GEOMETRICAL OPTICS - Puucho

GEOMETRICAL OPTICS

PHYSICS

TARGET IIT JEE 2010

XII (ALL)

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CONTENTS

KEY CONCEPT ............................................................. Page –2

EXERCISE–I .................................................................. Page –6

EXERCISE–II ................................................................ Page –8

EXERCISE–III ............................................................... Page –11

OBJECTIVE QUESTION BANK.................................. Page –16

ANSWER KEY ............................................................... Page –27

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Geometrical Optics [2]

KEY CONCEPTS

1. LAWS OF REFLECTION :

(i) The incident ray (AB), the reflected ray (BC) and normal (NN') to the surface (SS') of reflection at the

point of incidence (B) lie in the same plane. This plane is called the plane of incidence (also plane of

reflection).

(ii) The angle of incidence (the angle between normal and the incident

ray) and the angle of reflection (the angle between the reflected ray

and the normal) are equal

i = r

2. OBJECT :

(a) Real : Point from which rays actually diverge.

(b) Virtual : Point towards which rays appear to converge

3. IMAGE :

Image is decided by reflected or refracted rays only. The point image for a mirror is that point

(i) Towards which the rays reflected from the mirror, actually converge (real image).

OR

(ii) From which the reflected rays appear to diverge (virtual image) .

4. CHARACTERISTICS OF REFLECTION BY A PLANE MIRROR :

(a) The size of the image is the same as that of the object.

(b) For a real object the image is virtual and for a virtual object the image is real.

(c) For a fixed incident light ray, if the mirror be rotated through an angle the reflected ray turns through

an angle 2.

5. SPHERICAL MIRRORS :

Concave Convex

6. PARAXIAL RAYS : Rays which forms very small angle with axis are called paraxial rays.

7. SIGN CONVENTION :

We follow cartesian co-ordinate system convention according to which

(a) The pole of the mirror is the origin .

(b) The direction of the incident rays is considered as positive x-axis.

(c) Vertically up is positive y-axis.

Note : According to above convention radius of curvature and focus of concave mirror is negative and ofconvex mirror is positive.

8. MIRROR FORMULA : 1

f =

1 1

v u .

f = x- coordinate of focus ; u = x-coordinate of object ;

v = x-coordinate of image

Note : Valid only for paraxial rays.

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9. TRANSVERSE MAGNIFICATION : m = h

h

2

1

= v

u

h2 = y co-ordinate of image h

1 = y co-ordinate of the object

(both perpendicular to the principle axis of mirror)

10. NEWTON'S FORMULA :

Applicable to a pair of real object and real image position only . They are called conjugate positions

or foci. X,Y are the distance along the principal axis of the real object and real image respectively from

the principal focus .

XY = f 2

11. OPTICAL POWER : Optical power of a mirror (in Diopters) = – 1

f ;

f = focal length (in meters) with sign .

REFRACTION -PLANE SURFACE

1. LAWS OF REFRACTION (AT ANY REFRACTING SURFACE) :

(i) The incident ray (AB), the normal (NN') to the refracting surface (II') at

the point of incidence (B) and the refracted ray (BC) all lie in the same

plane called the plane of incidence or plane of refraction . i

r

C

B

A

I I

N

N

(ii)Sin i

Sin r = Constant :

for any two given media and for light of a given wave length. This is known as

SNELL'S Law .

Sin i

Sin r =

1n

2 =

n

n

2

1

= v

v

1

2

=

1

2

Note : Frequency of light does not change during refraction .

2. DEVIATION OF A RAY DUE TO REFRACTION :

3. REFRACTION THROUGH A PARALLEL SLAB :

(i) Emerged ray is parallel to the incident ray, if medium is same on

both sides.

(ii) Lateral shift x = t i r

r

sin( )

cos

r

iB

N A

N't

AIR

GLASS(M)

90°

ix

D

Ct = thickness of slab

Note : Emerged ray will not be parallel to the incident ray if the medium on both the sides

are different .

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4. APPARENT DEPTH OF SUBMERGED OBJECT :

(h < h)

at near normal incidence h =

2

1

h

Note : h and h' are always measured from surface.

5. CRITICAL ANGLE & TOTAL INTERNAL REFLECTION ( T. I. R.)

CONDITIONS OF T. I. R.(i) Ray is going from denser to rarer medium

(ii) Angle of incidence should be greater than the critical angle (i > c) .

Critical angle C = sin-1

i

r

n

n

6. REFRACTION THROUGH PRISM :

1. = (i + i) - (r + r)2. r + r = A

3. Variation of versus i (shown in diagram) .4. There is one and only one angle of incidence for which the angle

of deviation is minimum.When =

m then i = i & r = r , the ray passes symetrically

about the prism, & then

n =

sin

sin

A m

A

2

2

, where n = absolute R.I. of glass .

Note : When the prism is dipped in a medium thenn = R.I. of glass w.r.t. medium .

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5. For a thin prism ( A 10o) ; = ( n – 1 ) A

6. DISPERSION OF LIGHT :

The angular splitting of a ray of white light into a number of components when it is refracted in a medium

other than air is called Dispersion of Light.

7. Angle of Dispersion : Angle between the rays of the extreme colours in the refracted (dispersed) light

is called Angle of Dispersion . = v

– r .

8. Dispersive power () of the medium of the material of prism .

= angular dispersion

deviation of mean ray yellow( )

For small angled prism ( A 10o )

=

v R

y

=

n n

n

v R1

; n = n nv R

2

nv, n

R & n are R. I. of material for violet, red & yellow colours respectively .

9. COMBINATION OF TWO PRISMS :

(i) ACHROMATIC COMBINATION : It is used for deviation without dispersion .

Condition for this (nv

- nr) A = (n

v

- nr) A .

Net mean deviation = n nv R

21 A –

n nv R

21 A .

or + = 0 where , are dispersive powers for the two prisms & , are the mean deviation.

(ii) DIRECT VISION COMBINATION : It is used for producing disperion without deviation condition

for this n nv R

21 A =

n nv R

21 A .

Net angle of dispersion = (nv - n

r) A – (n

v - n

r) A .

REFRACTION AT SPERICAL SURFACE

1.(a)Ruv

1212

v, u & R are to be kept with sign

as v = PI

u = –PO

R = PC

(Note radius is with sign)

(b) m = u

v

2

1

2. LENS FORMULA :

(a)f

1

u

1

v

1

(b)f

1 = ( – 1)

21 R

1

R

1

(c) m = u

v

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EXERCISE # I

Q.1 Two flat mirrors have their reflecting surfaces facing each other, with an edge of one mirror in contact

with an edge of the other, so that the angle between the mirrors is 60° . Find all the angular positions of

the image with respect to x-axis. Take the case when a point object is between the mirrors at (1, 1).

Point of intersection is (0, 0) and 1st mirror is along x axis.

Q.2 In figure shown AB is a plane mirror of length 40cm placed at a height 40cm

from ground. There is a light source S at a point on the ground. Find the minimum

and maximum height of a man (eye height) required to see the

image of the source if he is standing at a point P on ground shown in figure.

A

B

40

cm

40 c

m

20cm 40cm

S P

Q.3 A plane mirror of circular shape with radius r = 20 cm is fixed to the ceiling. A bulb is to be placed on the

axis of the mirror. A circular area of radius R = 1 m on the floor is to be illuminated after reflection of light

from the mirror. The height of the room is 3m. What is maximum distance from the center of the mirror

and the bulb so that the required area is illuminated?

Q.4 A concave mirror of focal length 20 cm is cut into two parts from the

middle and the two parts are moved perpendicularly by a distance 1 cm

from the previous principal axis AB. Find the distance between the

images formed by the two parts?

