{2}-m\right)$
(D) $(m-1) d$

Ranjeet Singh

Numerade Educator

Problem 85

If a graph is drawn between the separation of slits and bandwidth in Young's double slit experiment, the graph will be
(A) a straight line having positive slope.
(B) a straight line having negative slope.
(C) a rectangular hyperbola.
(D) a parabola.

Ranjeet Singh

Numerade Educator

Problem 86

A point source of light $B$ is placed at a distance $L$ in front of the centre of a mirror of width $d$ hung vertically on a wall. A man walks in front of the mirror at a distance $2 L$ from it as shown. The greatest distance over which he can see the image of the light source in the mirror is
(A) $d / 2$
(B) $d$
(C) $2 d$
(D) $3 d$

Ranjeet Singh

Numerade Educator

Problem 87

A ray of light falls on the surface of a spherical glass paperweight making an angle $\alpha$ with the normal and is refracted in the medium at an angle $\beta$. The angle of deviation of the emergent ray from the direction of the incident ray is
(A) $(\alpha-\beta)$
(B) $2(\alpha-\beta)$
(C) $(\alpha-\beta) / 2$
(D) $(\alpha+\beta)$

Ranjeet Singh

Numerade Educator

Problem 88

An observer can see through a pinhole the top end of a thin rod of height $h$, placed as shown in the Fig. $18.49$. The beaker height is $3 h$ and its radius $h$. When the beaker is filled with a liquid up to a height $2 h$, he can see the lower end of the rod. Then the refractive index of the liquid is
Fig. $18.49$
(A) $5 / 2$
(B) $\sqrt{5 / 2}$
(C) $\sqrt{3 / 2}$
(D) $3 / 2$

Ranjeet Singh

Numerade Educator

Problem 89

A plane mirror is placed at the bottom of a tank containing a liquid of refractive index $\mu, P$ is a small object at a height $h$ above the plane mirror. An observer $O$, vertically above $P$, outside the liquid, observers $P$ and its image in the mirror. The apparent distance between object and its image will be
Plane mi
(A) $2 \mu h$
(B) $\frac{2 h}{\mu}$
(C) $\frac{2 h}{\mu-1}$
(D) $h\left(\frac{1}{\mu}\right)$

Ranjeet Singh

Numerade Educator

Problem 90

An object $O$ is placed in front of a small plane mirror $M_{1}$ and a large convex mirror $M_{2}$ of focal length $f$. The distance between $O$ and $M_{1}$ is $x$, and the distance between $M_{1}$ and $M_{2}$ is $y$. The images of $O$ formed by $M_{1}$ and $M_{2}$ coincide. The magnitude of $f$ is
(A) $\frac{x^{2}-y^{2}}{2 y}$
(B) $\frac{x^{2}+y^{2}}{2 y}$
(C) $x-y$
(D) $\frac{x^{2}+y^{2}}{x-y}$

Ranjeet Singh

Numerade Educator

Problem 91

In the given situation, for what value of $i$, the incidence ray will retrace its initial path
(A) $\cos ^{-1}\left[\mu_{1} \sin \left(\frac{\pi}{4}-\sin ^{-1} \frac{\mu_{2}}{\sqrt{2} \mu_{1}}\right)\right]$
(B) $\sin ^{-1}\left[\mu_{1} \sin \left(\frac{\pi}{4}-\sin ^{-1} \frac{\mu_{2}}{\sqrt{2} \mu_{1}}\right)\right]$
(C) $\sin ^{-1}\left[\mu_{2} \sin \left(\frac{\pi}{4}-\sin ^{-1} \frac{\mu_{1}}{\sqrt{2} \mu_{2}}\right)\right]$
(D) $\cos ^{-1}\left[\mu_{2} \sin \left(\frac{\pi}{4}-\sin ^{-1} \frac{\mu_{1}}{\sqrt{2} \mu_{2}}\right)\right]$

Ranjeet Singh

Numerade Educator

Problem 92

In the given situation, what is the angle of deviation?
(A) $53^{\circ}$
(B) $127^{\circ}$
(C) $37^{\circ}$
(D) $143^{\circ}$

Ranjeet Singh

Numerade Educator

Problem 93

One slit in a YDSE set up is covered by a glass plate (Refractive index $=\mu_{1}$ ) and other by another glass plate (Refractive index $=\mu_{2}$ ) of same thickness. If $I_{0}$ is the intensity of light through each slit and $\lambda$ is the wavelength of light, then intensity at point $P$ is ( $P$ is symmetrical with respect to slits $S_{1}$ and $S_{2}$ )
(A) $4 I_{0} \cos ^{2} \frac{\pi}{\lambda}\left(\mu_{1}-\mu_{2}\right) t$
(B) $4 I_{0} \cos ^{2} \frac{\pi}{\lambda}\left(\mu_{1}+\mu_{2}\right) t$
(C) $4 I_{0} \sin \frac{\pi}{\lambda}\left(\mu_{1}-\mu_{2}\right) t$
(D) $4 I_{0} \sin \frac{\pi}{\lambda}\left(\mu_{1}+\mu_{2}\right) t$

Ranjeet Singh

Numerade Educator

Problem 94

A plastic hemisphere has a radius of curvature of $8 \mathrm{~cm}$ and an index of refraction of $1.6 .$ On the axis half way between the plane surface and the spherical one ( $4 \mathrm{~cm}$ from each) is a small object $O .$ The distance between the two images when viewed along the axis from the two sides of the hemisphere is approximately.
(A) $1.0 \mathrm{~cm}$
(B) $1.5 \mathrm{~cm}$
(C) $3.75 \mathrm{~cm}$
(D) $2.5 \mathrm{~cm}$

Ranjeet Singh

Numerade Educator

Problem 95

$x$-axis is normal to the reflecting surface of a plane mirror. If object is moving with velocity $(3 \hat{i}+4 \hat{k}) \mathrm{m} / \mathrm{s}$ The relative velocity of image with respect to object will be along
(A) $-x$ axis
(B) $+x$ axis
(C) $-z$ axis
(D) $+z$ axis

