Arihant AIEEE Physics

D.B. Singh

Chapter 19

Reflection of Light - all with Video Answers

Educators

Chapter Questions

Problem 1

Mark correct option :
(a) The laws of reflection of light hold only for plane surfaces
(b) The size of virtual image can be measured by receiving it on screen
(c) Plane mirror alongs form an erect image
(d) Plane mirror may form inverted image

Supratim Pal

Supratim Pal

Numerade Educator

Problem 2

A plane mirror:
(i) can form real image of a real object(ii) neither converges nor diverges the rays
(iii) cannot form real image of a real object Choose the correct option or options:
(a) (i) is correct
(b) (i) and (ii) are correct
(c) (ii) and (iii) are correct
(d) none of the above

Supratim Pal

Numerade Educator

Problem 3

A hair dresser stands with her nose $20 \mathrm{~cm}$ infront of a plane mirror for what distance must she focus her eyes in order to see her nose in the mirror?
(a) $40 \mathrm{~cm}$
(b) $50 \mathrm{~cm}$
(c) $30 \mathrm{~cm}$
(d) $60 \mathrm{~cm}$

Supratim Pal

Numerade Educator

Problem 4

A plane mirror is placed along positive $x$ -axis facing along positive $y$ -axis. The equation of a linear object is $x=y$. The equation of its image is:
(a) $x=y$
(b) $x+y=0$
(c) $2 x+y=0$
(d) none of these

Mahendra Kumar

Numerade Educator

Problem 5

A man of height $1.8 \mathrm{~m}$ stands infront of a large vertical plane mirror. The distance of the image from the man if he stands at a distance of $1.5 \mathrm{~m}$ from the mirror is :
(a) $1 \mathrm{~m}$
(b) $2 \mathrm{~m}$
(c) $3 \mathrm{~m}$
(d) $4 \mathrm{~m}$

Supratim Pal

Numerade Educator

Problem 6

A clock fixed on a wall shows time $04: 25: 37 .$ What time will its image in a plane mirror show?
(a) $07: 43: 32$
(b) $07: 43: 32$
(c) $07: 35: 23$
(d) $43: 27: 36$

Supratim Pal

Numerade Educator

Problem 7

A car is moving towards a plane mirror at a speed of $30 \mathrm{~m} / \mathrm{s}$. Then the relative speed of its image with respect to the car will be :
(a) $30 \mathrm{~m} / \mathrm{s}$
(b) $60 \mathrm{~m} / \mathrm{s}$
(c) $15 \mathrm{~m} / \mathrm{s}$
(d) $45 \mathrm{~m} / \mathrm{s}$

Supratim Pal

Numerade Educator

Problem 8

A man is running towards a plane mirror with some velocity. If the relative velocity of his image with respect to him is $4 \mathrm{~m} / \mathrm{s}$, then the velocity of a man is :
(a) $2 \mathrm{~m} / \mathrm{s}$
(b) $4 \mathrm{~m} / \mathrm{s}$
(c) $8 \mathrm{~m} / \mathrm{s}$
(d) $16 \mathrm{~m} / \mathrm{s}$

Supratim Pal

Numerade Educator

Problem 9

A plane mirror is placed in $y-z$ plane. A point object approaches the plane mirror with velocity $3 \hat{1}+4 \hat{j}$. The velocity of image with respect to mirror is:
(a) $-3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}$
(b) $3 \hat{i}-4 \hat{j}$
(c) $-3 \hat{i}-4 \hat{j}$
(d) none of these

Supratim Pal

Numerade Educator

Problem 10

A plane mirror is placed along the $y$ -axis as such $x$ -axis is normal to the plane of the mirror. The reflecting surface of the mirror is towards negative $x$ -axis. The mirror moves in positive $x$ -direction with uniform speed of $5 \mathrm{~m} / \mathrm{s}$ and a point object $P$ is moving with constant speed $3 \mathrm{~m} / \mathrm{s}$ in negative $x$ -direction. The speed of image with respect to mirror is:
(a) $8 \mathrm{~m} / \mathrm{s}$
(b) $16 \mathrm{~m} / \mathrm{s}$
(c) $5 \mathrm{~m} / \mathrm{s}$
(d) $10 \mathrm{~m} / \mathrm{s}$