Q.5 A balloon is rising up along the axis of a concave mirror of radius of curvature 20 m. A ball is dropped

from the balloon at a height 15 m from the mirror when the balloon has velocity 20 m/s. Find the speed

of the image of the ball formed by concave mirror after 4 seconds? [Take : g=10 m/s2]

Q.6 A thin rod of length d/3 is placed along the principal axis of a concave mirror of focal length = d such that

its image, which is real and elongated, just touches the rod. Find the length of the image?

Q.7 A point object is placed 33 cm from a convex mirror of curvature radius = 40 cm. A glass plate of

thickness 6 cm and index 2.0 is placed between the object and mirror, close to the mirror. Find the

distance of final image from the object?

Q.8 A large temple has a depression in one wall. On the floor plan it appears as a indentation having spherical

shape of radius 2.50 m. A worshiper stands on the center line of the depression, 2.00 m out from its

deepest point, and whispers a prayer. Where is the sound concentrated after reflection from the back

wall of the depression?

Q.9 An opaque cylindrical tank with an open top has a diameter of 3.00 m and is completely filled with water.

When the setting Sun reaches an angle of 37° above the horizon, sunlight ceases to illuminate any part of

the bottom of the tank. How deep is the tank?

Q.10 A beam of parallel rays of width b propagates in glass at an angle to its

plane face . The beam width after it goes over to air through this face is

_______ if the refractive index of glass is

Q.11 A room contains air in which the speed of sound is 340 m/s. The walls of the room are made of concrete,

in which the speed of sound is 1 700 m/s. (a) Find the critical angle for total internal reflection of sound

at the concrete–air boundary. (b) In which medium must the sound be traveling to undergo total internal

reflection?

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Q.12 A rod made of glass ( = 1.5) and of square cross-section is bent into the shape

shown in figure. A parallel beam of light falls perpendicularly on the plane flat surface

A. Referring to the diagram, d is the width of a side & R is the radius of inner

semicircle. Find the maximum value of ratio R

dso that all light entering the glass

through surface A emerge from the glass through surface B.

Q.13 A prism of refractive index 2 has a refracting angle of 30°. One of the refracting surfaces of the prism

is polished. For the beam of monochromatic light to retrace its path, find the angle of incidence on the

refracting surface.

Q.14 An equilateral prism deviates a ray through 23° for two angles of incidence differing by 23°. Find of the prism?

Q.15 A ray is incident on a glass sphere as shown. The opposite surface of the

sphere is partially silvered. If the net deviation of the ray transmitted at the

partially silvered surface is 1/3rd of the net deviation suffered by the ray

reflected at the partially silvered surface (after emerging out of

the sphere). Find the refractive index of the sphere.

Q.16 A narrow parallel beam of light is incident on a transparent sphere of refractive index 'n'. If the beam finally gets

focussed at a point situated at a distance = 2×(radius of sphere) from the centre of the sphere, then find n?

Q.17 A point object is placed at a distance of 25 cm from a convex lens of focal length 20 cm. If a glass slab

of thickness t and refractive index 1.5 is inserted between the lens and object. The image is formed at

infinity. Find the thickness t ?

Q.18 An object is kept at a distance of 16 cm from a thin lens and the image formed is real. If the object is kept

at a distance of 6 cm from the same lens the image formed is virtual. If the size of the image formed are

equal, then find the focal length of the lens?

Q.19 A thin convex lens forms a real image of a certain object ‘p’ times its size. The size of real image becomes

‘q’ times that of object when the lens is moved nearer to the object by a distance ‘a’ find focal length of

the lens?

Q.20 In the figure shown, the focal length of the two thin convex lenses is

the same = f. They are separated by a horizontal distance 3f and

their optical axes are displaced by a vertical separation 'd' (d << f),

as shown. Taking the origin of coordinates O at the centre of the first

lens, find the x and y coordinates of the point where a parallel beam

of rays coming from the left finally get focussed?

Q.21 A point source of light is kept at a distance of 15 cm from a converging lens, on its optical axis. The focal

length of the lens is 10 cm and its diameter is 3 cm. A screen is placed on the other side of the lens,

perpendicular to the axis of lens, at a distance 20 cm from it. Then find the area of the illuminated part of

the screen?

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Q.22 A double convex lens has focal length 25.0 cm in air. The radius of one of the surfaces is double of the

other. Find the radii of curvature if the refractive index of the material of the lens is 1.5.

Q.23 A plano convex lens (=1.5) has a maximum thickness of 1 mm. If diameter of its aperture is

4 cm. Find (i) Radius of curvature of curved surface; (ii) its focal length in air.

Q.24 The refractive indices of the crown glass for violet and red lights are

1.51 and 1.49 respectively and those of the flint glass are 1.77 and 1.73

respectively. A prism of angle 6° is made of crown glass. A beam of

white light is incident at a small angle on this prism. The other thin flint

glass prism is combined with the crown glass prism such that the net

mean deviation is 1.5° anticlockwise.

(i) Determine the angle of the flint glass prism.

(ii) A screen is placed normal to the emerging beam at a distance of 2m from the prism combination. Find

the distance between red and violet spot on the screen. Which is the topmost colour on screen.

Q.25 A prism of refractive index n1 & another prism of refractive index n

2

are stuck together without a gap as shown in the figure. The angles

of the prisms are as shown . n1 & n

2 depend on , the wavelength of

light according to n1 = 1.20 + 2

4108.10

& n

2 = 1.45 + 2

41080.1

where is in nm.

(i) Calculate the wavelength 0 for which rays incident at any angle on the interface BC pass through

without bending at that interface .

(ii) For light of wavelength 0, find the angle of incidence i on the face AC such that the deviation produced

by the combination of prisms is minimum .

EXERCISE # II

Q.1 An observer whose least distance of distinct vision is 'd', views his own face in a convex mirror of radius

of curvature 'r'. Prove that the magnification produced can not exceed 22 rdd

r

.

Q.2 A thief is running away in a car with velocity of 20 m/s. A police jeep is following him, which is sighted bythief in his rear view mirror which is a convex mirror of focal length 10 m. He observes that the image ofjeep is moving towards him with a velocity of 1 cm/s. If the magnification of the mirror for the jeep at thattime is 1/10. Find

(a) actual speed of jeep;(b) rate at which magnification is changing.

Assume that police jeep is on axis of the mirror.

Q.3 A surveyor on one bank of canal observes the images of the 4 inch mark and 17 ft mark on a vertical

staff, which is partially immersed in the water and held against the bank directly opposite to him. He see

that reflected and refracted rays come from the same point which is the centre of the canal. If the 17ft

mark and the surveyor’s eye are both 6ft above the water level, estimate the width of the canal, assuming

that the refractive index of the water is 4/3. Zero mark is at the bottom of the canal.

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Q.4 A ray of light travelling in air is incident at grazing angle (incident angle = 90°)

on a long rectangular slab of a transparent medium of thickness t = 1.0 (see

figure). The point of incidence is the origin A (O, O). The medium has a

variable index of refraction n(y) given by:

n (y) = [ky3/2 + 1]1/2, where k=1.0 m3/2. The refractive index of air is 1.0.

(i) Obtain a relation between the slope (dy/dx) of the trajectory of the ray at a point B (x , y) in the medium

and the incident angle (i) at that point.

(ii) Find the value of n sin i.

(iii) Obtain an equation for the trajectory y (x) of the ray in the medium.

(iv) Determine the coordinates (x1 , y

1) of the point P, where the ray the ray intersects the upper surface of

the slab-air boundary .

(v) Indicate the path of the ray subsequently.

Q.5 A uniform, horizontal beam of light is incident upon a quarter cylinder of

radius R = 5 cm, and has a refractive index 32 . A patch on the table for

a distance 'x' from the cylinder is unilluminated. find the value of 'x'?

Q.6 A concave mirror has the form of a hemisphere with a radius of R = 60 cm. A thin layer of an unknown

transparent liquid is poured into the mirror. The mirror-liquid system forms one real image and another

real image is formed by mirror alone, with the source in a certain position. One of them coincides with

the source and the other is at a distance of l = 30 cm from source. Find the possible value(s) refractive

index µ of the liquid.