Ranjeet Singh

Numerade Educator

Problem 96

A monochromatic light of wavelength $4500 \AA$ fall on a single slit of width $1.5 \mathrm{~mm}$ and resulting diffraction pattern is observed with the help of a lens of focal length $10 \mathrm{~m}$. Angular width of central bright fringe will be
(A) $6 \times 10^{-40}$
(B) $0.034^{\circ}$
(C) $0.034$ radian
(D) $2.4^{\circ}$

Ranjeet Singh

Numerade Educator

Problem 97

A simple telescope, consisting of an objective of focal length $30 \mathrm{~cm}$ and a single eye lens of focal length $6 \mathrm{~cm}$. Eye observes final image in relaxed condition. If the angle subtended on objective is $1.5^{\circ}$ then image will subtend angle of
(A) $6.5^{\circ}$
(B) $7.5^{\circ}$
(C) $0.3^{\circ}$
(D) $2.5^{\circ}$

Ranjeet Singh

Numerade Educator

Problem 98

When an object is placed at a distance of $25 \mathrm{~cm}$ from a mirror, the magnification is $m_{1} .$ The object is moved $15 \mathrm{~cm}$ away with respect to the earlier position along principal axis, magnification becomes $m_{2}$. If $m_{1} \times m_{2}=4$, the focal length of the mirror is
(A) $10 \mathrm{~cm}$
(B) $30 \mathrm{~cm}$
(C) $15 \mathrm{~cm}$
(D) $20 \mathrm{~cm}$

Ranjeet Singh

Numerade Educator

Problem 99

Diameter of a plano-convex lens is $6 \mathrm{~cm}$ and thickness at the centre is $3 \mathrm{~mm}$. The radius of curvature of the curved part is approximately.
(A) $15 \mathrm{~cm}$
(B) $20 \mathrm{~cm}$
(C) $30 \mathrm{~cm}$
(D) $10 \mathrm{~cm}$

Saman Zulfiqar

Numerade Educator

Problem 100

$\eta$ number of identical equilateral prisms are kept in contact as shown in Fig. $18.50$. If deviation through a single prism is $\delta$ then consider the following statements ( $m$ is an integer).
Fig. $18.50$
(i) if $(\eta=2 \mathrm{~m})$ deviation through $\eta$ prisms is zero
(ii) if $(\eta=2 \mathrm{~m}+1)$ deviation through system of $\eta$ prisms is $\delta$
(iii) if $\eta=2 \mathrm{~m}$ deviation through system of $\eta$ prisms is $\delta$
(iv) if $\eta=2 \mathrm{~m}+1$ deviation through system of $\eta$ prisms is zero
(A) statements (i) and (iii) are true
(B) statements (i) and (ii) are true
(C) statements (i) and (iv) are true
(D) statements (iii) and (iv) are true

Vysakh M

Numerade Educator

Problem 101

At a point on the screen in YDSE, third maximum is observed at $t=0 .$ Now screen is slowly moved with constant speed away from the slits in such a way that the centre of slits and centre of screen lie on same line always and at $t=1 \mathrm{~s}$, the intensity at that point is observed to be $\left(\frac{3}{4}\right)^{\text {th }}$ of maximum intensity in between second and third maximum. The speed of screen will be $(D=1 \mathrm{~m})$
(A) $\frac{5}{13} \mathrm{~m} / \mathrm{s}$
(B) $\frac{5}{12} \mathrm{~m} / \mathrm{s}$
(C) $\frac{12}{5} \mathrm{~m} / \mathrm{s}$
(D) $\frac{13}{5} \mathrm{~m} / \mathrm{s}$

Ranjeet Singh

Numerade Educator

Problem 102

A thin converging lens of refractive index $1.5$ has power of $+5 \mathrm{D}$. When this lens is immersed in a liquid, it acts as a diverging lens of focal length $100 \mathrm{~cm}$. The refractive index of the liquid is
(A) 2
(B) $\frac{15}{11}$
(C) $\frac{4}{3}$
(D) $\frac{5}{3}$

Ranjeet Singh

Numerade Educator

Problem 103

In an astronomical telescope, the focal length of objective lens and eyepiece are $150 \mathrm{~cm}$ and $6 \mathrm{~cm}$, respectively. In case when final image is formed at least distance of clear vision $(D=25 \mathrm{~cm})$. The magnifying power is
(A) 29
(B) 30
(C) 31
(D) 32

Ranjeet Singh

Numerade Educator

Problem 104

Path difference for the first secondary maximum in the Fraunhofer diffraction pattern of a single slit is given by ( $a$ is the width of the slit)
(A) $a \sin \theta=\frac{\lambda}{2}$
(B) $a \cos \theta=\frac{3 \lambda}{2}$
(C) $a \sin \theta=\lambda$
(D) $a \sin \theta=\frac{3 \lambda}{2}$

Ranjeet Singh

Numerade Educator

Problem 105

A telescope of diameter $2 \mathrm{~m}$ uses light of wavelength $5000 \AA$ for viewing stars. The minimum angular separation between two stars whose image is just resolved by this telescope is
(A) $4 \times 10^{-4} \mathrm{rad}$
(B) $0.25 \times 10^{-6} \mathrm{rad}$
(C) $0.31 \times 10^{-6} \mathrm{rad}$
(D) $5.0 \times 10^{-3} \mathrm{rad}$

Prem Bijarniya

Numerade Educator

Problem 106

A microscope is focused on a needle lying in an empty tank. Now, the tank is filled with benzene to a height $120 \mathrm{~mm}$. The microscope is moved $40 \mathrm{~mm}$ to focus the needle again. The refractive index of benzene is
(A) $1.5$
(B) $2.5$
(C) $3.0$
(D) $4.5$

Ranjeet Singh

Numerade Educator

Problem 107

For which of the pairs of $u$ and $f$ for a mirror image is smaller in size than the object
(A) $u=-10 \mathrm{~cm}, f=20 \mathrm{~cm}$
(B) $u=-20 \mathrm{~cm}, f=-30 \mathrm{~cm}$
(C) $u=-45 \mathrm{~cm}, f=-10 \mathrm{~cm}$
(D) $u=-60 \mathrm{~cm}, f=30 \mathrm{~cm}$

Ranjeet Singh

Numerade Educator

Problem 108

A thin, symmetric double-convex lens of power $P$ is cut into three parts $A, B$, and $C$ as shown. The power of
(A) $A$ is $P$
(B) $A$ is $2 P$
(C) $B$ is $\frac{P}{2}$
(D) $B$ is $\frac{P}{4}$

Ranjeet Singh

Numerade Educator

Problem 109

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) half of the image will disappear.
(B) complete image will be formed.
(C) intensity of the image will increase.
(D) intensity of the image will decrease.

