Geometrical Optics

Topic Page No.

Theory 01 - 04

Exercise - 1 05 - 19



Exercise - 4 40

Answer Key 41 - 43

Contents

Syllabus

GEOMETRICAL OPTICS

Rectilinear propagation of light, Reflection and refraction at plane and

spherical surfaces ; Total internal reflection ; Deviation and dispersion of

light by a prism ; Thin lenses ; Combination of mirrors and thin lenses ;

Magnification.

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GEOMETRICAL OPTICS (Adv.) # 1

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 ofreflection).

(ii) The angle of incidence (the angle between normal and the incidentray) and the angle of reflection (the angle between the reflected rayand 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 of convex

mirror is positive.

8. MIRROR FORMULA :1f

= 1 1v u .

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

v = x-coordinate of image

Note : Valid only for paraxial rays.

GEOMETRICAL OPTICS



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9. TRANSVERSE MAGNIFICATION : m = 2

1

h

h= 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) = � 1f

;

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

r

C

B

A

I I

N

N

(ii)Sin iSin r

= Constant :

for any two given media and for light of a given wave length. This is known asSNELL'S Law .

Sin iSin r

= 1n

2 = 2

1

n

n = 1

2

v

v = 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 sin(i r)

cosr

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 sidesare 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 r

i

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 =

A m2

A2

sin

sin

, 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 mediumother than air is called Dispersion of Light.

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

1 ; n =

n nv R

2n

v, 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 - n

r) A = (n

v - n

r) 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 signas 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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PART - I : OBJECTIVE QUESTIONS

* Marked Questions are having more than one correct option.

SECTION (A) : PLANE MIRROR

A-1. A plane mirror makes an angle of 30o with horizontal. If a vertical ray strikes the mirror, find the anglebetween mirror and reflected ray(A) 30o (B) 45o (C) 60o (D) 90o

A-2. A ray of light is incident on the first mirror parallel to the second and is reflected from the second mirrorparallel to first mirror. The angle between two mirrors is(A) 30o (B) 60o (C) 75o (D) 90o

A-3. If incident ray MP and reflected ray QN are parallel to each other, find the angle between the mirrors.

1i1i

2i

2i

NM

P Q

(A) 60 (B) 45 (C) 90 (D) 180

A-4. A point source has been placed as shown in thefigure. What is the length on the screen that willreceive reflected lightfrom the mirror ?(A) 2H(B) 3H(C) H(D) None

A-5. A man of height H is standing in front of a mirror, which has been fixed on theground.

What length of his body can the man see in the mirror ? (The length of the mirror is H2.

(Neglect seperation between eyes and head of men)

(A) H (B) 2

12 2 2

H

(H L )

(C) zero (D) 22H

L



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A-6. A child is standing in front of a straight plane mirror. His father is standingbehind him, as shown in the figure. The height of the father is double theheight of the child. What is the minimum length of the mirror required so thatthe child cancompletely see his own image and his father�s image in the mirror?

H H(Height of child is H)

(A)H2

(B) 5H6

(C) 3H2

(D) None

A-7. Find the angle of deviation (anticlockwise) suffered by a ray incident on a plane mirror, (as shown in figure)at an angle of incidence 30º.

(A) 240º (B) 100º (C) 80º (D) 120º

A-8. Figure shows a plane mirror onto which a light ray is incident. If the incident light ray is turned by 10º and the

mirror by 20º, as shown, then the angle turned by the reflected ray is-

(A) 60º clockwise (B) 30º clockwise. (C) 30º anticlockwise (D) 60º anti clockwise

A-9. An unnumbered wall clock shows time 04: 25: 37, where 1st term represents hours, 2nd representsminutes & the last term represents seconds. What time will its image in a plane mirror show.

(A) 08: 35: 23 (B) 07: 35: 23

(C) 07: 34: 23 (D) none of these

A-10. A plane mirror is placed at origin parallel to y-axis, facing the positive x-axis. An object starts from

(2, 0, 0) with a velocity of � �(2i 2 j) m/s. The relative velocity of image with respect to object is along

(A) positive x-axis (B) negative x-axis

(C) positive y-axis (D) negative y-aixs



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A-11. Two mirrors are inclined at an angle as shown in the figure. Light ray is incident parallel to one of themirrors. Light will start retracing its path after third reflection if :

(A) = 45° (B) = 30°

(C) = 60° (D) all three

A-12. In the figure shown, the maximum number of reflections will be :

(A) 2 (B) 3 (C) 4 (D) 1

A-13. A person is in a room whose ceiling and two adjacent walls are mirrors. How many images are formed(A) 5 (B) 6 (C) 7 (D) 8

SECTION (B) : SPHERICAL MIRROR

B-1. The distance of an object from the pole of a concave mirror is equal to its radius of curvature. The imagemust be:(A) real (B) inverted (C) same sized (D) erect

B-2. The distance of an object from a spherical mirror is equal to the focal length of the mirror. Then the image:(A) must be at infinity (B) may be at infinity (C) may be at the focus (D) None of these

B-3. AB is an incident beam of light and CD is a reflected beam (the number of reflections for this may be 1 ormore than 1) of light. AB & CD are separated by some distance (may be large). It is possible by placingwhat type of mirror on the right side.

(A) one plane mirror (B) one concave mirror(C) one convex mirror (D) none of these

B-4. A convex mirror cannot form (for real or virtual object):(A) real, diminished image (B) virtual, diminished image(C) real, enlarged image (D) virtual, enlarged image

B-5. For a real object, all of the following statements are correct except :(A) the magnification produced by a convex mirror is always less than one (except at the pole)(B) a virtual, erect, same sized image can be obtained by using a plane mirror(C) a virtual, erect, magnified image can be formed using a concave mirror(D) a real, inverted, same sized image can be formed using a convex mirror.