Q.7 A parallel beam of light falls normally on the first face of a prism of small angle. At the second face it is

partly transmitted and partly reflected, the reflected beam striking at the first face again, and emerging

from it in a direction making an angle 6°30' with the reversed direction of the incident beam. The refracted

beam is found to have undergone a deviation of 1°15' from the original direction. Find the refractive

index of the glass and the angle of the prism.

Q.8 A light ray I is incident on a plane mirror M. The mirror is rotated in the

direction as shown in the figure by an arrow at frequency 9/ rev/sec.

The light reflected by the mirror is received on the wall W at a distance

10 m from the axis of rotation. When the angle of incidence becomes

37° find the speed of the spot (a point) on the wall?

Q.9 The diagram shows five isosceles right angled prisms. A light ray incident

at 90° at the first face emerges at same angle with the normal from the

last face. Find the relation between the refractive indices?

Q.10 Two rays travelling parallel to the principal axis strike a large plano–convex lens having a refractive index

of 1.60. If the convex face is spherical, a ray near the edge does not pass through the focal point

(spherical aberration occurs). If this face has a radius of curvature of magnitude 20.0 cm and the two

rays are h1 = 0.500 cm and h

2 = 12.0 cm from the principal axis, find the difference in the positions

where they cross the principal axis.

•C

R x

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Q.11 Two thin similar watch glass pieces are joined together, front to front, with rear convex portion silvered

and the combination of glass pieces is placed at a distance a = 60 cm from a screen. A small object is

placed normal to the optical axis of the combination such that its two times magnified image is formed on

the screen. If air between the glass pieces is replaced by water ( = 4/3), calculate the distance through

which the object must be displaced so that a sharp image is again formed on the screen.

Q.12 A spherical lightbulb with a diameter of 3.0 cm radiates light equally in all directions, with a power of

4.5 W. (a) Find the light intensity at the surface of the bulb. (b) Find the light intensity 7.50 m from the

center of the bulb. (c) At this 7.50-m distance, a convex lens is set up with its axis pointing toward the

bulb. The lens has a circular face with a diameter of 15.0 cm and a focal length of 30.0 cm. Find the

diameter of the image of the bulb formed on a screen kept at the location of the image. (d) Find the light

intensity at the image.

Q.13 A thin plano-convex lens fits exactly into a plano concave lens with their plane

surface parallel to each other as shown in the figure. The radius of curvature of

the curved surface R = 30 cm. The lens are made of difference material having

refractive index 1 = 3/2 and

2 = 5/4 as shown in figure.

(i) if plane surface of the plano-convex lens is silvered, then calculate the equivalent

focal length of this system and also calculate the nature of this equivalent mirror.

(ii) An object having transverse length 5 cm in placed on the axis of equivalent mirror (in

part 1), at a distance 15 cm from the equivalent mirror along principal axis. Find the

transverse magnification produced by equivalent mirror.

Q.14 Two identical convex lenses L1 and L

2 are placed at a distance of 20 cm from each other on the common

principal axis. The focal length of each lens is 15 cm and the lens L2 is to the right of lens A. A point

object is placed at a distance of 20 cm on the left of lens L1, on the common axis of two lenses. Find,

where a convex mirror of radius of curvature 5 cm should be placed to the right of L2 so that the final

image coincides with the object?

Q.15 A thin equiconvex lens of glass of refractive index =3/2

& of focal length 0.3 m in air is sealed into an opening

at one end of a tank filled with water ( = 4/3). On the

opposite side of the lens, a mirror is placed inside the

tank on the tank wall perpendicular to the lens axis, as

shown in figure . The separation between the lens and the

mirror is 0.8 m . A small object is placed outside the tank

in front of the lens at a distance of 0.9 m from the lens

along its axis . Find the position (relative to the lens) of the

image of the object formed by the system.

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EXERCISE # III

Q.1 A concave lens of glass, refractive index 1.5, has both surfaces of same radius of curvature R. On

immersion in a medium of refractive index 1.75, it will behave as a [JEE ’99]

(A) convergent lens of focal length 3.5R (B) convergent lens of focal length 3.0 R.

(C) divergent lens of focal length 3.5 R (D) divergent lens of focal length 3.0 R

Q.2 The x-y plane is the boundary between two transparent media. Medium-1 with z > 0 has refractive index

2 and medium – 2 with z < 0 has a refractive index 3 . A ray of light in medium –1 given by the

vector k10j38i36A is incident on the plane of separation. Find the unit vector in the

direction of refracted ray in medium -2. [JEE ’99]

Q.3 A quarter cylinder of radius R and refractive index 1.5 is placed on a table. A point

object P is kept at a distance of mR from it. Find the value of m for which a ray from

P will emerge parallel to the table as shown in the figure. [JEE '99]

Q.4 Two symmetric double-convex lenses L1 and L

2 with their radii of curvature 0.2m each are made from

glasses with refractive index 1.2 and 1.6 respectively. The lenses with a separation of 0.345 m are

submerged in a transparent liquid medium with a refractive index of 1.4. Find the focal lengths of lens L1

and L2. An object is placed at a distance of 1.3m from L

1, find the location of its image while the whole

system remains inside the liquid. [REE ’99]

Q.5 Select the correct alternative. [JEE '2000 (Scr)]

(a) A diverging beam of light from a point source S having divergence angle , falls

symmetrically on a glass slab as shown. The angles of incidence of the two

extreme rays are equal. If the thickness of the glass slab is t and the refractive

index n, then the divergence angle of the emergent beam is

(A) zero (B) (C) sin1(1/n) (D) 2sin1(1/n)

(b) A rectangular glass slab ABCD, of refractive index n1, is immersed in water

of refractive index n2(n

1> n

2). A ray of light is incident at the surface AB of the

slab as shown. The maximum value of the angle of incidence max

, such that

the ray comes out only from the other surface CD is given by

(A)

1

21

2

11

n

nsincos

n

nsin (B)

2

11

1

n

1sincosnsin

(C)

2

11

n

nsin (D)

1

21

n

nsin

(c) 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

along a line parallel to the mirror at a distance 2L 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) 2d (D) 3d

(d) A hollow double concave lens is made of very thin transparent material. It can be filled with air or either

of two liquids L1 or L

2 having refractive indices n

1 and n

2 respectively (n

2 > n

1 > 1). The lens will diverge

a parallel beam of light if it is filled with

(A) air and placed in air. (B) air and immersed in L1.

(C) L1 and immersed in L

2. (D) L

2 and immersed in L

1.

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Q.6 A convex lens of focal length 15 cm and a concave mirror of focal length

30 cm are kept with their optic axes PQ and RS parallel but separated

in vertical direction by 0.6 cm as shown. The distance between the lens

and mirror is 30 cm. An upright object AB of height 1.2 cm is placed on

the optic axis PQ of the lens at a distance of 20 cm from the lens . If AB is the image after refraction from the lens and reflection from the

mirror, find the distance A B from the pole of the mirror and obtain its

magnification. Also locate positions of A and B with respect to the

optic axis RS. [JEE 2000]

Q.7 A thin equiconvex lens of refractive index 3/2 is placed on a horizontal

plane mirror as shown in the figure. The space between the lens and the

mirror is then filled with water of refractive index 4/3. It is found that

when a point object is placed 15 cm above the lens on its principal axis,

the object coincides with its own image. On repeating with another liquid,

the object and the image again coincide at a distance 25 cm from

the lens. Calculate the refractive index of the liquid. [JEE 2001]

Q.8 The refractive indices of the crown glass for blue and red lights are 1.51 and 1.49 respectively and those

of the flint glass are 1.77 and 1.73 respectively. An isosceles prism of angle 6° is made of crown glass.