Ranjeet Singh

Numerade Educator

Problem 110

For a concave mirror
(A) virtual image is always larger in size.
(B) real image is always smaller in size.
(C) real image is always larger in size.
(D) real image may be smaller or larger in size.

Ranjeet Singh

Numerade Educator

Problem 111

Consider the situation shown in the Fig. $18.51$. Two slits $S_{1}$ and $S_{2}$ are placed symmetrically about the line $O P$ which is perpendicular to screen and bisector to line joining the slits. The space between screen and slits is filled with a liquid of refractive index $\mu_{3} . \mathrm{A}$ plate of thickness $t$ and refractive index $\mu_{2}$ is placed in front of one of the slit. A source $S$ is placed above $O P$ at a distance $d$ in front of slit. Given that $D=1 \mathrm{~m}, d=2 \mathrm{~mm}, t=6 \times 10^{-6} \mathrm{~m}, \mu_{2}=1.2$,
$\mu_{3}=1.8$, Choose the correct alternatives
(A) Position of central maximum from point $P$ is $2 \mathrm{~mm}$
(B) Position of central maximum from point $P$ is I $\mathrm{mm}$.
(C) If slab is removed, the central maximum shift by a distance of $2 \mathrm{~mm}$.
(D) If slab is removed, the central maximum shift by a distance of $1 \mathrm{~mm}$.

Ranjeet Singh

Numerade Educator

Problem 112

An object of length $1 \mathrm{~cm}$ is placed on the principal axis of biconvex lens of radius $5 \mathrm{~cm}$. Distance between the lens and object is $20 \mathrm{~cm}$. Space between the lens and object is filled with medium of two different refractive indices 2 and 1 as shown in the Fig. 18.52. Refractive index is 1 on the left of the object and on the right side of the lens. Boundary of both medium is midway between the object and lens as shown in Fig. $18.52$.
Fig.
(A) The image will be formed at distance of $7.5 \mathrm{~cm}$ from the optical centre.
(B) The image will be formed at distance of $10 \mathrm{~cm}$ from the optical centre.
(C) The size of the image is $0.5 \mathrm{~cm}$.
(D) The size of the image is $0.4 \mathrm{~cm}$.

Ranjeet Singh

Numerade Educator

Problem 113

The radius of curvature of the left and right surface of the concave lens are $10 \mathrm{~cm}$ and $15 \mathrm{~cm}$, respectively. The radius of curvature of the mirror is $15 \mathrm{~cm}$
(A) Equivalent focal length of the combination is $-18 \mathrm{~cm}$
(B) Equivalent focal length of the combination is $+36 \mathrm{~cm}$
(C) The system behaves like a concave mirror
(D) The system behaves like a convex mirror

Ranjeet Singh

Numerade Educator

Problem 114

A point object is placed at $30 \mathrm{~cm}$ from a convex glass lens $\left(\mu_{g}=\frac{3}{2}\right)$ of focal length $20 \mathrm{~cm}$. The final image of object will be formed at infinity if
(A) Another concave lens of focal length $60 \mathrm{~cm}$ is placed in contact with the previous lens.
(B) Another convex lens of focal length $60 \mathrm{~cm}$ is placed at a distance of $30 \mathrm{~cm}$ from the first lens.
(C) The whole system is immersed in a liquid of refractive index $\frac{4}{3}$.
(D) The whole system is immersed in a liquid of refractive index $\frac{9}{8}$

Ranjeet Singh

Numerade Educator

Problem 115

In an interference arrangement, similar to Young's double slit experiment, the slits $S_{1}$ and $S_{2}$ are illuminated with coherent microwave sources, each of frequency $10^{6} \mathrm{~Hz}$. The sources are synchronized to have zero phase difference. The slits are separated by distance $d=150.0 \mathrm{~m}$. The intensity $I_{(\theta)}$ is measured as a function of $\theta$, where $\theta$ is defined as shown in the Fig. 18.53. If $I_{0}$ is maximum intensity, then $I_{(\theta)}$ for $0 \leq \theta \leq 90$ is given by
(A) $I_{(\theta)}=I_{0}$ for $\theta=0^{\circ}$
(B) $I_{(\theta)}=\left(I_{0} / 2\right)$ for $\theta=30^{\circ}$
(C) $I_{(\theta)}=\left(I_{0} / 4\right)$ for $\theta=90^{\circ}$
(D) $I_{(\theta)}$ is constant for all values of $\theta$

Ranjeet Singh

Numerade Educator

Problem 116

A ray is incident on a spherical body $(\mu=\sqrt{3})$ making an angle $60^{\circ}$ with the normal drawn at that point. The ray after passing through sphere gets incident on the farther surface of sphere and gets reflected and refracted. Then choose the correct alternative
(A) The angle of refraction at first surface is $60^{\circ}$.
(B) The angle of refraction at first surface is $30^{\circ}$.
(C) The angle of incidence at second surface is $30^{\circ}$.
(D) The angle between reflected ray and refracted ray at second surface is $90^{\circ}$.