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B-6. The minimum distance of the real image of a real object, formed by a concave mirror of focal length� f � from the mirror is:

(A) 0 (B) f (C) 2 f (D) 4

f

B-7. In the figure shown, the image of a real object is formed at point I. AB is the principal axis of the mirror. Themirror must be :(A) concave & placed towards right of I(B) concave & placed towards left of I(C) convex and placed towards right of I(D) convex & placed towards left of I.

B-8.* The image (of a real object) formed by a concave mirror is twice the size of the object. The focallength of the mirror is 20 cm. The distance of the object from the mirror is (are)(A) 10 cm (B) 30 cm (C) 25 cm (D) 15 cm

B-9. The minimum sum of the distances of a real object and a real image from a concave mirror of radiusof curvature 20 cm is:(A) 10 cm (B) 40 cm(C) 20 cm (D) none of these

B-10. The sun (diameter d) subtends an angle radians at the pole of a concave mirror of focal length f. What is

the diameter of the image of the sun formed by the mirror?

(A) f (B) f/2 (C) f2 (D) f2

B-11. In the figure shown find the total magnification after two successive reflections first on M1 & then

on M2

(A) + 1 (B) � 2 (C) + 2 (D) � 1

B-12. A square ABCD of side 1mm is kept at distance 15 cm infront of the concave mirror as shown in the figure.The focal length of the mirror is 10 cm. The length of the perimeter of its image will be(nearly):

(A) 8 mm (B) 2 mm (C) 12 mm (D) 6 mm

B-13. A luminous point object is moving along the principal axis of a concave mirror of focal length 12 cm towardsit. When its distance from the mirror is 20 cm its velocity is 4 cm/s. The velocity of the image in cm/s at thatinstant is

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

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



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B-14. A particle executes SHM in front of a concave mirror of radius 1 m, about the center of curvature, with smallamplitude a. The amplitude of oscillation of the image is(A) a (B) 2a(C) a/2 (D) none of these

B-15. If x and y be the distances of the object and image formed by a concave mirror from its focus and f be thefocal length then(A) xf = y2 (B) xy = f2 (C) x/y = f (D) x/y = f2

B-16. Which of the following is a correct graph of relation between u, v & f (where u, v, f have standardmeaning) for a concave mirror.

(A) (B)

(C) (D)

B-17. Select a graph between �v� and �u� for a concave mirror.

(A)

v

O u

(B)

v

O u

(C)

v

O u

(D)

v

O u

B-18. A virtual erect image in a concave mirror is represented, in the above figures, by

(1) (2) (3) (4)

(A) 1 (B) 2 (C) 3 (D) 4



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SECTION (C) REFRACTION IN GENERAL , REFRACTION AT PLANE SURFACE AND T.I.R

C-1. When a ray of light of frequency 6×1014 Hz travels from water of refractive index 4/3 to glass of refractiveindex 8/5, its(A) frequency decreases by a factor of 5/6 (B) speed decreases by a factor of 5/6

(C) wavelength increases by a factor of 6/5 (D) speed increases by a factor of 6/5

C-2. A ray of light passes from vacuum into a medium of refractive index . If the angle of incidence is twicethe angle of refraction, then the angle of incidence is(A) cos�1(/2) (B) sin�1(/2)

(C) 2 cos�1(/2) (D) 2sin�1(/2)

C-3. A beam of light is converging towards a point on the screen. If a plane parallel plate of glass of refractive

index and thickness t is introduced in the path of the beam, the convergence point is shifted

(A)

11t away (B)

11t nearer (C)

11t away (D)

11t nearer

C-4. A 2 cm diameter coin rests flat on the bottom of a bowl in which the water is 20 cm deep water43

. If the

coin is viewed directly from above, what is its apparent diameter ?

(A) 2 cm (B) 1.5 cm (C) 2.67 cm (D) 1.67 cm

C-5. A vessel contains a slab of glass 8 cm thick and of refractive index 1.6.Over the slab, the vessel is filled by oil of refractive index µ upto height

4.5 cm and also by another liquid i.e. water of refractive index 43

and

height 6 cm. As shown in figure. As observer looking down from above,he observes that, a mark at the bottom of the glass slab appears to beraised up to position 6 cm from the bottom of the slab. Refractive index (µ) of oil is-

6 cm

6 cm

Oil

Water

4.5

cm

8 cm

Glassl

O

(A) 1.5 (B) 2.5 (C) 0.5 (D) 1.2

C-6. Locate the image of the point P as seen by the eye in the figure.

(A) 0.9 cm below P (B) 0.8 cm above P (C) 0.7 cm above P (D) 0.9 cm above P



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C-7. A bird is flying 3 m above the surface of water. If the bird is diving vertically down with speed = 6 m/s, hisapparent 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

C-8.* A ray of monochromatic light is incident on the plane surface of separation between two media x and y withangle of incidence �i� in the medium x and angle of refraction �r� in the medium y. The graph shows therelation between sin r and sin i.

(A) the speed of light in the medium y is (3)1/2 times in medium x.(B) the speed of light in the medium y is (1/3)1/2 times in medium x.(C) the total internal reflection can take place when the incidence is in x.(D) the total internal reflection can take place when the incidence is in y.

C-9. The critical angle of light going from medium A to medium B is . The speed of light in medium A is v.