Supratim Pal

Numerade Educator

Problem 11

A plane mirror is placed in $y-z$ plane facing towards negative $x$ -axis. The mirror is moving parallel to $y$ -axis with a speed of $5 \mathrm{~cm} / \mathrm{s}$. A point object $P$ is moving infront of the mirror with a velocity $3 \hat{i}+4 \hat{j}$. The velocity of image is:
(a) $-3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}$
(b) $3 \hat{i}-4 \hat{j}$
(c) $-3 \hat{i}$
(d) $3 \hat{i}+4 \hat{j}$

Supratim Pal

Numerade Educator

Problem 12

A plane mirror is placed in $y-z$ plane facing towards negative $x$ -axis. The mirror is moving parallel to $y$ -axis with a speed of $5 \mathrm{~cm} / \mathrm{s}$. A point object $P$ is moving

Supratim Pal

Numerade Educator

Problem 13

A bullet of mass $m_{2}$ is fired from a gun of mass $m_{1}$ with horizontal velocity $v .$ A plane mirror is fixed at gun facing towards bullet. The velocity of the image of bullet formed by the plane mirror with respect to bullet is:
(a) $\left(1+\frac{m_{2}}{m_{1}}\right)$
(b) $\left(\frac{m_{1}+m_{2}}{m_{1}}\right) v$
(c) $\frac{2\left(m_{1}+m_{2}\right)}{m_{1}} v$
(d) none of these

Mahendra Kumar

Numerade Educator

Problem 14

A cubical room is formed with 6 plane mirrors. An insect moves along diagonal of the floor with uniform speed. The velocity of its image in two adjacent walls are $20 \sqrt{2} \mathrm{~cm} / \mathrm{s}$. Then the velocity of image formed by the roof is :
(a) $20 \mathrm{~cm} / \mathrm{s}$
(b) $40 \mathrm{~cm} / \mathrm{s}$
(c) $20 \sqrt{2} \mathrm{~cm} / \mathrm{s}$
(d) $10 \sqrt{2} \mathrm{~cm} / \mathrm{s}$

Supratim Pal

Numerade Educator

Problem 15

On a plane mirror, a ray of light is incident at an angle of $30^{\circ}$ with horizontal. To make the reflected ray 'vertical, at what angle with horizontal must a plane mirror be placed?
(a) $30^{\circ}$
(b) $60^{\circ}$
(c) $45^{\circ}$
(d) $54^{\circ}$

Supratim Pal

Numerade Educator

Problem 16

A mirror is inclined at an angle of $\theta$ with the horizontal. If a ray of light is incident at an angle of incidence $\theta$, then the reflected ray makes the following angle with horizontal:
(a) $\theta$
(b) $2 \theta$
(c) $\theta / 2$
(d) none of these

Supratim Pal

Numerade Educator

Problem 17

The mirrors are perpendicular to each other as shown in fig. A light ray $A B$ is incident on the mirror $M_{1}$. Then the reflected ray will also suffer
a reflection from the mirror $M_{2}$. Then the final ray after reflection from $M_{2}$ will be parallel to the incident ray, if :
(a) $i=45^{\circ}$
(b) $i=60^{\circ}$
(c) $i<30^{\circ}$
(d) for any $i$ between $0^{\circ}$ and $90^{\circ}$

Supratim Pal

Numerade Educator

Problem 18

Two mirrors each $1.6 \mathrm{~m}$ long are facing each other. The distance between the mirrors is $20 \mathrm{~cm}$. A light ray is incident on one end of the mirror at an angle of incidence of $30^{\circ} .$ How many times is the ray reflected before it reaches the other end?

Supratim Pal

Numerade Educator

Problem 19

Two plane mirrors $M_{1}$ and $M_{2}$ each have length $1 \mathrm{~m}$ are separated by $1 \mathrm{~cm}$. A ray of light is incident on one end of mirror $M_{1}$ at angle $45^{\circ} .$ How many reflections the ray will have before going at from the other end?
(a) 50
(b) 51
(c) 100
(d) 101

Mahendra Kumar

Numerade Educator

Problem 20

A pole $5 \mathrm{~m}$ high is situated on a horizontal surface. Sun rays are incident at an angle $30^{\circ}$ with the vertical. The size of shadow on horizontal surface is :
(a) $5 \mathrm{~m}$
(b) $\frac{5}{\sqrt{3}}=\mathrm{m}$
(c) $\frac{10}{\sqrt{3}} \mathrm{~m}$
(d) none of these

Supratim Pal

Numerade Educator

Problem 21

A man wants to distinguish between two pillars located at a distance of $11 \mathrm{~km}$. What should be the minimum distance between pillars?
(a) $3.2 \mathrm{~m}$
(b) $1.2 \mathrm{~m}$
(c) $1.1 \mathrm{~m}$
(d) $1.8 \mathrm{~m}$