Ranjeet Singh

Numerade Educator

Problem 117

Total numbers of fringes can be seen on the screen will be
(A) 2001
(B) 4001
(C) 6001
(D) 8001

Ranjeet Singh

Numerade Educator

Problem 118

Distance between centre of second bright fringe on one side to centre of third bright fringe on other side of central bright fringe $(O)$ will be
(A) $0.25 \mathrm{~mm}$
(B) $0.75 \mathrm{~mm}$
(C) $1.75 \mathrm{~mm}$
(D) $2.50 \mathrm{~mm}$

Ranjeet Singh

Numerade Educator

Problem 119

At point $P$, which is $y \mathrm{~mm}$ above the centre of central bright fringe $(O)$ intensity is found to be $I_{0}$. The value of $y$ can be nearly
(A) $0.17 \mathrm{~mm}$
(B) $0.5 \mathrm{~mm}$
(C) $1.2 \mathrm{~mm}$
(D) $1.5 \mathrm{~mm}$

Ranjeet Singh

Numerade Educator

Problem 120

The focal length of the convex lens measured by Peter is
(A) $22.5 \mathrm{~cm}$
(B) $30 \mathrm{~cm}$
(C) $45 \mathrm{~cm}$
(D) None of these

Ranjeet Singh

Numerade Educator

Problem 121

Which image, as seen by Peter, is brighter?
(A) Smaller
(B) Bigger
(C) Both are equally bright
(D) Cannot be judged

Ranjeet Singh

Numerade Educator

Problem 122

The separation between the two halves as measured by Paul is
(A) $50 \mathrm{~cm}$
(B) $40 \mathrm{~cm}$
(C) $60 \mathrm{~cm}$
(D) $70 \mathrm{~cm}$

Ranjeet Singh

Numerade Educator

Problem 123

The relation between $\theta$ (if slope of the trajectory of the path of ray at a point $B(x, y)$ in the medium is $\tan \theta$ ) and refractive index $n$ at point $B$ is
(A) $\frac{\sin \theta}{\theta}=\frac{\sqrt{n^{2}-1}}{\sin ^{-1}(1 / n)}$
(B) $\frac{\cos \theta}{\theta}=\frac{\sqrt{n^{2}-1}}{\sin ^{-1}(1 / n)}$
(C) $\frac{\tan \theta}{\theta}=\frac{\sqrt{n^{2}-1}}{\sin ^{-1}(1 / n)}$
(D) $\frac{\cot \theta}{\theta}=\frac{\sqrt{n^{2}-1}}{\sin ^{-1}(1 / n)}$

Ranjeet Singh

Numerade Educator

Problem 124

The equation of the trajectory of the ray in the medium is
(A) $4 y^{1 / 4}=k^{1 / 2} x$
(B) $4 y^{1 / 2}=k^{1 / 2} x$
(C) $4 y^{1 / 4}=k^{1 / 2} x^{1 / 2}$
(D) $4 y^{1 / 2}=k^{1 / 2} x^{1 / 2}$

Ranjeet Singh

Numerade Educator

Problem 125

The coordinates $\left(x_{1}, y_{1}\right)$ of the point $P$, where the ray intersects upper surface of the slab-air boundary are
(A) $P\left(x_{1}, y_{1}\right)=P(1,4)$
(B) $P\left(x_{1}, y_{1}\right)=P(4,1)$
(C) $P\left(x_{1}, y_{1}\right)=P(1,2)$
(D) $P\left(x_{1}, y_{1}\right)=P(2,1)$

Ranjeet Singh

Numerade Educator

Problem 126

After coming out of medium, ray of light will move
(A) Parallel to $x$-axis
(B) Parallel to $y$-axis
(C) At an angle $45^{\circ}$ with $x$-axis
(D) On a zig-zag path

Ranjeet Singh

Numerade Educator

Problem 127

Find the position of image if one face of the lens is silvered [Fig. $18.55$ (a)].
(A) $12 \mathrm{~m}$ from the lens towards right
(B) $12 \mathrm{~m}$ from the lens towards left
(C) $6 \mathrm{~m}$ from the lens towards right
(D) At infinity

Ranjeet Singh

Numerade Educator

Problem 128

Find the position of image if lens is cut into two symmetrical plano-convex lens and one of the plano-convex lens is removed [Fig. $18.55$ (b)].
(A) $12 \mathrm{~m}$ from the lens towards right
(B) $12 \mathrm{~m}$ from the lens towards left
(C) $6 \mathrm{~m}$ from the lens towards right
(D) $6 \mathrm{~m}$ from the lens towards left

Hunza Gilgit

Numerade Educator

Problem 129

Find the position of image if plano-convex surfaces are displaced by $100 \mathrm{~cm}$ [Fig. $18.55$ (d) $]$.
(A) $2.94 \mathrm{~m}$ towards right of second lens
(B) $2.94 \mathrm{~m}$ towards right of first lens
(C) $3.31 \mathrm{~m}$ towards right of second lens
(D) $4.31 \mathrm{~m}$ towards right of first lens

Hunza Gilgit

Numerade Educator

Problem 130

If we put $v=V+f$ and $u=U+f$, the mirror formula $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$ becomes
(A) $(V+f)(U+f)=f^{2}$
(B) $V U=f^{2}$
(C) $(V-f)(U-f)=f^{2}$
(D) $V U=2 f^{2}$

Vysakh M

Numerade Educator

Problem 131

To use the formula, which we get in above question, we have to shift the origin, from pole at
(A) $+f$
(B) $-f$
(C) $2 f$
(D) $-2 f$

Vysakh M

Numerade Educator

Problem 132

Assuming that we have taken the origin at the same place as in previous question. A point object is placed on the principal axis $18 \mathrm{~cm}$ from the origin in front of a convex mirror of focal length $6 \mathrm{~cm}$. The distance of image from the pole of mirror is
(A) $6 \mathrm{~cm}$
(B) $10 \mathrm{~cm}$
(C) $25 \mathrm{~cm}$
(D) $4 \mathrm{~cm}$

Vysakh M

Numerade Educator

Problem 133

Assertion: A lens has two principal focal lengths which may differ. Reason: Light can fall on either surface of the lens. The two principal focal lengths differ when medium on the two sides have different refractive indices.
(A) A
(B) B
(C) $\mathrm{C}$
(D) D

Saman Zulfiqar

Numerade Educator

Problem 134

Assertion: Image formed by concave lens is not always virtual. Reason: Image formed by a lens is real if the image is formed in the direction of ray of light with respect to the lens.
(A) $\mathrm{A}$
(B) $\bar{B}$
(C) $\mathrm{C}$
(D) D