A beam of white light is incident at a small angle on this prism. The other flint glass isosceles prism is

combined with the crown glass prism such that there is no deviation of the incident light. Determine the

angle of the flint glass prism. Calculate the net dispersion of the combined system. [JEE 2001]

Q.9 An observer can see through a pin-hole the top end of a thin rod of

height h, placed as shown in the figure. The beaker height is 3h and its

radius h. When the beaker is filled with a liquid up to a height 2h, he can

see the lower end of the rod. Then the refractive index of the liquid is

(A) 5/2 (B) 2/5

3h

2h

h

(C) 2/3 (D) 3/2 [JEE 2002 (Scr)]

Q.10 Which one of the following spherical lenses does not exhibit dispersion? The radii of curvature of the

surfaces of the lenses are as given in the diagrams. [JEE 2002 (Scr)]

(A) (B) (C) (D)

Q.11 Two plane mirrors A and B are aligned parallel to each other, as shown

in the figure. A light ray is incident at an angle of 30° at a point just inside

one end of A. The plane of incidence coincides with the plane of the

figure. The maximum number of times the ray undergoes reflections

(including the first one) before it emerges out is [JEE 2002 (Scr)]

(A) 28 (B) 30 (C) 32 (D) 34

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Q.12 A convex lens of focal length 30 cm forms an image of height 2 cm for an object situated at infinity. If a

convcave lens of focal length 20 cm is placed coaxially at a distance of 26 cm in front of convex lens then

size image would be [JEE 2003 (Scr)]

(A) 2.5 cm (B) 5.0 (C) 1.25 (D) None

Q.13 A meniscus lens is made of a material of refractive index 2. Both its surfaces

have radii of curvature R. It has two different media of refractive indices 1

and 3 respectively, on its two sides (see figure). Calculate its focal length for

1 <

2 <

3, when light is incident on it as shown. [JEE 2003]

Q.14 White light is incident on the interface of glass and air as shown in the figure. If

green light is just totally internally reflected then the emerging ray in air contains

(A) yellow, orange, red (B) violet, indigo, blue

(C) all colours (D) all coloure except green

[JEE 2004 (Scr)]

Q.15 A ray of light is incident on an equilateral glass prism placed on a horizontal

table. For minimum deviation which of the following is true ? [JEE 2004 (Scr)]

(A) PQ is horizontal (B) QR is horizontal

(C) RS is horizontal (D) Either PQ or RS is horizontal.

Q.16 A point object is placed at the centre of a glass sphere of radius 6 cm and refractive index 1.5. The

distance of the virtual image from the surface of the sphere is [JEE 2004 (Scr)]

(A) 2 cm (B) 4 cm (C) 6 cm (D) 12 cm

Q.17 Figure shows an irregular block of material of refractive index 2 . AA

ray of light strikes the face AB as shown in the figure. After refraction it

is incident on a spherical surface CD of radius of curvature 0.4 m and

enters a medium of refractive index 1.514 to meet PQ at E. Find the

distance OE upto two places of decimal. [JEE 2004]

Q.18 An object is approaching a thin convex lens of focal length 0.3 m with a speed of 0.01 m/s. Find the

magnitudes of the rates of change of position and lateral magnification of image when the object is at a

distance of 0.4 m from the lens. [JEE 2004]

Q.19 The ratio of powers of a thin convex and thin concave lens is 2

3 and equivalent focal length of their

combination is 30 cm. Then their focal lengths respectively are [JEE' 2005 (Scr)]

(A) 75, – 50 (B) 75, 50 (C) 10, – 15 (D) – 75, 50

Q.20 Figure shows object O. Final image Iis formed after two refractions and one

reflection is also shown in figure. Find the focal length of mirror. (in cm) :

(A) 10 (B) 15 (C) 20 (D) 25

[JEE' 2005 (Scr)]

Q.21 What will be the minimum angle of incidence such that the total internal reflection

occurs on both the surfaces?

[JEE 2005]

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Q.22 Two identical prisms of refractive index 3 are kept as shown in the figure. A light ray strikes the first

prism at face AB. Find,

(a) the angle of incidence, so that the emergent ray from the first prism has

minimum deviation.

(b) through what angle the prism DCE should be rotated about C so that

the final emergent ray also has minimum deviation.

[JEE 2005]

Q.23 A point object is placed at a distance of 20 cm from a thin plano-convex lens of focal

length 15 cm, if the plane surface is silvered. The image will form at

(A) 60 cm left of AB

(B) 30 cm left of AB

(C) 12 cm left of AB

(D) 60 cm right of AB [JEE 2006]

Q.24 Parallel rays of light from Sun falls on a biconvex lens of focal length f and the circular image of radius r

is formed on the focal plane of the lens. Then which of the following statement is correct?

(A)Area of image r2 directly proportional to f

(B) Area of image r2 directly proportional to f2

(C) Intensity of image increases if f is increased.

(D) If lower half of the lens is covered with black paper area of image will become half. [JEE 2006]

Q.25 A simple telescope used to view distant objects has eyepiece and objective lens of focal lengths fe and f

0,

respectively. Then [JEE 2006]

Column 1 Column 2

(A) Intensity of image formed by lens (P) Radius of aperture (R)

(B) Angular magnification (Q) Dispersion of lens

(C) Length of telescope (R) focal length f0, f

e

(D) Sharpness of image (S) spherical aberration

Q.26 A ray of light travelling in water is incident on its surface open to air. The angle of incidence is , which is

less than the critical angle. Then there will be [JEE 2007]

(A) only a reflected ray and no refracted ray

(B) only a refracted ray and no reflected ray

(C) a reflected ray and a refracted ray and the angle between them would be less than 180° – 2(D) a reflected ray and a refracted ray and the angle between them would be greater than 180° – 2

Q.27 STATEMENT-1

The formula connecting u, v and f for a spherical mirror is valid only for mirrors whose sizes are very

small compared to their radii of curvature

because

STATEMENT-2

Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

(C) Statement-1 is True, Statement-2 is False

(D) Statement-1 is False, Statement-2 is True [JEE 2007]

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Q.28 Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is

60°). In the position of minimum deviation, the angle of refraction will be : [JEE-2008]

(A) 30° for both the colours (B) greater for the violet colour

(C) greater for the red colour (D) equal but not 30° for both the colours

Q.29 A light beam is traveling from Region I to Region IV (Refer Figure). The refractive index in Regions I, II,

III and IV are n0,

2

n0,

6

n0 and

8

n0, respectively. The angle of incidence for which the beam just

misses entering Region IV is [JEE-2008]

Figure :

Region I Region II Region III Region IV

2

n0n0 6

n0

8

n0

0 0.2 m 0.6 m

(A) sin–1

4

3(B) sin–1

8

1(C) sin–1

4

1(D) sin–1

3

1

Q.30 An optical component and an object S placed along its optic axis are given in Column I. The distance

between the object and the component can be varied. The properties of images are given in Column II.

Match all the properties of images from Column II with the appropriate components given in Column

I Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.

[JEE-2008]

Column I Column II

(A)S

(p) Real image

(B)S

(q) Virtual image

(C)

S

(r) Magnified image

(D)S

(s) Image at infinite

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OBJECTIVE QUESTION BANKONLY ONE OPTION IS CORRECT.

Take approx. 2 minutes for answering each question.

Q.1 Two plane mirrors are inclined at 70º. A ray incident on one mirror at angle after reflection falls on the

second mirror and is reflected from there parallel to the first mirror, is :

(A) 50º (B) 45º (C) 30º (D) 55º

Q.2 There are two plane mirror with reflecting surfaces facing each other. Both the mirrors are moving with

speed v away from each other. A point object is placed between the mirrors. The velocity of the image

formed due to n-th reflection will be

(A) nv (B) 2nv (C) 3nv (D) 4nv

Q.3 A man of height ‘h’ is walking away from a street lamp with a constant speed ‘v’. The height of the street

lamp is 3h. The rate at which of the length of the man’s shadow is increasing when he is at a distance 10h

from the base of the street lamp is :

(A) v/2 (B) v/3 (C) 2v (D) v/6

Q.4 A boy of height 1.5 m with his eye level at 1.4 m stands before a plane mirror of length 0.75 m fixed on

the wall. The height of the lower edge of the mirror above the floor is 0.8 m. Then :

(A) the boy will see his full image (B) the boy cannot see his hair

(C) the boy cannot see his feet (D) the boy cannot see neither his hair nor his feet.