Supratim Pal

Numerade Educator

Problem 22

If distance between the wheel and mirror is ' $d$ ' then the velocity of light is : (Given that $m$ be the number of teeth and ' $n$ ' the number of revolutions made in one second).
(a) $\mathrm{mnd}$
(b) $2 \mathrm{mnd}$
(c) $3 \mathrm{mnd}$
(d) $4 \mathrm{mnd}$

Supratim Pal

Numerade Educator

Problem 23

A ray is incident on a plane surface. If $\hat{i}+\hat{j}-\hat{k}$ represents a vector along the direction of incident ray. $\hat{i}+\hat{j}$ is a vector along normal on incident point in the plane of incident and reflected ray. Then vector along the direction of reflected ray is:
(a) $-\frac{1}{\sqrt{19}}(-3 \hat{\mathbf{i}}+3 \hat{j}+\mathbf{k})$
(b) $\frac{1}{\sqrt{19}}(3 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-\cdot \hat{\mathrm{k}})$
(c) $-\frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k})$
(d) $\hat{\mathbf{k}}$

Supratim Pal

Numerade Educator

Problem 24

A point object $P$ is situated infront of plane mirror shown in figure. The width of mirror $A B$ is $d .$ The visual region on a line passing through point $P$ and parallel to the mirror is :
(a) $d$
(b) $2 d$
(c) $3 d$
(d) none of the above

Supratim Pal

Numerade Educator

Problem 25

A point source $S$ is centred infront of a $70 \mathrm{~cm}$ wide plane mirror. A man starts walking from the source along a line parallel to the mirror. The maximum distance that can be walked by man without losing sight of the image of source is:
(a) $80 \mathrm{~cm}$
(b) $60 \mathrm{~cm}$
(c) $70 \mathrm{~cm}$
(d) $90 \mathrm{~cm}$

Supratim Pal

Numerade Educator

Problem 26

A beautiful girl with two normal eyes wants to see full width of her face by a plane mirror. The eye to eye and ear to ear distances of her face are 4 inch and 6 inch respectively. The minimum widti. of the required mirror is :
(a) 1 inch
(b) 2 inch
(c) 3 inch
(d) 4 inch

Supratim Pal

Numerade Educator

Problem 27

The size of the face of a dancer is $24 \mathrm{~cm} \times 16 \mathrm{~cm}$. The minimum size of a plane mirror required to see the face of dancer completely by:
(i) one eyed dancer.
(ii) two eyed dancer. (Distance between the eyes is $4 \mathrm{~cm}$.)
(a) (i) $12 \times 8 \mathrm{~cm}^{2}$
(b) (i) $8 \times 10 \mathrm{~cm}^{2}$
(ii) $12 \times 6 \mathrm{~cm}^{2}$
(ii) $12 \times 2 \mathrm{~cm}^{2}$
(c) (i) $10 \times 12 \mathrm{~cm}^{2}$
(d) (i) $12 \times 2 \mathrm{~cm}^{2}$
(ii) $9 \times 8 \mathrm{~cm}^{2}$
(ii) $6 \times 13 \mathrm{~cm}^{2}$

Supratim Pal

Numerade Educator

Problem 28

A narrow beam of light after reflection by a plane mirror falls on a scale $100 \mathrm{~cm}$ from the mirror. When the mirror is rotated a little the spot moves through $2 \mathrm{~cm}$, the angle, through which the mirror is rotated is :
(a) $0.02 \mathrm{rad}$
(b) $0.01 \mathrm{rad}$
(c) $200 \mathrm{rad}$
(d) $\frac{0.01}{180} \pi \mathrm{rad}$

Supratim Pal

Numerade Educator

Problem 29

A ray of light falls on a plane mirror. When the mirror is turned, about an axis at right angle to the plane of the mirror through $20^{\circ}$, the angle between the incident ray and new reflected ray is $45^{\circ}$. The angle between the incident ray and original reflected ray is:
(a) $15^{\circ}$
(b) $30^{\circ}$
(c) $45^{\circ}$
(d) $60^{\circ}$

Supratim Pal

Numerade Educator

Problem 30

A lamp and scale arrangement, used to measure small deflection is shown in the figure. $S S^{\prime}$ is the glass scale placed at a distance of $1 \mathrm{~m}$ from the plane mirror. $M M$ and $I$ is the position of the light spot formed after reflection from the underdeflectedmirror $M M$. The mirror is deflected by $10^{\circ}$ and comes to the deflected position $M^{\prime} M^{\prime} .$ The distance moved by the spot on the scale $(I R)$ is :
(a) $24.6 \mathrm{~cm}$
(b) $36.4 \mathrm{~cm}$
(c) $46.4 \mathrm{~cm}$
(d) $34.9 \mathrm{~cm}$