Saman Zulfiqar

Numerade Educator

Problem 135

Assertion: Different colours of light have same velocity in vacuum, but they have different velocities in any other transparent medium. Reason: $v=c / \mu$, where symbols have standard meaning. For different colours, refractive index, $\mu$ of transparent medium has different values. Therefore, $v$ is different
(A) $\mathrm{A}$
(B) B
(C) $\mathrm{C}$
(D) D

Saman Zulfiqar

Numerade Educator

Problem 136

Assertion: Light from an object falls on a concave mirror forming a real image of the object. If both the object and mirror are immersed in water, there is no change in the position of the image. Reason: The formation of image by reflection does not depend on surrounding medium, so there is no change in position of image, provided it is also formed in water.
(A) $\mathrm{A}$
(B) B
(C) $\overline{\mathrm{C}}$
(D) D

Saman Zulfiqar

Numerade Educator

Problem 137

Assertion: If a convex lens is placed in water, its converging power decreases.
Reason: The focal length of a lens is independent of the refractive index of the material of the lens.
(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) $\mathrm{D}$

Saman Zulfiqar

Numerade Educator

Problem 138

Assertion: If lower half of a lens is covered with a black paper; the full image of the object is formed. Reason: Every portion of lens forms the full image of the object.
(A) A
(B) $\mathrm{B}$
(C) $\bar{C}$
(D) D

Saman Zulfiqar

Numerade Educator

Problem 139

Assertion: The images formed by total internal reflections are much brighter than those formed by mirrors or lenses. Reason: There is no loss of intensity in total internal reflection.
(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\bar{C}$
(D) D

Saman Zulfiqar

Numerade Educator

Problem 140

Assertion: No interference pattern is detected when two sources are infinitely close to each other. Reason: The fringe width is inversely proportional to the distance between the two slits.
(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) D

Saman Zulfiqar

Numerade Educator

Problem 141

Assertion: The coating of optical fibres of a light pipe is of a material having refractive index more than that of the fibre, to optically insulate from each other. Reason: The optical fibre works on the principal of total internal reflection.
(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) D

Nikhil Choudhary

Nikhil Choudhary

Numerade Educator

Problem 142

Assertion: A plano-convex lens is silvered on plane surface. It can act as a diverging mirror. Reason: Focal length of concave mirror is independent of medium.
(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) D

Nikhil Choudhary

Nikhil Choudhary

Numerade Educator

Problem 143

Match the following
\begin{tabular}{lll}
\hline \multicolumn{1}{c} { Column-I } & \multicolumn{1}{c} { Column-II } \\
\hline (A) Young's double slit experiment uses & 1. Incoherent sources \\
(B) Sources of variable phase & 2. Coherent \\
difference & sources
\end{tabular}
(C) A point on a wave front
3. Superposition behaves as a light source principle
(D) Net displacement is the
4. Huygens vector sum of individual principle displacement.

Saikat Chatterjee

Saikat Chatterjee

Numerade Educator

Problem 144

Match the statement given in Column-I with those given in Column-II. \begin{tabular}{ll}
\hline \multicolumn{1}{c} { Column-I } & \multicolumn{1}{c} { Column-II } \\
\hline (A) & In refraction & 1. Speed of wave \\
& does not change \\
(B) & In reflection & 2. Wavelength is decreased \\
$\begin{array}{ll}\text { (C) } & \text { In refraction of a ray } \\
\text { moving from rarer to a } \\
\text { denser medium. }\end{array}$ & 3. Frequency doesn't change \\
(D) & In reflection of a ray & 4. Phase change of \\
& moving in rarer from a denser medium. & place
\end{tabular}

Hunza Gilgit

Numerade Educator

Problem 145

Four rays of light parallel to optic axis and their path after passing through an optical system are shown in Column-I. Match the corresponding optical instrument from Column-II

Saman Zulfiqar

Numerade Educator

Problem 146

$A B C$ is a right-angled prism kept in air. A ray (1) is incident on the face $A B$ along the normal. Refractive index of the material of prism is the minimum value that will be required so that ray (1) undergoes total internal reflection at the face $A C$. Another ray (2) is incident on the face $A B$ such that it emerges from face $A C$ along the normal to $A C$. A third ray (3) falls on the face $B C$ and emerges from face $A C$ such that its angle of emergence is the same as that of incidence. Assuming light (1), (2), and
(3) have the same wavelength, then match the following.
\begin{tabular}{l}
\multicolumn{1}{c} { Column-I } & Column-II \\
\hline (A) Refractive index of the material 1. 120 \\
of prism is \\
(B) Angle of incidence in degree of \\
ray (2) is \\
(C) Deviation in degree suffered by \\
ray (2) is \\
(D) Deviation in degree suffered by & 4. 60 \\
ray (3) is & 5. $1.5$
\end{tabular}

Prem Bijarniya

Numerade Educator

Problem 147

We have a thin plano-convex lens of focal length $40 \mathrm{~cm}$ and reflective index $\mu=1.25$. It is used in various experiments as given in Column-I and results obtained are given in Column-II.
\begin{tabular}{ll}
\hline \multicolumn{1}{c} { Column-I } & Column-II \\
\hline (A) & If we obtain virtual two times & 1. 10 \\
magnified image, then object &
\end{tabular} $s($ in $\mathrm{cm}) \mathrm{i}$ distance from lens (in $\mathrm{cm}$ ) is of le :
2
4 )
(B) Curved surface of lens is pol- ished, then lens behave like is is pol-
ve like a ce a concave mirror. Focal length of mirror (in $\mathrm{cm}$ ) is nlac ed at a
(C) If an object is placed at a
3
1
$=$ distance of $8 \mathrm{~cm}$ in front of polished lens of part (B), then distance of image from lens 11 (in $\mathrm{cm}$ ) is fthi 2
(D) If a slab of thickness $5 \mathrm{~cm}$ and
4. 20 refractive index $=1.25$ is placed between object and pole perpendicular to the principal axis in part (C), then distance (in $\mathrm{cm}$ ) by which object should 4. be shifted to coincide image [ with object is $5.8$
5. 8