Q.5 A point source of light S is placed in front of two large mirrors as shown. Which

of the following observers will see only one image of S?

(A) only A (B) only C

(C) Both A and C (D) Both B and C

Q.6 The reflecting surface of a plane mirror is vertical. A particle is projected in a vertical plane which is also

perpendicular to plane of the mirror. The initial velocity of the particle is 10 m/s and the angle of projection

is 60°. The point of projection is at a distance 5 m from the mirror. The particle moves towards the

mirror. Just before the particle touches the mirror the velocity of approach of the particle and its image is:

(A) 10 m/s (B) 5 m/s (C) 310 m/s (D) 35 m/s

Q.7 The circular boundary of the concave mirror subtends a cone of half angle at

its centre of curvature. The minimum value of for which ray incident on this

mirror parallel to the principle axis suffers more than one reflection is

(A) 30° (B) 45° (C) 60° (D) 75°

Q.8 The passenger side-view mirror on an automobile often has the notation. "Objects seen in mirror are

closer than they appear". Is the image really farther away than the object?

(A) Yes, the image is smaller and farther away than the object

(B) No, the image is smaller and closer than the object

(C) No, the image is larger and closer than the object

(D) Yes, the image is larger and farther away than the object

Q.9 In the figure shown, the image of a real object is formed at point I.

AB is the principal axis of the mirror. The mirror must be :

(A) concave & placed towards right I

(B) concave & placed towards left of I

(C) convex and placed towards right of I

(D) convex & placed towards left of I.

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Q.10 A straight line joining the object point and image point is always perpendicular to the mirror

(A) if mirror is plane only (B) if mirror is concave only

(C) if mirror is convex only (D) irrespective of the type of mirror.

Q.11 An object is placed in front of a convex mirror at a distance of 50 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 cm, it is found that

there is no gap between the images formed by the two mirrors. The radius of the convex mirror is :

(A) 12.5 cm (B) 25 cm (C) 50 cm (D) 100 cm

Q.12 An infinitely long rod lies along the axis of a concave mirror of focal length f. The near end of the rod is

at a distance u > f from the mirror. Its image will have a length

(A) f 2/(u–f) (B) uf / (u–f) (C) f 2 /(u + f) (D) uf /(u + f)

Q.13 A luminous point object is moving along the principal axis of a concave mirror of focal length 12 cm towards it.

When its distance from mirror is 20 cm its velocity is 4 cm/s. The velocity of the image in cm/s at that instant is :

(A) 6 towards the mirror (B) 6 away from the mirror

(C) 9 away from the mirror (D) 9 towards the mirror

Q.14 In the figure shown if the object ‘O’ moves towards the plane mirror, then the image

I (which is formed after successive reflections from M1 & M

2 respectively)

will move:

(A) towards right (B) towards left

(C) with zero velocity (D) cannot be determined

Q.15 A point source of light is 60 cm from a screen and is kept at the focus of a concave mirror which reflects

light on the screen. The focal length of the mirror is 20 cm. The ratio of average intensities of the illumination

on the screen when the mirror is present and when the mirror is removed is :

(A) 36 : 1 (B) 37 : 1 (C) 49 : 1 (D) 10:1

Q.16 A ray of sunlight enters a spherical water droplet (n = 4/3) at an angle of incidence 53° measured with

respect to the normal to the surface. It is reflected from the back surface of the droplet and re-enters into

air. The angle between the incoming and outgoing ray is [Take sin 53° = 0.8]

(A) 15° (B) 34° (C) 138° (D) 30°

Q.17 A ray of light moving along the unit vector (– i – 2j) undergoes refraction at an interface of two media,

which is the x-z plane. The refractive index for y > 0 is 2 while for y < 0, it is 25 . The unit vector along

which the refracted ray moves is :

(A) 34

)j5i3( (B)

5

)j3i4( (C)

5

)j4i3( (D) None of these

Q.18 A bird is flying 3 m above the surface of water. If the bird is diving vertically down with speed = 6 m/s,

his apparent velocity as seen by a stationary fish underwater is :

(A) 8 m/s (B) 6 m/s (C) 12 m/s (D) 4 m/s

Q.19 A parallel sided block of glass of refractive index 1.5 which is 36 mm thick rests on the

floor of a tank which is filled with water (refractive index = 4/3). The difference between

apparent depth of floor at A & B when seen from vertically above is equal to

(A) 2 mm (B) 3 mm (C) 4 mm (D) none of these

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Q.20 A beam of light is converging towards a point I. A plane

parallel plate of glass of thickness t , refractive index

is introduced in the path of the beam. The convergent

point is shifted by (assume near normal incidence) :

(A)

11t away (B)

11t away

(C)

11t nearer (D)

11t nearer

Q.21 A concave mirror is placed on a horizontal table, with its axis directed vertically upwards. Let O be the

pole of the mirror and C its centre of curvature. A point object is placed at C. It has a real image, also

located at C (a condition called auto-collimation). If the mirror is now filled with water, the image will be:

(A) real, and will remain at C (B) real, and located at a point between C and (C) virtual, and located at a point between C and O (D) real, and located at a point between C and O

Q.22 In the diagram shown below, a point source O is placed vertically below the center of a circular plane

mirror. The light rays starting from the source are reflected from the mirror such that a circular area A on

the ground receives light. Now, a glass slab is placed between the mirror and the source O. What will the

magnitude of the new area on the ground receiving light?

(A) A

(B) Greater than A

(C) Less than A

(D) Cannot tell, as the information given is insufficient

Q.23 In the figure ABC is the cross section of a right angled prism and BCDE is the

cross section of a glass slab. The value of so that light incident normally on the

face AB does not cross the face BC is (given sin–1 (3/5) = 37°)

(A) 37° (B) > 37° (C) 53° (D) < 53°

Q.24 A small source of light is 4m below the surface of a liquid of refractive index 5/3. In order to cut off all the

light coming out of liquid surface, minimum diameter of the disc placed on the surface of liquid is :

(A) 3m (B) 4m (C) 6m (D)

Q.25 A point source of light is placed at a distance h below the surface of a large deep lake. What is the

percentage of light energy that escapes directly from the water surface? of the water = 4/3? (neglect

partial reflection)

(A) 50% (B) 25% (C) 20% (D) 17%

Q.26 A vertical pencil of rays comes from bottom of a tank filled with a liquid. When it is accelerated horizontally

with an acceleration of 7.5 m/s2, the ray is seen to be totally reflected by liquid surface. What is minimum

possible refractive index of liquid?

(A) slightly greater than 4/3 (B) slightly greater than 5/3

(C) slightly greater than 1.5 (D) slightly greater than 1.75

Q.27 Two glass blocks of triangular cross section (n = 1.5) are used to make a periscope. Which of the

following is the correct arrangement?

(A) (B) (C) (D)

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Q.28 A ray of light from a denser medium strike a rarer medium. The angle of reflection is r and that of refraction

is r'. The reflected and refracted rays make an angle of 90° with each other. The critical angle will be :

(A) sin–1(tan r) (B) tan–1(sin r) (C) sin–1 (tan r') (D) tan–1 (sin r')

Q.29 Consider a common mirage formed by super-heated air just above a roadway. A truck driver is in a

medium of = 1.000 3 looks forward. He perceives the illusion of a patch of water ahead on the road,

where his line of sight makes an angle of 1.20° below the horizontal. Find the index of refraction of the air

just above the road surface. (Hint: Treat this as a problem in total internal reflection.)