The speed of light in medium B is:

(A) v

sin(B) v sin (C) v cot (D) v tan

SECTION (D) : REFRACTION BY PRISM

D-1. A ray of monochromatic light is incident on one refracting face of a prism of angle 750. It passes through theprism and is incident on the other face at the critical angle. If the refractive index of the material of the prism

is 2 , the angle of incidence on the first face of the prism is

(A) 300 (B) 450 (C) 600 (D) 00

D-2. A prism has two acute angles of 30º each and refractive index of 1.6. If

two parallel light rays AB and CD are incident as shown in the figure, theangle between the emergent rays is [Use sin�1 (0.75) = 48.6º].

(A) 48° (B) 37º

30º

30º

A B

DC

(C) 52º (D) 46º

D-3. The refracting angle of a prism is A and the refractive index of the material of the prism is cot A2

. The angle

of minimum deviation is-

(A) 180° � 3A (B) 180° + 2A (C) 90° � A (D) 180° � 2A

D-4. On an equilateral prism, it is observed that a ray strikes grazingly at one face and if refractive indexof the prism is 2 , then the angle of deviation is :

(A) 60º (B) 120º (C) 30º (D) 90º



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D-5. A prism having an apex angle of 4º and refractive index of 1.50 is located in front of a vertical plane mirroras shown in the figure. A horizontal ray of light is incident on the prism. The total angle through which theray is deviated is:

M

P

(A) 4º clockwise (B) 178º clockwise (C) 2º clockwise (D) 8º clockwise

D-6. The angle of deviation suffered by the light ray shown in figure for following two conditions

(refractive index for the prism material is µ = 3/2).

(a) When the prism is placed in air ( = 1)

(A) 2º (B) 0.5º (C) 1.5º (D) 2.5º

(b) When the prism is placed in water ( = 4/3)

(A) 2º (B) 8º3

(C) 5º

8(D) 2.5º

SECTION (E) : REFRACTION BY SPHERICAL SURFACE

E-1. A transparent sphere of radius R and refractive index µ is kept in air. At what distance from the surface of

the sphere should a point object be placed so as to form a real image at the same distance from the otherside of the sphere ?

(A) Rµ

(B) µR (C) R

µ 1(D)

Rµ 1

E-2. In the given figure a plano-concave lens is placed on a paper on which a flower is drawn. How farabove its actual position does the flower appear to be ?

(A) 10 cm (B) 15 cm (C) 50 cm (D) none of these



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E-3. There is a small air bubble inside a glass sphere (µ = 1.5) of radius 5 cm. The bubble is at 'O' at 7.5

cm below the surface of the glass. The sphere is placed inside water (µ = 34

) such that the top

surface of glass is 10 cm below the surface of water. The bubble is viewed normally from air. Thenthe apparent depth of the bubble is

(A) 272

cm (B) 252

cm (C) 312

cm (D) 232

cm

E-4. An object is placed 10 cm away from a glass piece (n = 1.5) of length 20 cm bound by spherical surfacesof radii of curvature 10 cm. Then the position of final image formed after two refractions at the sphericalsurfaces.

(A) 50 cm left of B (B) 40 cm right of B(C) 50 cm right of B (D) 60 cm right of B

E-5. 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

E-6. A small object Q of length 1 mm lies along the principal axis of a spherical glass of radius R = 10 cmand refractive index is 3/2. The object is seen from air along the principal axis from left. The distanceof object from the centre P is 5 cm. Then the size of the image is

(A) 8/3 mm, (B) 103

cm (C) 73

cm (D) 53

cm



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SECTION (F) : LENS

F-1. An object is placed in front of a thin convex lens of focal length 30 cm and a plane mirror is placed 15 cmbehind the lens. If the final image of the object coincides with the object, the distance of the object from thelens is

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

F-2. When a lens of power P (in air) made of material of refractive index is immersed in liquid of refractive

index 0. Then the power of lens is:

(A)

1

0

P (B)

0

1 P

(C)

0

1.

P

0

(D) none of these

F-3. A lens behaves as a converging lens in air and diverging lens in water. The refractive index of material is

(A) equal to 1 (B) between 1 and 1.33

(C) 1.33 (D) > 1.33

F-4. From the figure shown establish a relation among , 1,

2,

3.

(A) 3 >

2 >

1(B)

3 <

2 <

1

(C) 2 >

3 ;

3 =

1(D)

2 >

1 ;

3 =

2

F-5. Focal length of a convex lens of refractive index 1.5 is 2 cm. Focal length of lens when immersed in a liquidof refractive index 1.25 will be

(A) 5 cm (B) 7.5 cm (C) 10 cm (D) 2.5 cm

F-6. In the figure given below, there are two convex lens L1 and L

2 having focal length of f

1 and f

2 respectively.

The distance between L1 and L

2 will be

L1 L2

(A) f1 (B) f2 (C) f1 + f2 (D) f1 - f2



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F-7.* The values of d1 & d2 for final rays to be parallel to the principal axis are : (focal lengths of the lensesare written above the respective lenses in the given figure)

(A) d1 = 10 cm, d2 = 15 cm (B) d1 = 20 cm, d2 = 15 cm

(C) d1 = 30 cm, d2 = 15 cm (D) None of these

F-8.* An object O is kept in front of a converging lens of focal length 30 cm behind which there is a planemirror at 15 cm from the lens as shown in the figure.

(A) the final image is formed at 60 cm from the lens towards right of it

(B) the final image is at 60 cm from lens towards left of it

(C) the final image is real

(D) the final image is virtual.