Prem Bijarniya

Numerade Educator

Problem 148

In Young's double slit experiment, the two slits act as coherent sources of equal amplitude $A$ and wavelength $\lambda$. In another experiment with the same set-up, the two slits are source of equal amplitude $A$ and wavelength $\lambda$, but are incoherent. The ratio of the intensity of light at the midpoint of the screen in the first case to that of second case is

Vysakh M

Numerade Educator

Problem 149

In the given Fig. $18.56, A B C$ is a right-angled isosceles prism kept in air. A ray of light is incident on it normally as shown in Fig. 18.56. Refractive index of the prism is varying with time $t$ as $\mu=1+0.4 t$, here $t$ is in seconds. The angular velocity of the emergent ray at time $t=1 \mathrm{~s}$ is

Prem Bijarniya

Numerade Educator

Problem 150

Unpolarized light of intensity $32 \mathrm{Wm}^{-2}$ passes through three polarizers such that transmission axes of the first and second polarizer makes an angle $30^{\circ}$ with each other and the transmission axis of the last polarizer is crossed with that of the first. The intensity of final emerging light will be

Vysakh M

Numerade Educator

Problem 151

Magnification of a compound microscope is $30 .$ Focal length of eyepiece is $5 \mathrm{~cm}$, and the image is formed at a distance of distinct vision of $25 \mathrm{~cm}$. The magnification of objective lens is

Vysakh M

Numerade Educator

Problem 152

A point object is moving along the principal axis of a concave mirror at rest of focal length $30 \mathrm{~cm}$ with speed $5 \mathrm{~m} / \mathrm{s}$ towards the mirror. Find the speed of image of object when object is at a distance $60 \mathrm{~cm}$ from mirror.

Saman Zulfiqar

Numerade Educator

Problem 153

A parallel narrow beam of light is incident on the surface of a transparent hemisphere of radius $R=1 \mathrm{~m}$ and refractive index $\mu=1.5$ as shown. The position of the image formed by refraction at the spherical surface only is

Vysakh M

Numerade Educator

Problem 154

Two coherent sources $S_{1}$ and $S_{2}$ emitting light of wavelength $5000 \AA$ are placed at $0.1 \mathrm{~mm}$ apart, as shown in the Fig. 18.57. A detector is moved along a line perpendicular to $S_{1} S_{2}$ and passing through $S_{1}$. The position of farthest maximum from $S_{1}$ is approximately at a distance of (in $\mathrm{cm}$ )

Prem Bijarniya

Numerade Educator

Problem 155

A ray of light enters into a transparent liquid from air as shown in the Fig. $18.58$. The refractive index of the liquid varies with depth $x$ from the topmost surface as $\mu=\sqrt{2}-\frac{1}{\sqrt{2}} x$, where $x$ in metres. The depth of the liquid medium is sufficiently large. The maximum depth reached by the ray inside the liquid is

Prem Bijarniya

Numerade Educator

Problem 156

What will be the angular width of central maximum in Fraunhofer diffraction when light of wavelength $6000 \AA$ is used and slit width is $12 \times 10^{-5} \mathrm{~cm} ?$

Vysakh M

Numerade Educator

Problem 157

The distance between an object and the screen is $100 \mathrm{~cm} .$ A lens produces an image on the screen when placed at either of the positions $40 \mathrm{~cm}$ apart. The power of the lens is nearly

Vysakh M

Numerade Educator

Problem 158

If two mirrors are kept at $60^{\circ}$ to each other, then the number of images formed by them is $[\mathbf{2 0 0 2}]$
(A) 5
(B) 6
(C) 7
(D) 8

Vysakh M

Numerade Educator

Problem 159

Wavelength of light used in an optical instrument are $\lambda_{1}=400 \AA$ and $\lambda_{2}=500 \AA$, then ratio of their respective resolving powers (corresponding to $\lambda_{1}$ and $\lambda_{2}$ ) is $[2002]$
(A) $16: 25$
(B) $9: 1$
(C) $4: 5$
(D) $5: 4$

Vysakh M

Numerade Educator

Problem 160

Which of the following is used in optical fibres? $[\mathbf{2 0 0 2}]$
(A) Total internal reflection
(B) Scattering
(C) Diffraction
(D) Refraction

Vysakh M

Numerade Educator

Problem 161

To demonstrate the phenomenon of interference, we require two sources which emit radiation $[2003]$
(A) of nearly the same frequency.
(B) of the same frequency.
(C) of different wavelengths.
(D) of the same frequency and having a definite phase relationship.

Vysakh M

Numerade Educator

Problem 162

To get three images of single object, one should have two plane mirrors at an angle of
(A) $60^{\circ}$
(B) $90^{\circ}$
(C) $120^{\circ}$
(D) $30^{\circ}$

Vysakh M

Numerade Educator

Problem 163

A light ray is incident perpendicularly to one face of a $90^{\circ}$ prism and is totally internally reflected at the glass-air interface. If the angle of reflection is $45^{\circ}$, we conclude that the refractive index
(A) $n>\frac{1}{\sqrt{2}}$
(B) $n>\sqrt{2}$
(C) $n<\frac{1}{\sqrt{2}}$
(D) $n>\sqrt{2}$

Saman Zulfiqar

Numerade Educator

Problem 164

A plano-convex lens of refractive index $1.5$ and radius of curvature $30 \mathrm{~cm}$ is silvered at the curved surface. Now this lens has been used to form the image of an object. At what distance from this lens an object be placed in order to have a real image of size of the object [2004]
(A) $60 \mathrm{~cm}$
(B) $30 \mathrm{~cm}$
(C) $20 \mathrm{~cm}$
(D) $80 \mathrm{~cm}$

Saman Zulfiqar

Numerade Educator

Problem 165

The maximum number of possible interference maximum for slit separation equal to twice the wavelength in Young's double-slit experiment is [2004]
(A) Three
(B) Five
(C) Infinite
(D) Zero