(A) 1.00006 (B) 1.0001 (C) 1.00008 (D) None of these

Q.30 A concave spherical surface of radius of curvature 10cm separates two medium

X & Y of refractive index 4/3 & 3/2 respectively. If the object is placed along

principal axis in medium X then

(A) image is always real

(B) image is real if the object distance is greater than 90cm

(C) image is always virtual

(D) image is virtual if the object distance is less than 90cm

Q.31 A fish is near the centre of a spherical water filled ( = 4/3) fish bowl. A child stands in air at a distance

2R (R is the radius of curvature of the sphere) from the centre of the bowl. At what distance from the

centre would the child nose appear to the fish situated at the centre :

(A) 4R (B) 2R (C) 3R (D) 4R

Q.32 A beam of diameter ‘d’ is incident on a glass hemisphere as shown. If the radius

of curvature of the hemisphere is very large in comparison to d, then the diameter

of the beam at the base of the hemisphere will be:

(A) 4

3 d (B) d (C)

3

d(D)

3

2 d

Question No. 33 to 35 (3 questions)

The figure, shows a transparent sphere of radius R and refractive index . Anobject O is placed at a distance x from the pole of the first surface so

that a real image is formed at the pole of the exactly opposite surface.

Q.33 If x = 2R, then the value of is(A) 1.5 (B) 2 (C) 3 (D) none of these

Q.34 If x = , then the value of is(A) 1.5 (B) 2 (C) 3 (D) none of these

Q.35 If an object is placed at a distance R from the pole of first surface, then the real image is formed at adistance R from the pole of the second surface. The refractive index of the sphere is given by

(A) 1.5 (B) 2 (C) 2 (D) none of these

Q.36 When the object is at distances u1 and u

2 the images formed by the same lens are real and virtual

respectively and of the same size. Then focal length of the lens is :

(A) 21uu2

1(B) )uu(

2

121 (C) 21uu (D) 2 (u

1 + u

2)

Q.37 Parallel beam of light is incident on a system of two convex lenses of focal

lengths f1 = 20 cm and f

2 = 10 cm. What should be the distance between the

two lenses so that rays after refraction from both the lenses pass undeviated :

(A) 60 cm (B) 30 cm

(C) 90 cm (D) 40 cm

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Q.38 An object is placed at a distance of 15 cm from a convex lens of focallength 10 cm. On the other side of the lens, a convex mirror is placed atits focus such that the image formed by the combination coincides withthe object itself. The focal length of the convex mirror is

(A) 20 cm (B) 10 cm (C) 15 cm (D) 30 cm

Q.39 A thin lens of focal length f and its aperture has a diameter d. It forms an image of intensity I. Now the

central part of the aperture upto diameter (d/2) is blocked by an opaque paper. The focal length and

image intensity would change to

(A) f/2, I/2 (B) f, I/4 (C) 3f/4, I/2 (D) f, 3I/4

Q.40 An object is placed in front of a thin convex lens of focal length 30 cm and a plane mirror is placed 15 cm

behind the lens. If the final image of the object coincides with the object, the distance of the object from

the lens is

(A) 60 cm (B) 30 cm (C) 15 cm (D) 25 cm

Question No. 41 to 43 (3 questions)

A turnip sits before a thin converging lens, outside the focal point of the

lens. The lens is filled with a transparent gel so that it is flexible; by squeezing

its ends toward its center [as indicated in figure(a)], you can change the

curvature of its front and rear sides.

Q.41 When you squeeze the lens, the image.

(A) moves towards the lens (B) moves away from the lens

(C) shifts up (D) remains as it is

Q.42 When you squeeze the lens, the lateral height of image.

(A) increases (B) decreases (C) remains same (D) data insufficient

Q.43 Suppose that a sharp image must be formed on a card which is at a certain

distance behind the lens [figure(b)], while you move the turnip away from

the lens, then you should

(A) decrease the squeeze of the lens

(B) increase the squeeze of the lens

(C) keep the card and lens as it is.

(D) move the card away from the lens

Q.44 If an object is placed at A (OA>f); Where f is the focal length of

the lens the image is found to be formed at B. A perpendicular is

erected at O and C is chosen on it such that the angle BCA is

a right angle. Then the value of f will be

(A) AB/OC2 (B) (AC)(BC)/OC (C) (OC)(AB)/AC+BC (D) OC2/AB

Q.45 The height of the image formed by a converging lens on a screen is 8cm. For the same position of the

object and screen again an image of size 12.5cm is formed on the screen by shifting the lens. The height

of the object :

(A) 625/32cm (B) 64/12.5cm (C) 10cm (D) none

Q.46 A converging lens of focal length 20 cm and diameter 5 cm is cut along the

line AB. The part of the lens shown shaded in the diagram is now used to

form an image of a point P placed 30 cm away from it on the line XY. Which

is perpendicular to the plane of the lens. The image of P will be formed.

(A) 0.5 cm above XY (B) 1 cm below XY

(C) on XY (D) 1.5 cm below XY

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Q.47 A screen is placed 90 cm from an object. The image of an object on the screen is formed by a convex

lens at two different locations separated by 20 cm. The focal length of the lens is

(A) 18 cm (B) 21.4 cm (C) 60 cm (D) 85.6 cm

Q.48 In the above problem, if the sizes of the images formed on the screen are 6 cm and 3 cm, then the height

of the object is nearly :

(A) 4.2 cm (B) 4.5 cm (C) 5 cm (D) 9 cm

Q.49 Look at the ray diagram shown, what will be the focal

length of the 1st and the 2nd lens, if the incident light ray

is parallel to emergent ray.

(A) –5cm and –10cm

(B) +5cm and +10cm

(C) –5cm and +5cm

(D) +5cm and +5cm

Q.50 A point object is kept at the first focus of a convex lens. If the lens starts moving towards right with a

constant velocity, the image will

(A) always move towards right

(B) always move towards left

(C) first move towards right & then towards left.

(D) first move towards left & then towards right.

Q.51 Two planoconvex lenses each of focal length 10 cm & refractive index 3/2 are

placed as shown. In the space left, water (R.I = 4/3) is filled. The whole

arrangement is in air. The optical power of the system is (in diopters) :

(A) 6.67 (B) – 6.67 (C) 33.3 (D) 20

Q.52 The curvature radii of a concavo-convex glass lens are 20 cm and 60 cm. The convex surface of the lens

is silvered. With the lens horizontal, the concave surface is filled with water. The focal length of the

effective mirror is ( of glass = 1.5, of water = 4/3)

(A) 90/13 cm (B) 80/13 cm (C) 20/3 cm (D) 45/8 cm

Q.53 An object is placed in front of a symmetrical convex lens with refractive index 1.5 and radius of curvature

40 cm. The surface of the lens further away from the object is silvered. Under auto-collimation condition,

the object distance is

(A) 20 cm (B) 10 cm (C) 40 cm (D) 5 cm

Q.54 A planoconvex lens, when silvered at its plane surface is equivalent to a concave mirror of focal length

28cm. When its curved surface is silvered and the plane surface not silvered, it is equivalent to a concave

mirror of focal length 10cm, then the refractive index of the material of the lens is :

(A) 9/14 (B) 14/9 (C) 17/9 (D) none

Q.55 A beam of monochromatic light is incident at i =50° on one face of an equilateral prism, the angle of

emergence is 40°, then the angle of minimum deviation is :

(A) 30° (B) < 30° (C) 30° (D) 30°

Q.56 A ray incident at an angle 53° on a prism emerges at an angle at 37° as shown. If the

angle of incidence is made 50°, which of the following is a possible value of the angle

of emergence.

(A) 35° (B) 42° (C) 40° (D) 38°

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Q.57 A prism has a refractive index 2

3 and refracting angle 90°. Find the minimum deviation produced by prism.

(A) 40° (B) 45° (C) 30° (D) 49°

Q.58 A certain prism is found to produce a minimum deviation of 38°. It produces a deviation of 44° when the angle

of incidence is either 42° or 62°. What is the angle of incidence when it is undergoing minimum deviation?