F-9. How many image are formed by the lens shown, if an object is kept on its axis-

(A) one (B) twoµ2µ1

(C) three (D) four

F-10. A convex lens of focal length 10 cm is painted black at the middle portionas shown in figure. An object is placed at a distance of 20 cm from thelens. Then-

(A) only one image will be formed by the lens

20cm

2mmO

(B) the distance between the two images formed by such a lens is 6 mm

(C) the distance between the images is 4 mm

(D) the distance between the images is 2 mm

F-11. A thin lens has focal length f and its aperture has a diameter d. It forms an image of intensity I. Now thecentral part of the aperture upto diameter (d/2) is blocked by an opaque paper. The focal length and imageintensity would change to

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



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SECTION (G) : COMBINATION OF LENSES/LENS AND MIRRORS

G-1. Two planoconvex lenses each of focal length 10 cm & refractive index 3/2 are placed as shown. In thespace left, water (R.I = 4/3) is filled. The whole arrangement is in air. The optical power of the system is (indiopters) :

(A) 6.67 (B) � 6.67 (C) 33.3 (D) 20

G-2.* If a symmetrical biconcave thin lens is cut into two identical halves. They are placed in different waysas shown:

(A) three images will be formed in case (i)

(B) two images will be formed in the case (i)

(C) the ratio of focal lengths in (ii) & (iii) is 1

(D) the ratio of focal lengths in (ii) & (iii) is 2

G-3.* In the figure shown the radius of curvature of the left & right surface of the concave lens are 10 cm &15 cm respectively. The radius of curvature of the mirror is 15 cm.

(A) equivalent focal length of the combination is -18 cm

(B) equivalent focal length of the combination is +36 cm

(C) the system behaves like a concave mirror

(D) the system behaves like a convex mirror.

G-4. The focal length of a plano-concave lens is 10 cm, then its focal length when its plane surface is

polished is (n = 3/2):




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SECTION (H) : DISPERSION OF LIGHT

H-1. Find the dispersion produced by a thin prism of 18 having refractive index for red light = 1.56 and for violet

light = 1.68.

(A) 4.16 (B) 6.16 (C) 2.16 (D) 8.16

H-2. Calculate the dispersive power for crown glass prism from the given data V = 1.523, and

R = 1.5145

(A) 0.1639 (B) 0.01639 (C) 1.639 (D) 2.639

H-3. Four similar prisms of same material and same angle of prism are arranged. Which of the followingarrangements give no net angular deviation-

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

H-4. A thin prism P1 with angle 4º and made from glass of refractive index 1.54 is combined with another thin

prism P2 made of another type of glass of refractive index 1.72 to produce dispersion without deviation.The angle of the prism P2 is

(A) 2.6º (B) 3º (C) 4º (D) 5.33º

H-5. Critical angle of light passing from glass to air is minimum for:

(A) red (B) green (C) yellow (D) violet

H-6. Light of wavelength 4000 Å is incident at small angle on a prism of apex angle 4º. The prism has nv =1.5 & nr = 1.48. The angle of dispersion produced by the prism in this light is:

(A) 0.2º (B) 0.08º (C) 0.192º (D) None of these

H-7.* By properly combining two prisms made of different materials, it is possible to

(A) have dispersion without average deviation (B) have deviation without dispersion

(C) have both dispersion and average deviation (D) have neither dispersion nor average deviation

H-8. A plane glass slab is placed over various coloured letters. The letter which appears to be raisedthe least is:

(A) violet (B) yellow (C) red (D) green

H-9. All the listed things below are made of flint glass. Which one of these have greatest dispersive power ().

(A) prism (B) glass slab (C) biconvex lens (D) all have same



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PART - II : MISLLANEOUS QUESTIONS

MATCH THE COLUMN1. Match the following :

A white light ray is incident on a glass prism, and it create four refracted rays a, b, c and d. Match therefracted rays with the colours given (e and d are rays due to total internal reflection) :

Column I (RAY) Column II (Colour)(A) a (p) Red

(B) b (q) Green

(C) c (r) Yellow

(D) d (s) Blue

2. Match the following :An object O (real) is placed at focus of an equi-biconvex lens as shown infigure. The refractive index of lens is = 1.5 and the radius of curvatureof either surface of lens is R. The lens is surrounded by air. In each state-ment of Column-I some changes are made to situation given above andinformation regarding final image formed as a result is given in Column-II. The distance between lens and object is unchanged in all statementsof Column-I. Match the statement in Column-I with resulting imagein Column-II.

Column-I Column-II(A) If the refractive index of the lens is doubled (p) Final image is is real

(that is, made 2) then(B) If the radius of curvature is doubled (that is, (q) Final image is virtual

made 2R) then(C) If a glass slab of refrative index = 1.5 is (r) Final image becomes smaller in

introduced between the object and lens size in comparison to size ofas shown, then image before the change was made

(D) If the left side of lens is filled with a medium of (s) Final image is of same size ofrefractive index = 1.5 as shown, then object.



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3. A small particle is placed at the pole of a concave mirror and then moved along the principal axis to

a large distance. During the motion, the distance between the pole of the mirror and the image is

measured. The procedure is then repeated with a convex mirror, a concave lens and a convex lens.

The graph is plotted between image distance versus object distance. Match the curves shown in the

graph with the mirror or lens that is corresponding to it. (Curve 1 has two segments)

Lens/Mirror Curve

(A) Converging lens (p) 1

(B) Converging Mirror (q) 2

(C) Diverging Lens (r) 3

(D) Diverging Mirror (s) 4



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PART - I : MIXED OBJECTIVE


1. An object is placed at the origin. The position of its image afterreflection from both mirrors will be at

(A) (a, a) (B) (�a, a)

(C) (a, �a) (D) (�a, �a)

2. In the figure shown. A particle �P� moves with velocity 10 m/s towards the intersection point �O� of theplane mirror kept at right angle to each other. I

1 and I

2 are the images formed due to direct reflection from

m1 and m respectively. In the position shown, the relative speed of I

1 w.r.t to I

2 will be :