Saman Zulfiqar

Numerade Educator

Problem 166

A fish looks up through the water sees the outside world contained in a circular horizon. If the refractive index of water is $4 / 3$ and the fish is $12 \mathrm{~cm}$ below the surface, the radius of this circle in $\mathrm{cm}$ is $\quad$ [2005]
(A) $\frac{36}{\sqrt{7}}$
(B) $36 \sqrt{7}$
(C) $4 \sqrt{5}$
(D) $36 \sqrt{5}$

Saman Zulfiqar

Numerade Educator

Problem 167

Two pointed white dots are $1 \mathrm{~mm}$ apart on a block paper. They are viewed by eye of pupil diameter $3 \mathrm{~mm}$ approximately. What is the maximum distance at which these dots can be resolved by the eyes? [Take wavelength of light $=500 \mathrm{~nm}]$ [2005]
(A) $1 \mathrm{~m}$
(B) $5 \mathrm{~m}$
(C) $3 \mathrm{~m}$
(D) $6 \mathrm{~m}$

Saman Zulfiqar

Numerade Educator

Problem 168

A Young's double slit experiment uses a monochromatic source. The shape of the interference fringes formed on a screen is
(A) Circle
(B) Hyperbola
(C) Parabola
(D) Straight line

Prem Bijarniya

Numerade Educator

Problem 169

If $I_{0}$ is the intensity of the principle maximum in the single-slit diffraction pattern, then what will be its intensity when the slit width is doubled? [2005]
(A) $4 I_{0}$
(B) $2 I_{0}$
(C) $\frac{I_{0}}{2}$
(D) $I_{0}$

Vysakh M

Numerade Educator

Problem 170

When an unpolarized light of intensity $I_{0}$ is incident on a polarizing sheet, the intensity of the light which does not get transmitted is
(A) $\frac{1}{4} I_{0}$
(B) $\frac{1}{2} I_{0}$
(C) $I_{0}$
(D) Zero

Vysakh M

Numerade Educator

Problem 171

The refractive index of a glass is $1.520$ for red light and $1.525$ for blue light. Let $D_{1}$ and $D_{2}$ be angles of minimum deviation for red and blue light, respectively, in a prism of this glass. Then, [2006]
(A) $D_{1}<D_{2}$
(B) $D_{1}=D_{2}$
(C) $D_{1}$ can be less than or greater than $D_{2}$ depending upon the angle of prism
(D) $D_{1}>D_{2}$

Vysakh M

Numerade Educator

Problem 172

In a Young's double slit experiment, the intensity at a point where the path difference is $\frac{\lambda}{6}(\lambda$ being the wavelength of light used) is $I$. If $I_{0}$ denotes the maximum intensity, $\frac{I}{I_{0}}$ is equal to [2007]
(A) $\frac{3}{4}$
(B) $\frac{1}{\sqrt{2}}$
(C) $\frac{\sqrt{3}}{2}$
(D) $\frac{1}{2}$

Saman Zulfiqar

Numerade Educator

Problem 173

Two lenses of power $-15 D$ and $+5 D$ are in contact with each other. The focal length of the combination is $\quad$ [2007]
(A) $+10 \mathrm{~cm}$
(B) $-20 \mathrm{~cm}$
(C) $-10 \mathrm{~cm}$
(D) $+20 \mathrm{~cm}$

Vysakh M

Numerade Educator

Problem 174

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 $[\mathbf{2 0 0 8}]$
(A)
(B)
(C)
(D)

Saman Zulfiqar

Numerade Educator

Problem 175

A mixture of light, consisting of wavelength $590 \mathrm{~nm}$ and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincide. Further, it is observed that the third bright fringe of known light coincides with the 4 th bright fringe of the unknown light. From this data, the wavelength of the unknown light is
(A) $885.0 \mathrm{~nm}$
(B) $442.5 \mathrm{~nm}$
(C) $776.8 \mathrm{~nm}$
(D) $393.4 \mathrm{~nm}$

Saman Zulfiqar

Numerade Educator

Problem 176

A transparent solid cylindrical rod has a refractive index of $\frac{2}{\sqrt{3}}$. It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the Fig. $18.59$. [2009] The incident angle $\theta$ for which the light ray grazes along the wall of the rod is
Fig. $18.59$
(A) $\sin ^{-1}\left(\frac{\sqrt{3}}{2}\right)$
(B) $\sin ^{-1}\left(\frac{2}{\sqrt{3}}\right)$
(C) $\sin ^{-1}\left(\frac{1}{\sqrt{3}}\right)$
(D) $\sin ^{-1}\left(\frac{1}{2}\right)$

Saman Zulfiqar

Numerade Educator

Problem 177

In Young's double slit experiment, one of the slit is wider than other, so that the amplitude of the light from one slit is double of that from other slit. If $I_{\mathrm{m}} \underline{\text { be }}$ the maximum intensity, the resultant intensity $I$ when they interfere at phase difference $\phi$ is given by [2012]
(A) $\frac{I_{m}}{9}(4+5 \cos \phi)$
(B) $\frac{I_{m}}{3}\left(1+2 \cos ^{2} \frac{\phi}{2}\right)$
(C) $\frac{I_{m}}{5}\left(1+4 \cos ^{2} \frac{\phi}{2}\right)$
(D) $\frac{I_{m}}{9}\left(1+8 \cos ^{2} \frac{\phi}{2}\right)$

Saman Zulfiqar

Numerade Educator

Problem 178

An object $2.4 \mathrm{~m}$ in front of a lens forms a sharp image on a film $12 \mathrm{~cm}$ behind the lens. A glass plate $1 \mathrm{~cm}$ 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) $7.2 \mathrm{~m}$
(B) $2.4 \mathrm{~m}$
(C) $3.2 \mathrm{~m}$
(D) $5.6 \mathrm{~m}$

Saman Zulfiqar

Numerade Educator

Problem 179

A beam of unpolarized light of intensity $I_{0}$ is passed through a polaroid $A$ and then through another polaroid $B$ which is oriented so that its principal plane makes an angle of $45^{\circ}$ relative to that of $A$. The intensity of the emergent light is [2013]
(A) $I_{0} / 2$
(B) $I_{0} / 4$
(C) $I_{0} / 8$
(D) $I_{0}$