Supratim Pal

Numerade Educator

Problem 31

One end of the strip of a plane mirror is fixed and the other end rests on the top of the small vertical rod. The length of the plane mirror strip is $25 \mathrm{~cm}$. A ray of light is incident on the mirror and reflected from the mirror and forms a spot on a screen $3 \mathrm{~m}$ away from the mirror. Now, if the top of the rod is moved upwards $0.1 \mathrm{~mm}$, then what will be movement of the spot?
(a) $0.24 \mathrm{~cm}$
(b) $3.4 \mathrm{~cm}$
(c) $5 \mathrm{~cm}$
(d) $4.5 \mathrm{~cm}$

Supratim Pal

Numerade Educator

Problem 32

A plane mirror is mounted parallel to a vertical wall at the distance ' $d^{\prime}$ from light fixed on the wall gets reflected by the mirror to form a path of light on the wall. When the mirror is moved parallel to itself towards the wall, the path of light on the wall:
(a) remains unchanged in position and vertical height
(b) moves along the wall away from the source without changing in vertical length
(c) will increase in vertical length with the lower end fixed
(d) moves along the wall away from the source and is increasing in vertical length.

Supratim Pal

Numerade Educator

Problem 33

The shape of spot light produced when bright sunshine passes perpendicular through a hole of very small size, is:
(a) square because hole is square
(b) round because it is an image of the sun
(c) round with a small pinumbra around it
(d) square with a small pinumbra

Supratim Pal

Numerade Educator

Problem 34

Images in spherical mirrors suffer from several defects. Some of which is/are:
(a) diffraction effect
(b) the magnification varies with the distance of the object from mirror
(c) a point source will not produce a point image
(d) all of the above

Supratim Pal

Numerade Educator

Problem 35

A flat mirror revolves at a constant angular velocity making 2 revolutions/sec. With what velocity will a light spot move along a spherical screen with a radius of $10 \mathrm{~m}$, if the mirror is at a centre of curvature of the screen?
(a) $251.2 \mathrm{~m} / \mathrm{s}$
(b) $261.2 \mathrm{~m} / \mathrm{s}$
(c) $271.2 \mathrm{~m} / \mathrm{s}$
(d) $241.2 \mathrm{~m} / \mathrm{s}$

Supratim Pal

Numerade Educator

Problem 36

A plane mirror which rotates $10^{4}$ times per minute reflects light on to a stationary mirror $50 \mathrm{~m}$ away. This mirror reflects the light normally so that it strikes the rotating mirror again. The image observed in the rotating mirror is shifted through $2.4$ minutes from the position it occupies. When the rotating mirror is stationary, what is the speed of light?
(a) $3 \times 10^{8} \mathrm{~m} / \mathrm{s}$
(b) $4 \times 10^{8} \mathrm{~m} / \mathrm{s}$
(c) $5 \times 10^{8} \mathrm{~m} / \mathrm{s}$
(d) $6 \times 10^{8} \mathrm{~m} / \mathrm{s}$

Supratim Pal

Numerade Educator

Problem 37

Infront of a vertical wall, a plane mirror of square shape is mounted parallel to the wall at some distance from it. On the wall, a point light source is fixed and light from it gets reflected from the mirror and forms a path on the wall. If the mirror is moved parallel to itself towards the wall, then
(i) centre of the patch may remain stationary
(ii) the patch may remain square in shape
(iii) area of patch decreases Choose correct statement:
(a) (i) and (ii) are correct
(b) (i) and (iii) are correct
(c) (ii) and (iii) are correct
(d) none of the above

Supratim Pal

Numerade Educator

Problem 38

The shortest height of a vertical mirror required to see the entire image of a man, will be
(a) one-third the man's height
(b) half the man's height
(c) two-third the man's height
(d) data insufficient

Supratim Pal

Numerade Educator

Problem 39

A fluorescent lamp of length $1 \mathrm{~m}$ is placed horizontal at a depth of $1.2 \mathrm{~m}$ below a ceiling. A plane mirror of length $0.6 \mathrm{~m}$ is placed below the lamp parallel to and symmetric to the lamp at a distance $2.4 \mathrm{~m}$ from it. The length of the reflected patch of light on the ceiling is:
(a) $3 \mathrm{~m}$
(b) $4 \mathrm{~m}$
(c) $7 \mathrm{~m}$
(d) none of these