(A) 20 m/s (B) 12 m/s (C) 210 m/s (D) 16 m/s

3. An object and a plane mirror are shown in figure. Mirror is moved with velocity V as shown. Thevelocity of image is :

(A) 2 V sin (B) 2 V(C) 2V cos (D) None of these

4. A light ray is incident on a plane mirror M. The mirror is rotated in thedirection as shown in the figure by an arrow at frequency 9/ rps. Thelight reflected by the mirror is received on the wall W at a distance 10 mfrom the axis of rotation. When the angle of incidence becomes 37º thespeed of the spot (a point) on the wall is:

(A) 10 m/s (B) 1000 m/s

(C) 500 m/s (D) None of these



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5. The incorrect statement for a concave mirror producing a virtual image of an object.(A) The linear magnification is always greater than one, Except at the pole(B) The linear magnification is always less than one.(C) The magnification tends to one as the object moves nearer to the pole of the mirror.(D) The distance of the object from the pole of the mirror is less than the focal length of mirror.

6. In the figure shown a thin parallel beam of light is incident on a plane mirror m1 at small angle ��. m

2 is a

concave mirror of focal length �f�. After three successive reflections of this beam the x and y coordinates of

the image is

(A) x = f � d, y = f (B) x = d + f , y = f

(C) x = f � d, y = � f (D) x = d � f , y = � f

7. An object is placed in front of a concave mirror of focal length f as shown in figure. Choose the correctshape of the image:

(A) a' c'

b' d'

(B) d' b'

c' a'

(C) d' b'

c' a'(D)

a'c'

b' d'

8. 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 onereflection is :

(A) 30° (B) 45°

(C) 60° (D) 75°



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9. A point object ' O

' is at the centre of curvature of a concave mirror. The mirror starts to move at a

speed u, in a direction perpendicular to the principal axis. Then the initial velocity of the image is:(A) 2

u, in the direction opposite to that of mirror's velocity

(B) 2 u, in the direction same as that of mirror's velocity

(C) zero(D) u, in the direction same as that of mirror's velocity.

10. A virtual erect image in a convex mirror is represented by: (u, v, f are co-ordinates)

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

11. In the figure shown a point object O is placed in air. A spherical boundary of radius of curvature1.0 m separates two media. AB is principal axis. The refractive index above AB is 1.6 and belowAB is 2.0. The separation between the images formed due to refraction at spherical surface is:

(A) 12 m (B) 20 m(C) 14 m (D) 10 m

12. A beam of white light is incident on hollow prism of glass as shown in figure. Then

(A) the light emerging from prism gives no dispersion(B) the light emerging from prism gives spectrum but the bending of all

colours is away from base.(C) the light emerging from prism gives spectrum, all the colours bend towards

base, the violet the most and red the least.(D) the light emerging from prism gives spectrum, all the colours bend towards base, the violet the least

and red the most.

13. A horizontal ray of light passes through a prism of refractive index 1.5 whose apex angle is 4° and then

strikes a vertical mirror M as shown in the Fig. In order to have total deviation equal to 180°, the angle

through which the mirror should be rotated is.

(A) 1° (B) 2°

(C) 3° (D) 4°



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14. A point source of light is placed at a distance of 2f from a converging lens of focal length. f. The intensity onthe other side of the lens is maximum at a distance.

(A) f (B) between f and 2f (C) 2f (D) more than 2f

15. In the given figure a parallel beam of light is incident on the upper part of a prism of angle 1.8º and

R.I. 3/2. The light coming out of the prism falls on a concave mirror of radius of curvature 20 cm. Thedistance of the point (where the rays are focused after reflection from the mirror) from the principalaxis is: [use = 3.14]

(A) 9 cm (B) 1.5 7 mm

(C) 3.14 mm (D) none of these

16. Parallel beam of light is incident on a system of two convex lenses of focal lengthsf1 = 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

17. A ray of light strikes a plane mirror at an angle of incidence 45º as shown in the figure. After reflection,

the ray passes through a prism of refractive index 1.50, whose apex angle is 4º. The angle through

which the mirror should be rotated if the total deviation of the ray is to be 90º is :

(A) 10 clockwise (B) 10 anticlockwise

(C) 20 clockwise (D) 20 anticlockwise

18. In the given figure an object ' O ' is kept in air in front of a thin plano convex lens of radius of curvature10 cm. It's refractive index is 3/2 and the medium towards right of plane surface is water of refractiveindex 4/3. What should be the distance ' x ' of the object so that the rays become parallel finally.




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MULTIPLE CHOICE QUESTION :

19. A flat mirror M is arranged parallel to a wall W at a distance L from it as shown in the figure. The lightproduced by a point source S kept on the wall is reflected by the mirror and produces a light patch on thewall. The mirror moves with velocity v towards the wall.

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

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

(C) As the mirror comes closer the patch of light will become larger and shift away from the wall with speedlarger than v.

(D) The width of the light patch on the wall remains the same.

20. A man wants to photograph a white donkey as a Zebra after fitting a glass with black streaks onto the lensof 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.

21. An equiconvex lens of refractive index n2 is placed such that the refractive index of the surrounding

media is as shown. Then the lens :

(A) must be diverging if n2 is less than the arithmetic mean of n

1 and n

3

(B) must be converging if n2 is greater than the arithmetic mean of n

1 and n

3

(C) may be diverging if n2 is less than the arithmetic mean of n

1 and n

3

(D) will neither be diverging nor converging if n2 is equal to arithmetic mean of n

1 and n

3

22. In the figure shown a point object O is placed in air on the principal axis. The radius of curvature ofthe spherical surface is 60 cm. I

f is the final image formed after all the refractions and reflections.

(A) If d1 = 120 cm, then the �

If � is formed on �

O

� for any value of d

2.

(B) If d1 = 240 cm, then the �


O

� only if d

2 = 360 cm.