Saman Zulfiqar

Numerade Educator

Problem 180

Two coherent point sources $S_{1}$ and $S_{2}$ are separated by a small distance $d$ as shown. The fringes obtained on the screen will be
(A) Straight lines
(B) Semi-circles
(C) Concentric circles
(D) Points

Saman Zulfiqar

Numerade Educator

Problem 181

The graph between angle of deviation $(\delta)$ and angle of incidence (i) for a triangular prism is represented by
(A)
(B)
(C)
(D)

Saman Zulfiqar

Numerade Educator

Problem 182

Diameter of a plano-convex lens is $6 \mathrm{~cm}$ and thickness at the centre is $3 \mathrm{~mm}$. If speed of light in material of lens is $2 \times 10^{8} \mathrm{~m} / \mathrm{s}$, the focal length of the lens is $[2013]$
(A) $20 \mathrm{~cm}$
(B) $30 \mathrm{~cm}$
(C) $10 \mathrm{~cm}$
(D) $15 \mathrm{~cm}$

Saman Zulfiqar

Numerade Educator

Problem 183

A thin convex lens made from crown glass $\left(\mu=\frac{3}{2}\right)$ has focal length $f$. When it is measured in two different liquids having refractive indices $\frac{4}{3}$ and $\frac{5}{3}$, it has the focal lengths $f_{1}$ and $f_{2}$, respectively. The correct relation between the focal lengths is
(A) $f_{1}=f_{2}<f$
(B) $f_{1}>f$ and $f_{2}$ becomes negative
(C) $f_{2}>f$ and $f_{1}$ becomes negative
(D) $f_{1}$ and $f_{2}$ both become negative

Saman Zulfiqar

Numerade Educator

Problem 184

A green light is incident from the water to the air-water interface at the critical angle $(\theta)$. Select the correct statement.
(A) The entire spectrum of visible light will come out of the water at an angle of $90^{\circ}$ to the normal.
(B) The spectrum of visible light whose frequency is less than that of green light will come out to the air medium.
(C) The spectrum of visible light whose frequency is more than that of green light will come out to the air medium.
(D) The entire spectrum of visible light will come out of the water at various angles to the normal.

Saman Zulfiqar

Numerade Educator

Problem 185

Two beams, $A$ and $B$, of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam $A$ has maximum intensity (and beam $B$ has zero intensity), a rotation of polaroid through $30^{\circ}$ makes the two beams appear equally bright. If the initial intensities of the two beams are $I_{A}$ and $I_{B}$, respectively, then $\frac{I_{A}}{I_{B}}$ equals [2014]
(A) 3
(B) $3 / 2$
(C) 1
(D) $1 / 3$

Saman Zulfiqar

Numerade Educator

Problem 186

Monochromatic light is incident on a glass prism of angle
A. If the refractive index of the material of the prism is $\mu$, a ray, incident at an angle $\theta$, on the face $A B$ would get transmitted through the face $A C$ of the prism provided
(A) $\theta<\sin ^{-1}\left[\mu \sin \left(A-\sin ^{-1}\left(\frac{1}{\mu}\right)\right)\right]$
(B) $\theta>\cos ^{-1}\left[\mu \sin \left(A+\sin ^{-1}\left(\frac{1}{\mu}\right)\right)\right]$
(C) $\theta<\cos ^{-1}\left[\mu \sin \left(A+\sin ^{-1}\left(\frac{1}{\mu}\right)\right)\right]$
(D) $\theta>\sin ^{-1}\left[\mu \sin \left(A-\sin ^{-1}\left(\frac{1}{\mu}\right)\right)\right]$

Saman Zulfiqar

Numerade Educator

Problem 187

Assuming human pupil to have a radius of $0.25 \mathrm{~cm}$ and a comfortable viewing distance of $25 \mathrm{~cm}$, the minimum separation between two objects that human eye can resolve at $500 \mathrm{~nm}$ wavelength is $\quad$ [2015]
(A) $30 \mu \mathrm{m}$
(B) $100 \mu \mathrm{m}$
(C) $300 \mu \mathrm{m}$
(D) $1 \mu \mathrm{m}$

Saman Zulfiqar

Numerade Educator

Problem 188

On a hot summer night, the refractive index of air is smallest near the ground and increases with height from the ground. When a light beam is directed horizontally, the Huygens' principle leads us to conclude that as it travels, the light beam
(A) goes horizontally without any deflection
(B) bends downwards
(C) bends upwards
(D) becomes narrower

Saman Zulfiqar

Numerade Educator

Problem 189

An observer looks at a distant tree of height $10 \mathrm{~m}$ with a telescope of magnifying power of $20 .$ To the observer the tree appears [2016]
(A) 10 times nearer
(B) 20 times taller
(C) 20 times nearer
(D) 10 times taller

Vysakh M

Numerade Educator

Problem 190

The box of a pin hole camera, of length $L$, has a hole of radius $a$. It is assumed that when the hole is illuminated by a parallel beam of light of wavelength the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size (say $b_{\min }$ ) when $[2016]$
(A) $a=\sqrt{\lambda L}$ and $b_{\min }=\left(\frac{2 \lambda^{2}}{L}\right)$
(B) $a=\sqrt{\lambda L}$ and $b_{\min }=\sqrt{4 \lambda L}$
(C) $a=\frac{\lambda^{2}}{L}$ and $b_{\min }=\sqrt{4 \lambda L}$
(D) $a=\frac{\lambda^{2}}{L}$ and $b_{\min }=\left(\frac{2 \lambda^{2}}{L}\right)$

Vysakh M

Numerade Educator

Problem 191

In an experiment for determination of refractive index of glass of a prism by $i-\delta$ plot, it was found that a ray incident at an angle $35^{\circ}$, suffers a deviation of $40^{\circ}$ and that it emerges at an angle $79^{\circ}$. In that case which of the following is closest to the maximum possible value of the refractive index? $[2016]$
(A) $1.6$
(B) $1.7$
(C) $1.8$
(D) $1.5$

Saman Zulfiqar

Numerade Educator