(A) 45° (B) 49° (C) 40° (D) 55°

Q.59 A thin prism of angle 5° is placed at a distance of 10 cm from object. What is the distance of the image

from object? (Given of prism = 1.5)

(A) 8

cm (B)

12

cm (C)

36

5 cm (D)

7

cm

Q.60 Light ray is incident on a prism of angle A = 60° and refractive index = 2 . The angle of incidence at

which the emergent ray grazes the surface is given by

(A)

2

13sin 1

(B)

2

31sin 1

(C) sin–1

2

3(D) sin–1

3

2

Q.61 When a monochromatic light ray is incident on a medium of refractive index with angle of incidence

i , the angle of refraction is

r. If

i is changed slightly by

i , then the corresponding change in

r will be

(A) i

(B) i

(C) ir

i ·cos

cos·

1

(D) · ir

i ·sin

sin

Q.62 Two lenses in contact made of materials with dispersive powers in the ratio 2 : 1, behaves as an achromatic

lens of focal length 10 cm. The individual focal lengths of the lenses are:

(A) 5 cm, –10 cm (B) – 5 cm, 10 cm (C) 10 cm, – 20 cm (D) – 20 cm, 10 cm

Q.63 A beam of light consisting of red, green and blue is incident on a right angled prism. The refractive index

of the material of the prism for the above red, green and blue wavelengths are 1.39, 1.44 and 1.47

respectively. The prism will :

(A) separate part of the red color from the green and blue colors.

(B) separate part of the blue color from the red and green colours.

(C) separate all the three colors from the other two colors.

(D) not separate even partially any color from the other two colors.

Q.64 It is desired to make an achromatic combination of two lenses (L1 & L

2) made of materials having

dispersive powers 1 and

2 (<

1). If the combination of lenses is converging then

(A) L1 is converging (B) L

2 is converging

(C) Power of L1 is greater than the power of L

2(D) None of these

ASSERTION AND REASON

Q.1 Statement 1 : If a source of light is placed in front of rough wall its image is not seen.

Statement 2 : The wall does not reflect light.

(A) Statement-1 is true, statement-2 is true; statement-2 is correct explanation for statement-1.

(B) Statement-1 is true, statement-2 is true; statement-2 is NOT the correct explanation for statement-1.

(C) Statement-1 is true, statement-2 is false.

(D) Statement-1 is false, statement-2 is true.

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Q.2 Statement 1 : As the distance x of a parallel ray from axis increases,

focal length decreases

Statement 2 : As x increases, the distance from pole to the point of

intersection of reflected ray with principal axis decreases

(A) Statement-1 is true, statement-2 is true; statement-2 is correct explanation for statement-1.

(B) Statement-1 is true, statement-2 is true; statement-2 is NOT the correct explanation for statement-1.



Q.3 Statement-1 : When an object dipped in a liquid is viewed normally, the distance between the image

and the object is independent of the height of the liquid above the object.

Statement-2 : The normal shift is independent of the location of the slab between the object and the

observer.

(A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.

(B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.



Q.4 Statement-1 : When two plane mirrors are kept perpendicular to each other as shown (O is the point

object), 3 images will be formed.

O

Statement-2 : In case of multiple reflection, image of one surface can act as an object for the next

surface.





Q.5 Statement-1 : Keeping a point object fixed, if a plane mirror is moved, the image will definitely move.

Statement-2 : In case of a plane mirror, distance of a point object and its image from a given point on

mirror is equal.





ONE OR MORE THAN ONE OPTION MAY BE CORRECT

Take approx. 3 minutes for answering each question.

Q.1 A man of height 170 cm wants to see his complete image in a plane mirror (while standing). His eyes are

at a height of 160 cm from the ground.

(A) Minimum length of the mirror = 80 cm

(B) Minimum length of the mirror = 85 cm.

(C) Bottom of the mirror should be at a height 80 cm or less

(D) Bottom of the mirror should be at a height 85 cm.

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Q.2 A flat mirror M is arranged parallel to a wall W at a distance l from it. The light

produced by a point source S kept on the wall is reflected by the mirror and produces

a light spot on the wall. The mirror moves with velocity v towards the wall.

(A) The spot of light will move with the speed v on the wall.

(B) The spot of light will not move on the wall.

(C) As the mirror comes closer the spot of light will become larger and shift away from the wall with

speed larger then v.

(D) The size of the light spot on the wall remains the same.

Q.3 A reflecting surface is represented by the equation Y =

L

xsin

L2 , 0 x L. A ray travelling

horizontally becomes vertical after reflection. The coordinates of the point (s) where this ray is incident is

(A)

L2

,4

L (B)

L3

,3

L (C)

L2

,4

L3 (D)

L3

,3

L2

Q.4 A concave mirror cannot form

(A) virtual image of virtual object (B) virtual image of a real object

(C) real image of a real object (D) real image of a virtual object.

Q.5 In the figure shown consider the first reflection at the plane mirror

and second at the convex mirror. AB is object.

(A) the second image is real , inverted of 1/5 th magnification w.r.t AB

(B) the second image is virtual and erect with magnification1/5 w.r.t AB

(C) the second image moves towards the convex mirror

(D) the second image moves away from the convex mirror.

Q.6 A ray of light is incident normally on one face of 30° – 60° – 90° prism

of refractive index 5/3 immersed in water of refractive index 4/3 as

shown in figure.30°

1

2

P

(A) The exit angle 2 of the ray is sin–1(5/8)

(B) The exit angle 2 of the ray is sin–1( 345 )

(C) Total internal reflection at point P ceases if the refractive index of water is increased to 325 by

dissolving some substance.

(D) Total internal reflection at point P ceases if the refractive index of water is increased to 5/6 by

dissolving some substance.

Q.7 Point A(0, 1) and B (12, 5) are object – image pair (one of the point acts as object and the other point

as image) x-axis is the principal axis of the mirror. Then this object image pair is:

(A) due to a convex mirror of focal length 2.5 cm

(B) due to a concave mirror having its pole at (2, 0)

(C) real virtual pair

(D) data is insufficient for options (A) and (B)

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Q.8 A ray of light in a liquid of refractive index 1.4, approaches the boundary surface between the liquid and

air at an angle of incidence whose sine is 0.8. Which of the following statements is correct about the

behaviour of the light

(A) It is impossible to predict the behavior of the light ray on the basis of the information supplied.

(B) The sine of the angle of refraction of the emergent ray will less than 0.8.

(C) The ray will be internally reflected

(D) The sine of the angle of refraction of the emergent ray will be greater than 0.8.

Q.9 The figure shows a ray incident at an angle i = /3. If the plot drawn shown the variation of | r – i | versus

2

1

= k, (r = angle of refraction)

(A) the value of k1 is

3

2(B) the value of

1 = /6

(C) the value of 2 = /3 (D) the value of k

2 is 1

Q.10 In the figure shown a point object O is placed in air on the principal axis. The

radius of curvature of the spherical surface is 60 cm. If is the final image formed

after all the refractions and reflections.

(A) If d1 = 120 cm, then the ‘I

f’ is formed on ‘O’ for any value of d

2.

(B) If d1 = 240 cm, then the ‘I

f’ is formed on ‘O’ only if d

2= 360 cm.

(C) If d1 = 240 cm, then the ‘I

f’ is formed on ‘O’ for all values of d

2.

(D) If d1 = 240 cm, then the ‘I

f’ cannot be formed on ‘O’.

Q.11 In the diagram shown, a ray of light is incident on the interface between 1 and 2 at

angle slightly greater than critical angle. The light suffers total internal reflection at

this interface. After that the light ray falls at the interface of 1 and 3, and again it

suffers total internal reflection. Which of the following relations should hold true?

(A) 1 <

2 <

3(B)

22

21

> 23

(C) 23

21

> 22

(D) 22

21

> 23

Q.12 Two refracting media are separated by a spherical interface as shown in the figure. PP’ is the principal

axis, 1 and

2 are the refractive indices of medium of incidence and medium of refraction respectively.