(C) If d1 = 240 cm, then the �


O

� for all values of d

2.

(D) If d1 = 240 cm, then the �

If � cannot be formed on �

O

�.



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PART - II : SUBJECTIVE QUESTIONS

1. 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 (in cm) between

the images formed by the two parts?

2. Two plane mirrors are placed as shown in the figure and a point object 'O' is placed at the origin.

Find how many images will be formed.

3. In the situation shown in figure, the velocity of image is � 5(1 + 3 ) �i + a 3 �j , then find the

value of a ?

4. The radius of curvature of a convex spherical mirror is 1.2 m. An object of height 1.2 cm is placed in

front of mirror, if the distance between its virtual image and the mirror is 0.35 m? What is the height

(in mm) of the image?



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PART-I IIT-JEE (PREVIOUS YEARS PROBLEMS)


1. [JEE '2000 (Screening) 3/105 Each](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 ofthe 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 n

2(n

1>

n2). 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) sin 1

1

21

2

1

n

nsincos

n

n(B) sin 1

2

11 n

1sincosn

(C) sin 1

2

1

n

n(D) sin 1

1

2

n

n

(c) A point source of light B is placed at a distance L in front of the centre of a mirror of width d hungvertically on a wall. A man walks in front of the mirror along a line parallel to the mirror at a distance2L from it as shown. The greatest distance over which he can see the image of the light source in themirror 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 oreither of two liquids L

1 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 L

1.

(C) L1 and immersed in L

2. (D) L

2 and immersed in L

1.



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2. A convex lens of focal length 15 cm and a concave mirror of focal length 30 cm are kept with theiroptic axes PQ and RS parallel but separated in vertical direction by 0.6 cm as shown. The distancebetween the lens and mirror is 30 cm. An upright object AB of height 1.2 cm is placed on the opticaxis PQ of the lens at a distance of 20 cm from the lens. If A B is the image after refraction from thelens and reflection from the mirror, find the distance A B from the pole of the mirror and obtainits magnification. Also locate positions of A and B with respect to the optic axis RS.

/////////////////////////// //// //////////

0.6cmP

R

A

B

S

Q

30cm 20cm

3. [ JEE 2001 (Screening 3/105 Each ]

(i) A given ray of light suffers minimum deviation in an equilateral prism P. Additional prisms Q and R ofidentical shape and of the same material as P are now added as shown in the figure. The ray will nowsuffer.

(A) greater deviation (B) no deviation(C) same deviation as before (D) total internal reflection

(ii) A ray of light passes through four transparent media with refractive indices 1,

2,

3 &

4 as shown in

the figure. The surfaces of all media are parallel. If the emergent ray CD is parallel to the incident rayAB, we must have:

(A) 1 =

2(B)

2 =

3(C)

3 =

4(D)

4 =

1

4. [ JEE 2001 (Mains) 5/100 Each ](i) The

refractive

indices

of

the crown

glass

for blue and red lights are 1.51 & 1.49 respectively and

those of the flint glass are 1.77 & 1.73 respectively. An isosceles prism of angle 6º is made of crown

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

(ii) A thin biconvex lens of refractive index 3/2 is placed on a horizontal plane mirror as shown in thefigure. The space between the lens and the mirror is then filled with water of refractive index 4/3. It isfound that when a point object is placed 15 cm above the lens on its principal axis, the object coincideswith its own image. On repeating with another liquid, the object and the image again coincide at adistance 25 cm from the lens. Calculate the refractive index of the liquid.



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5. [ JEE Screening 2002, 3/90, �1]

(i) Two plane mirrors A & B are aligned parallel to each other, as shown in the figure. A light ray isincident to an angle of 30º 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 thefirst one) before it emerges out is:

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

(ii) An observer can see through a pinhole the top end of a thin rod of height h, placed as shown in thefigure. The beaker height is 3h and its radius h. When the beaker is filled with a liquid up to a height2h, he can see the lower end of the rod. Then the refractive index of the liquid is:

(A) 25

(B) 25

(C) 23

(D) 23

(iii) Which one of the following spherical lenses does not exhibit dispersion? The radii of curvature of thesurface of the lenses are as given in the diagrams.

(A) (B)

(C) (D)



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6. [ JEE 2003 (Screening) 3/90, � 1]

(i) In ray of light (GH) is incident on the glass-water interface DC at an angle 'i'. It emerges in air alongthe water-air interface EF (see figure). If the refractive index of water µ

w is 4/3, the refractive index of

glass µg is :

(A) isin43

(B) isin1

(C) 3

isin4(D) isin3

4

(ii) A thin convex lens of focal length 30 cm forms an image 2 cm high, of an object at infinity. A thinconcave lens of focal length 20 cm is placed 26 cm from the convex lens on the side of the image.The height of the image now is :(A) 1.0 cm (B) 1.25 cm (C) 2 cm (D) 2.5 cm

7. 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 (shown in the

figure). Calculate its focal length for 1 <

2 <

3, when light is incident on it as shown

8. A point object is situated at the centre of a solid glass sphere of radius 6cm and refractive index 1.5 . Thedistance of its virtual image from the surface of the sphere is : [ JEE 2004 (Scr.) 3/84, �1]

(A) 4 cm (B) 6 cm (C) 9 cm (D) 12 cm

9. An equilateral prism is kept on a horizontal surface. A typical ray of light PQRS is shown in the figure. Forminimum deviation [ JEE 2004 (Scr.), 3/84, �1]

(A) the ray PQ must be horizontal (B) the ray RS must be horizontal(C) the ray QR must be horizontal (D) any one of them can be horizontal