Supratim Pal

Numerade Educator

Problem 40

In figure shown, a ray of light is incident at $50^{\circ}$ on the middle of one of a pair of mirrors arranged at $60^{\circ}$ :
(i) Calculate the image at which the ray is incident on the second mirror
(ii) Calculate the angle at which the ray is incident on the first mirror after being reflected from the second mirror.
(a) (i) $45^{\circ}$
(b) (i) $30^{\circ}$
(ii) $10^{\circ}$
(ii) $45^{\circ}$
(c) (i) $10^{\circ}$
(d) (i) $20^{\circ}$
(ii) $70^{\circ}$
(ii) $50^{\circ}$

Supratim Pal

Numerade Educator

Problem 41

In the given figure, the angle between reflected rays is equal to:
(a) $\mathrm{A}$
(b) $2 \mathrm{~A}$
(c) $3 \mathrm{~A}$
(d) $4 \mathrm{~A}$

Mahendra Kumar

Numerade Educator

Problem 42

Two plane mirrors are perpendicular to each other. A ray after suffering reflection from the two mirrors will be
(a) perpendicular to the original ray
(b) parallel to the original ray
(c) parallel to the first mirror
(d) at $45^{\circ}$ to the original ray

Supratim Pal

Numerade Educator

Problem 43

A vessel consists of two plane mirrors at right angles (as shown in figure). The vessel is filled with water. The total deviation in incident ray is:
(a) $0^{\circ}$
(b) $90^{\circ}$
(c) $180^{\circ}$
(d) none of the above

Supratim Pal

Numerade Educator

Problem 44

Two plane mirrors are inclined at an angle $\theta$. A ray of light is reflected from the first mirror and is then incident on the second mirror from which it is again reflected. What is deviation of incident ray ?
(a) $360^{\circ}+2 \theta$
(b) $360^{\circ}-\theta$
(c) $360^{\circ}-2 \theta$
(d) $360^{\circ}+\theta$

Supratim Pal

Numerade Educator

Problem 45

A light ray is incident on a horizontal plane mirror at an angle of $45^{\circ}$. At what angle should a second plane mirror be placed in order that the reflected ray finally be reflected horizontally from the second mirror, as shown in figure:
(a) $\theta=30^{\circ}$
(b) $\theta=24^{\circ}$
(c) $\theta=22.5^{\circ}$
(d) $\theta=67.5^{\circ}$

Supratim Pal

Numerade Educator

Problem 46

A number of images of a bright bulb can be seen in a thick mirror. The image is seen at a large angle of reflection. The brightest image is:
(a) the first one
(b) the second one
(c) the third one
(d) the fourth one

Supratim Pal

Numerade Educator

Problem 47

Two plane mirrors are combined to each other as such one is in $y-z$ plane and other is in $x-z$ plane. A ray of light along vector $\hat{i}+\hat{j}+k$ is incident on the first mirror. The unit vector in the direction of emergence ray after successive reflections through the mirror is:
(a) $-\frac{1}{\sqrt{3}} \hat{i}-\frac{1}{\sqrt{3}} \hat{j}+\frac{1}{\sqrt{3}}$
(w) $-\frac{1}{\sqrt{3}} \hat{i}-\frac{1}{\sqrt{3}} \hat{j}-\frac{1}{\sqrt{3}}$
(c) $-\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$
(d) none of these

Supratim Pal

Numerade Educator

Problem 48

A source of light lies on the angle bisector of two plane mirrors inclined at an angle $\theta$. The values of $\theta$, so that the light reflected from one mirror does not reach the other mirror will be :
(a) $\theta>120^{\circ}$
(b) $\theta>90^{\circ}$
(c) $\theta \leqslant 120^{\circ}$
(d) none of these

Supratim Pal

Numerade Educator

Problem 49

Two plane mirrors are placed parallel to each other. A. point object is placed between them. The distance of image formed in one of the mirror is in :(a) harmonic progression
(b) arithmetic progression
(c) geometric progression
(d) both harmonic and arithmetic progression

Supratim Pal

Numerade Educator

Problem 50

(a) harmonic progression
(b) arithmetic progression
(c) geometric progression
(d) both harmonic and arithmetic progression