Then :

(A) if 2 >

1, then there cannot be a real image of real object.

(B) if 2 >

1, then there cannot be a real image of virtual object.

(C) if 1 >

2, then there cannot be a virtual image of virtual object.

(D) if 1 >

2, then there cannot be a real image of real object.

Q.13 A luminous point object is placed at O, whose image is formed at I as shown in the figure. AB is the

optical axis. Which of the following statements are correct?

(A) If a lens is used to obtain image, the lens must be converging

(B) If a mirror is used to obtain image, the mirror must be a convex mirror

having pole at the point of intersection of lines OI and AB

(C) Position of principal focus of mirror cannot be found

(D) I is real image

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Q.14 A lens is placed in the XYZ coordinate system such that its optical center is at the origin and principal

axis is along the X axis. The focal length of the lens is 20 cm. A point object has been placed at the point

(– 40 cm, + 1cm, –1 cm). Which of the following are correct about coordinates of the image?

(A) x = 40 cm (B) y = + 1 cm (C) z = + 1 cm (D) z = – 1 cm

Q.15 Which of the following can form diminished, virtual and erect image of your face.

(A) Converging mirror (B) Diverging mirror (C) Converging lens (D) Diverging lens

Q.16 A convex lens forms an image of an object on a screen. The height of the image is 9 cm. The lens is now

displaced until an image is again obtained on the screen. The height of this image is 4 cm. The distance

between the object and the screen is 90cm.

(A) The distance between the two positions of the lens is 30cm.

(B) The distance of the object from the lens in its first position is 36cm.

(C) The height of the object is 6cm.

(D) The focal length of the lens is 21.6 cm.

Q.17 A thin lens with focal length f is to be used as a magnifying glass. Which of the following statements

regarding the situation is true?

(A) A converging lens may be used, and the object be placed at a distance greater than 2f from the lens.

(B) A diverging lens may be used, and the object be placed between f and 2f from the lens.

(C) A converging lens may be used, and the object be placed at a distance less than f from the lens.

(D) A diverging lens may be used, and the object be placed at any point other than the focal point.

Q.18 A man wanted to get a picture of a Zebra. He photographed a white donkey after fitting a glass withblack streaks onto the objective of his camera.(A) the image will look like a white donkey on the photograph.(B) the image will look like a Zebra on the photograph.(C) the image will be more intense compared to the case in which no such glass is used.(D) the image will be less intense compared to the case in which no such glass is used.

Q.19 For refraction through a small angle prism, the angle of deviation :

(A) increases with the increase in R.I. of prism.

(B) will decrease with the increase in R.I. of prism.

(C) is directly proportional to the angle of prism.

(D) will be 2D for a ray of R.I.=2.4 if it is D for a ray of R.I.=1.2

Q.20 For the refraction of light through a prism

(A) For every angle of deviation there are two angles of incidence.

(B) The light travelling inside an equilateral prism is necessarily parallel to the base when prism is set for

minimum deviation.

(C) There are two angles of incidence for maximum deviation.

(D) Angle of minimum deviation will increase if refractive index of prism is increased keeping the outside

medium unchanged if P >

S.

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ANSWER KEY

EXERCISE # I

Q.1 (i) 75° (ii) 165° (iii) 195° (iv) 285° (v) 315° Q.2 160cm; 320cm

Q.3 75 cm Q.4 2 cm Q.5 80 m/s Q.6 d/2

Q.7 42 cm Q.8

m

3

10Q.9 4m Q.10

sin

)cos1(b 2/122

Q.11 (a) sin–1

5

1 (b) air Q.12

maxR

d

=

1

2Q.13 45° Q.14

5

43

Q.15 3 Q.16 4/3 Q.17 15 cm Q.18 11 cm

Q.19)pq(

apq

Q.20 (5f, 2d) Q.21 (/4) cm2 Q.22 75/4 cm, 75/2 cm

Q.23 (i) 0.2 m ,(ii) 0.4 m Q.24 (i) 2° ,(ii) mm9

4

Q.25 (i) 0 = 600 nm, n = 1.5 (ii) i = sin1 (0.75) = 48.59º

EXERCISE # II

Q.2 (a) 21 m/s, (b) 1 × 10–3 /sec Q.3 16 feet

Q.4 (i) tan = d y

d x = cot i ; (ii) 1 ; (iii) y = k2 44x ; (iv) 4.0, 1; (v) It will become parallel to x-axis

Q.5 5 cm Q.6 1.5 or )15( Q.7 = 8

13, A = 2° Q.8 1000 m/s

Q.9 24

22

25

23

21

2 Q.103

52 cm

Q.11 15 cm towards the combination

Q.12 (a) 5000 W/m2 (b) 0.02 W/m2 (c) 0.125 cm (d) 288 W/m2

Q.13 + 60, + 4/5 Q.14 5.9 cm,10.9 cm Q.15 90 cm from the lens towards right

EXERCISE # III

Q.1 A Q.2 )45r;60incidenceofangle(k2

1j

5

22i

25

3r 00

Q.3 m = 4/3 Q.4 f1 = -70cm, f

2 = 70cm, V= 560 cm to the right of L

2

Q.5 (a) B (b) A (c) D (d) D

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Q.6 A B at 15cm to the right of mirror. B is 0.3cm above RS and A is 1.5cm below RS. Magnification is 1.5

Q.7 1.6 Q.8 40 and –0.040 Q.9 B Q.10 C

Q.11 B Q.12 A Q.1313

3Rvf

Q.14 A

Q.15 B Q.16 C Q.17 06.61.0

4.0514.1

m correct upto two places of decimal.

Q.18 0.09 m/s ; Magnitude of the rate of change of lateral magnification is 0.3 s–1.

Q.19 C Q.20 C Q.21 60°

Q.22 (a) i = 60°, (b) 60° (anticlockwise)

Q.23 C Q.24 B Q.25 (A) P ; (B) R; (C) R; (D) P, Q, S

Q.26 C Q.27 C Q.28 A Q.29 B

Q.30 (A) p, q, r, s (B) q, (C) p, q, r, s (D) p, q, r, s

OBJECTIVE QUESTION BANKONLY ONE OPTION IS CORRECT.

Q.1 A Q.2 B Q.3 A Q.4 C Q.5 B

Q.6 A Q.7 B Q.8 B Q.9 B Q.10 D

Q.11 B Q.12 A Q.13 C Q.14 A Q.15 D

Q.16 C Q.17 B Q.18 A Q.19 B Q.20 A

Q.21 D Q.22 A Q.23 A Q.24 C Q.25 D

Q.26 B Q.27 D Q.28 A Q.29 C Q.30 C

Q.31 C Q.32 D Q.33 C Q.34 B Q.35 B

Q.36 B Q.37 B Q.38 B Q.39 D Q.40 B

Q.41 A Q.42 B Q.43 A Q.44 D Q.45 C

Q.46 D Q.47 B Q.48 A Q.49 C Q.50 D

Q.51 A Q.52 A Q.53 A Q.54 B Q.55 B

Q.56 D Q.57 C Q.58 B Q.59 C Q.60 A

Q.61 C Q.62 A Q.63 A Q.64 B

ASSERTION AND REASON

Q.1 C Q.2 D Q.3 D Q.4 D Q.5 D

ONE OR MORE THAN ONE OPTION MAY BE CORRECT

Q.1 B, C Q.2 B, D Q.3 B, D Q.4 A Q.5 B, C

Q.6 A, C Q.7 B, C, D Q.8 C Q.9 B, C, D Q.10 A, B

Q.11 B, C, D Q.12 A, C Q.13 A, D Q.14 A, C Q.15 B, D

Q.16 B, C, D Q.17 C Q.18 A, D Q.19 A, C Q.20 B,C,D

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GEOMETRICAL OPTICS - Puucho

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