10. A ray of white light is incident on an interface between glass and air from glass towards air. The angle ofincidence is such that the green light just suffers total internal reflection. The ray of light emerging fromglass to air contains: [ JEE 2004 (Scr.), 3/84, �1]

(A) red, orange and yellow colours (B) violet, indigo and blue colour

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



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11. A ray of light in air is incident on face AB of an irregular block made of material with refractive index 2 , as

shown in figure. The face CD opposite to AB is a spherical surface of radius of curvature 0.4 m. From thisface the refracted ray enters a medium of refractive index 1.514 and meets the axis PQ at point E. Deter-mine the distance OE correct to two decimal places. [ JEE 2004 (Mains), 2/84, �1]

12. An object is placed at a distance of 0.4 m from a lens having focal length 0.3 m. The object is movingtowards the lens at a speed of 0.01 m/s. Find the rates of change of position of image and lateral magnificationof image. [ JEE 2004 (Mains) 4/60 ]

13. In the figure two triangular prisms are shown each of refractive index 3 .

[ JEE 2005 (Mains) 4/60 ]

(a) Find the angle of incidence on the face AB for minimum deviation from the prism ABC?(b) Find the angle through which the prism DCE should be rotated about the edge passing through

point C so that there should be minimum deviation from the system?

14. A point object is placed at distance of 20 cm from a thin plano-convex lens of focal length 15 cm. The planesurface of the lens is now silvered. The image created by the system is at : [ JEE 2006, 3 /184 ]

(A) 60 cm to the left of the system. (B) 60 cm to the right of the system.(C) 12 cm to the left of the system. (D) 12 cm to the right of the system.

15. The graph between object coordinate u and image coordinate v for a lens is given below. The focal lengthof the lens is: [ JEE 2006, 3 /184 ]

(A) 5 ± 0.1 (B) 5 ± 0.05 (C) 0.5 ± 0.1 (D) 0.5 ± 0.05



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16. A biconvex lens of focal length f forms a circular image of radius r of sun in focal plane. Then which optionis correct : [ JEE 2006, 3/184 ]

(A) r2 f

(B) r2 f2

(C) If lower half part is covered by black sheet, then area of the image is equal to r2/2

(D) if f is doubled, intensity will increase

17. A ray of light traveling in water is incident on its surface open to air. The angle of incidence is , which is lessthan the critical angle. Then there will be : [JEE - 2007' 3/81]

(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 180º � 2

(D) a reflected ray and a refracted ray and the angle between them would be greater than 180º � 2.

18. STATEMENT-1 [JEE - 2007' 3/81]

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

19. Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is60º). In the position of minimum deviation, the angle of refraction will be [JEE' 2008_, 3/163]

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

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

20. 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, 3/163]

Figure

(A) sin�1

43

(B) sin�1

81

(C) sin�1

41

(D) sin�1

31



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21. An optical component and an object S placed along its optic axis are given in Column I. The distancebetween 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.

[JEE' 2008, 6/163, �1]

Column I Column II

(A) (p) Real image

(B) (q) Virtual image

(C) (r) Magnified image

(D) (s) Image at infinity

22. A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive index of water is4/3. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At an instant, When the ball is 12.8 mabove the water surface, the fish sees the speed of ball as [Take g = 10 m/s2] [JEE' 2009, 3/160, �1]

(A) 9 m/s (B) 12 m/s (C) 16 m/s (D) 21.33 m/s

23. A student performed the experiment of determination of focal length of a concave mirror by u-v methodusing an optical bench of length 1.5 meter. The focal length of the mirror used is 24 cm. The maximumerror in the location of the image can be 0.2 cm. The 5 sets of (u, v) values recorded by the student (in cm)are : (42, 56), (48, 48), (60, 40), (66, 33), (78, 39). The data set(s) that cannot come from experiment andis (are) incorrectly recorded, is (are) [JEE' 2009, 4/160, �1]

(A) (42, 56) (B) (48, 48) (C) (66, 33) (D) (78, 39)

24. A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident

angle of 60º (see figure). If the refractive index of the material of the prism is 3 , which of the following is

(are) correct ? [JEE' 2010, 3/163]

(A) The ray gets totally internally reflected at face CD(B) The ray comes out through face AD(C) The angle between the incident ray and the emergent ray is 90º

(D) The angle between the incident ray and the emergent ray is 120º



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25. The focal length of a thin biconvex lens is 20cm. When an object is moved from a distance of 25cm in front of

it to 50cm, the magnification of its image changes from m25 to m50. The ratio 50

25

m

m is : [JEE' 2010, 3/163]

26. A biconvex lens of focal length 15 cm is in front of a plane mirror. The distance between the lens and themirror is 10 cm. A small object is kept at a distance of 30 cm from the lens. The final image is(A) Virtual and at a distance of 16 cm from mirror [JEE' 2010, 5/163, �2]

(B) Real and at distance of 16 cm from the mirror(C) Virtual and at a distance of 20 cm form the mirror(D) Real and at a distance of 20 cm from the mirror

27. Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move

from 3

25 m to

750

m in 30 seconds. What is the speed of the object in km per hour.. [JEE' 2010, 3/163]

28. A large glass slab ( = 5/3) of thickness 8 cm is placed over a point source of light on a plane surface. It isseen that light emerges out of the top surface of the slab from a circular area of radius R cm. What is thevalue of R? [JEE' 2010, 3/163]

29. Two transparent media of refractive indices 1 and 3 have a solid lens shaped transparent material ofrefractive index 2 between them as shown in figures in column . A ray traversing these media is alsoshown in the figures. In Column different relationships between 1, 2 and 3 are given. Match them tothe ray diagrams shown in Column . [JEE' 2010, 8/163]Column Column

(A) 1 < 2 (p)