Supratim Pal

Numerade Educator

Problem 51

Two plane mirrors are placed parallel to each other as shown in the figure. There is an object ' $O^{\prime}$ placed between the mirrors, at $5 \mathrm{~cm}$ from mirror $M_{2}$ What are the distance of first three images from the $M_{2} ?$ $\mathrm{M}_{1}$
(a) $5,10,15$
(b) $5,15,30$
(c) $5,25,25$
(d) $5,15,25$

Supratim Pal

Numerade Educator

Problem 52

If an object is placed between two plane mirrors. a distance $2 b$ apart, the object is situated at mid-point between mirrors, the position of $n^{\text {th }}$ image formed by one of the mirrors with respect to the object is:
(a) $n b$
(b) $2 n b$
(c) $3 n b$
(d) $4 n b$

Supratim Pal

Numerade Educator

Problem 53

If two mirrors are inclined at some angle and an object is placed between the mirrors and there are 7 images formed for an object. Then what is angle between the mirrors?
(a) $54^{\circ}$
(b) $50^{\circ}$
(c) $60^{\circ}$
(d) $64^{\circ}$

Supratim Pal

Numerade Educator

Problem 54

Two plane mirrors are placed at some angle. There are five images formed, when an object is placed symmetrically between them, the angle between the mirrors is :
(a) $60^{\circ}$
(b) $65^{\circ}$
(c) $30^{\circ}$
(d) $45^{\circ}$

Supratim Pal

Numerade Educator

Problem 55

Two plane mirrors are inclined at an angle such that a ray incident on a mirror undergoes a total deviation of $240^{\circ}$ after two reflections. The angle between mirrors. Also discuss the formation of image :
(a) $60^{\circ}, 5$
(b) $5^{\circ}, 60$
(c) $45^{\circ}, 5$
(d) $30^{\circ}, 6$

Supratim Pal

Numerade Educator

Problem 56

Two plane mirrors are inclined at $90^{\circ}$. An object is placed between them whose coordinates are $(a, b)$. Find the position vectors of all the images formed : (Take $\ddot{\mathbf{i}}, \overrightarrow{\mathbf{j}}$ are unit vectors along $x-y$ axis)
(a) $-a \hat{\mathbf{i}}-b \hat{\mathbf{j}}, a \hat{\mathbf{i}}-b \hat{\mathbf{j}},-a \hat{\mathbf{i}}+b \hat{\mathbf{j}}$(b) $-a \hat{\mathbf{i}}+b \hat{\mathbf{j}},-a \hat{\mathbf{i}}-b \hat{\mathbf{j}}, a \hat{\mathbf{i}}-b \hat{\mathbf{j}}$
(c) $a \hat{\mathbf{i}}+b \hat{\mathbf{j}},-a \hat{\mathbf{i}}-b \hat{\mathbf{j}},+a \hat{\mathbf{i}}-b \hat{\mathbf{j}}$
(d) none of the above

Supratim Pal

Numerade Educator

Problem 57

If two adjacent walls and the ceiling of a rectangular room are mirror surfaced, then how many images of himself, a man can see?
(a) 3
(b) 5
(c) 6
(d) 9

Supratim Pal

Numerade Educator

Problem 58

A convex mirror of focal length $10 \mathrm{~cm}$ is shown in figure. A linear object $A B=5 \mathrm{~cm}$ is placed along the optical axis. Point $B$ is at distance $25 \mathrm{~cm}$ from the pole of mirror. The size of image of $A B$ is :
(a) $2.5 \mathrm{~cm}$
(b) $0.64 \mathrm{~cm}$
(c) $0.36 \mathrm{~cm}$
(d) none of these

Supratim Pal

Numerade Educator

Problem 59

A point object $P$ is placed at centre of curvature of a concave mirror of focal length $25 \mathrm{~cm}$. The mirror is cut into two halves and shifted symmetrically $1 \mathrm{~cm}$ apart in perpendicular to the optical axis. The distance between images formed by both parts is:
(a) $2 \mathrm{~cm}$
(b) $1 \mathrm{~cm}$
(c) $3 \mathrm{~cm}$
(d) $4 \mathrm{~cm}$

Supratim Pal

Numerade Educator

Problem 60

In the measurement of the focal length $f$ of a concave mirror, the object distance $u=40 \pm 0.1 \mathrm{~cm}$ and image distance $v=20 \pm 0.2 \mathrm{~cm}$. The maximum $\%$ error in the measure of $f$ is :
(a) $1.75$
(b) $0.75$
(c) $0.3$
(d) $2.25$

Supratim Pal

Numerade Educator

Problem 61

If $u$ represents object distance from pole of spherical mirror and $v$ represents image distance from pole of mirror and $f$ is the focal length of the mirror, then a straight line $u=v$ will cut $u$ versus $v$ graph at :
(a) $(f, f)$
(b) $(2 f, 2 f)$
(c) $(f, 2 f)$
(d) $(0,0)$

Supratim Pal

Numerade Educator

Problem 62

A short linear object of Iength $l$ lies on the axis of a spherical mirror of focal length $f$, at a distance $x$ from the mirror. Then the length of the image $(P)$ so obtained will be :
(a) $\frac{l f}{(x-f)}$
(b) $\frac{l f^{2}}{(x-f)^{2}}$
(c) $\frac{l f}{x}$
(d) $\frac{l(x-f)}{x}$

Supratim Pal

Numerade Educator

Problem 63

A rear view mirror of a vehicle is cylindrical having radius of curvature $5 \mathrm{~cm}$ and length of arc of curved surface is $10 \mathrm{~cm}$. The field of view in radian, if it is assumed that the eye of the driver is at a large distance from the mirror, is:
(a) $0.5$
(b) 1
(c) 2
(d) 4

Supratim Pal

Numerade Educator

Problem 64

In the figure, $A B$ and $B K$ represent incident and reflected rays. If angle $B C F=\theta$, then $\angle B F P$ will be equal to :
(a) $\theta$
(b) $2 \theta$
(c) $3 \theta$
(d) $3.5 \theta$

Supratim Pal

Numerade Educator

Problem 65

The speed at which the image of the luminous point object is moving, if the luminous point object is moving at speed $v_{0}$ towards a spherical mirror, along its axis, is :
(Given : $R=$ radius of curvature, $u=$ object distance $)$
(a) $v_{t}=-v_{o}$
(b) $v_{t}=-v_{o}\left(\frac{R}{2 u-R}\right)$
(c) $v_{i}=-v_{0}\left(\frac{2 u-R}{R}\right)$
(d) $v_{i}=-v_{o}\left(\frac{R}{2 u-R}\right)^{2}$

Supratim Pal

Numerade Educator

Problem 66

A concave mirror produces an image $n$ times the size of an object. If the focal length of the mirror is ' $f^{\prime}$ and image formed is real, then the distance of the object from the mirror is :
(a) $(n-1) f$
(b) $\frac{(n-1)}{n} f$
(c) $\frac{(n+1)}{n} f$
(d) $(n+1) f$

Supratim Pal

Numerade Educator

Problem 67

The sun subtends an angle $\alpha=0.5^{\circ}$ at the pole of a concave mirror. The radius of curvature of concave mirror is $R(=1.5 \mathrm{~m}) .$ The size of image formed by the concave mirror is :
(a) $0.785 \mathrm{~cm}$
(b) $0.654 \mathrm{~cm}$
(c) $0.755 \mathrm{~cm}$
(d) $0.622 \mathrm{~cm}$

Supratim Pal

Numerade Educator

Problem 68

An observer is sitting $20 \mathrm{~cm}$ away from a circular convex mirror, with his eyes on the axis of the mirror. The mirror has diameter of $6 \mathrm{~cm}$ and focal length $30 \mathrm{~cm}$ is fixed with its principal axis horizontal. The image is formed at distance $12 \mathrm{~cm}$ from the mirror and the distance of mid-point of diameter from the pole is $0.75 \mathrm{~cm}$. The angular field of view in the horizontal plane seen in the mirror by the observer is :
(a) $\tan \theta=0.5672$
(b) $\tan =0.3014$
(c) $\tan \theta=0.5279$
(d) $\tan \theta=0.2516$

Mishal Gul

Numerade Educator

Problem 69

The position of $1 \mathrm{~cm}$ tall object which is placed $8 \mathrm{~cm}$ infront of a concave mirror of radius of curvature $24 \mathrm{~cm}$ is:
(a) $24 \mathrm{~cm}$
(b) $25 \mathrm{~cm}$
(c) $26 \mathrm{~cm}$
(d) $27 \mathrm{~cm}$

Supratim Pal

Numerade Educator

Problem 70

A convex driving mirror of focal length $20 \mathrm{~cm}$, is fitted in a motor car. If the second car $2 \mathrm{~m}$ broad and $1.6 \mathrm{~m}$ high is $6 \mathrm{~m}$ away from first car and overtakes the first car at a relative speed of $15 \mathrm{~m} / \mathrm{s}$, then how fast will the image be moving?
(a) $0.016 \mathrm{~m} / \mathrm{s}$
(b) $0.0257 \mathrm{~m} / \mathrm{s}$
(c) $0.162 \mathrm{~m} / \mathrm{s}$
(d) $0.0073 \mathrm{~m} / \mathrm{s}$

Mahendra Kumar

Numerade Educator

Problem 71

When an object is placed at a distance of $25 \mathrm{~cm}$ from a mirror, the magnification is $m_{1}$. But the magnification becomes $m_{2}$, when the object is moved $15 \mathrm{~cm}$ farther
away with respect to the earlier position. If $\frac{m_{1}}{m_{2}}=4$, then find the focal length of the mirror and what type of mirror it is?
(a) $20 \mathrm{~cm}$, convex
(b) $20 \mathrm{~cm}$, concave
(c) $10 \mathrm{~cm}$, convex
(d) $10 \mathrm{~cm}$, concave

Mahendra Kumar

Numerade Educator

Problem 72

Two objects ' $A^{\prime}$ and ' $B$ ' when placed in turns infront of a concave mirror, give images of equal size. The focal length of the concave mirror is $7.5 \mathrm{~cm}$ and size of object $A$ is three times the size of object $B$. The distance of $B$ from the mirror, if $A$ is placed $30 \mathrm{~cm}$ from the mirror, is :
(a) $18 \mathrm{~cm}$
(b) $15 \mathrm{~cm}$
(c) $20 \mathrm{~cm}$
(d) $25 \mathrm{~cm}$

Supratim Pal

Numerade Educator

Problem 73

An object of height $5 \mathrm{~cm}$ is placed in midway between a concave mirror of radius of curvature $30 \mathrm{~cm}$ and a convex mirror of radius of curvature $30 \mathrm{~cm}$. The mirrors are placed opposite to each other and are $60 \mathrm{~cm}$ apart. The position of the image formed by reflection at convex mirror is :
(a) $10 \mathrm{~cm}$
(b) $20 \mathrm{~cm}$
(c) $15 \mathrm{~cm}$
(d) $13 \mathrm{~cm}$

Supratim Pal

Numerade Educator

Problem 74

An object of height $5 \mathrm{~cm}$ is placed in midway between a concave mirror of radius of curvature $30 \mathrm{~cm}$ and a convex mirror of radius of curvature $30 \mathrm{~cm}$. The mirrors are placed opposite to each other and are $60 \mathrm{~cm}$ apart. The position of the image formed by reflection at convex mirror is :
(a) $10 \mathrm{~cm}$
(b) $20 \mathrm{~cm}$
(c) $15 \mathrm{~cm}$
(d) $13 \mathrm{~cm}$

Supratim Pal

Numerade Educator

Problem 75

An object is placed at a distance of $40 \mathrm{~cm}$ from a convex spherical mirror as shown in figure. The radius ofcurvature of the convex mirror is $20 \mathrm{~cm}$. At what distance from the object a plane mirror should be placed so that the image in the spherical mirror and plane mirror may be in one plane?
(a) $20 \mathrm{~cm}$
(b) $24 \mathrm{~cm}$
(c) $28 \mathrm{~cm}$
(d) $32 \mathrm{~cm}$

Supratim Pal

Numerade Educator

Problem 76

A body of mass $100 \mathrm{~g}$ is tied to one end of spring of constant $20 \mathrm{~N} / \mathrm{m}$. The distance between pole of mirror and mean position of the body is $20 \mathrm{~cm}$. The focal length of convex mirror is $10 \mathrm{~cm}$. The amplitude of vibration of image is :(a) $10 \mathrm{~cm}$
(b) $50 \mathrm{~cm}$
(c) $0.67 \mathrm{~cm}$
(d) $0.33 \mathrm{~cm}$

Supratim Pal

Numerade Educator

Problem 77

In the given figure, the angle of reflection is:
(a) $30^{\circ}$
(b) $60^{\circ}$
(c) $45^{\circ}$
(d) none of these

Supratim Pal

Numerade Educator

Problem 78

The reflective surface is given by $y=2 \sin x .$ The reflective surface is facing positive axis. What is the least values of co-ordinate of the point where a ray parallel to positive $x$ -axis becomes parallel to positive $y$ -axis after reflection?
(a) $\left(\frac{\pi}{3}, \sqrt{3}\right)$
(b) $\left(\frac{\pi}{2}, \sqrt{2}\right)$
(c) $\left(\frac{\pi}{3}, \sqrt{2}\right)$
(d) $\left(\frac{\pi}{4}, \sqrt{3}\right)$

Supratim Pal

Numerade Educator