(B) 1 > 2 (q)

(C) 2= 3 (r)

(D) 2 > 3 (s)

(t)



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30. A light ray traveling in glass medium is incident on glass-air interface at an angle of incidence . The reflected (R)

and transmitted (T) intensities, both as function of , are plotted. The correct sketch is : [JEE' 2011, 3/160]

(A) (B)

(C) (D)

31. Water (with refractive index = 43

) in a tank is 18 cm deep. Oil of refractive index 74

lies on water making a convex

surface of radius of curvature R = 6 cm as shown. A source S is placed 24 cm above water surface as shown infigure. Consider its image is at �x� cm above the bottom of the tank. Then �x� is: [JEE' 2011, 4/160]

32. A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index n ofthe first lens is 1.5 and that of the second lens is 1.2. Both the curved surfaces are of the same radius ofcurvature R = 14 cm. For this bi-convex lens, for an object distance of 40 cm, the image distance will be?

[JEE 2012 (3, �1)/136]

(A) � 280.0 cm (B) 40.0 cm (C) 21.5 cm (D) 13.3 cm



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Paragraph for Questions 33 and 34

Most materials have the refractive index, n > 1. So, when a light ray from air enters a naturally occurring

material, then by Snell�s law, 1 2

2 1

sin nsin n

, it is understood that the refracted ray bends towards the normal.

But it never emerges on the same side of the normal as the incident ray. According to electromagnetism,

the refractive index of the medium is given by the relation. r r

cn µ

v

, where c is the speed of

electromagnetic waves in vacuum, v its speed in the medium, r and µ

r are the relative permittivity and

permeability of the medium respectively.

In normal materials, both r and µ

r are positive, implying positive n for the medium. When both

r and µ

r are

negative, one must choose the negative root of n. Such negative refractive index materials can now beartifically prepared and are called meta-materials. They exhibit significantly different optical behaviour,without violating any physical laws. Since n is negative, it results in a change in the direction of propagationof the refracted light. However, similar to normal materials, the frequency of light remains unchanged uponrefraction even in meta-materials.

33. Choose the correct statement [JEE 2012 (3, �1)/136]

(A) The speed of lihgt in the meta-metrial is v = c|n|

(B) The speed of light in the meta-material is v = c

| n |

(C) The speed of light in the meta-material is v = c.

(D) The wavelength of the light in the meta-material (m) is given by

m =

air|n|, where

air is the wavelength

of the light in air.

34. For light incident from air on a meta-material, the appropriate ray diagram is [JEE 2012 (3, �1)/136]

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

35. The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is

one-third the size of the object. The wavelength of light inside the lens is 23

times the wavelength in free

space. The radius of the curved surface of the lens is: [JEE Advanced (P-1) 2013]

(A) 1 m (B) 2 m (C) 3 m (D) 6 m



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36. A right angled prism of refractive index µ1 is placed in a rectangular block of refractive index µ2, which is

surrounded by a medium of refractive index µ3, as shown in the figure. A ray of light �e� entres the rectangular

block at normal incidence. Depending upon the relationships between µ1, µ2 and µ3 it takes one of the four

possible paths �ef�, �eg�, �eh� or �ei�. [JEE Advanced (P-2) 2013]

45ºe

iµ1

µ2 µ3

f

g

h

Match the paths in List I with conditions of refractive indices in List II and select the correct answer using

the codes given below the lists :

List - I List-II

P. e f 1. µ1 > 22µ

Q. e g 2. µ2 > µ1 & µ2>µ3

R. e h 3. µ1 = µ2

S. e i 4. µ2 < µ1 < 22 µ

and µ2 > µ3

Codes :

P Q R S

(A) 2 3 1 4

(B) 1 2 4 3

(C) 4 1 2 3

(D) 2 3 4 1



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PART-II AIEEE (PREVIOUS YEARS PROBLEMS)

1. An astronomical telescope has a large aperture to [AIEEE-2002, 4/300](1) reduce spherical aberration (2) have high resolution(3) increase span of observation (4) have low dispersion

2. If two mirrors are kept at 60º to each other, then the number of images formed by them is

[AIEEE-2002, 4/300](1) 5 (2) 6 (3) 7 (4) 8

3. Wavelength of light used in an optical instrument are 1 = 4000 Å and 2 = 5000 Å, then ratio of their

respective resolving powers (corresponding to 1 and 2) is [AIEEE-2002, 4/300](1) 16 : 25 (2) 9 : 1 (3) 4 : 5 (4) 5 : 4

4. Which of the following is used in optical fibers ? [AIEEE-2002, 4/300](1) total internal reflection (2) scattering(3) diffraction (4) refraction

5. The image formed by an objective of a compound microscope is [AIEEE-2003, 4/300](1) virtual and diminished (2) real and diminished(3) real and enlarged (4) virtual and enlarged

6. To get three images of a single object, one should have two plane mirrors at an angle of [AIEEE-2003, 4/300](1) 60º (2) 90º (3) 120º (4) 30º

7. A light ray is incident perpendicularly to one face to a 90º prism and is totally internally reflected at the glass-

air interface. If the angle of reflection is 45º, we conclude that the refractive index n� [AIEEE-2004, 4/300]

(1) n < 2

1(2) n > 2 (3) n >

2

1(4) n < 2

8. A plano convex lens of refractive index 1.5 and radius of curvature 30 cm is silvered at the curved surface.Now this lens has been used to from the image of an object. At what distance from this lens an object beplaced in order to have a real image of the size of the object. [AIEEE-2004, 4/300](1) 20 cm (2) 30 cm (3) 60 cm (4) 80 cm

9. The angle of incidence at which reflected light in totally polarized for reflection from air to glass (refractiveindex n), is [AIEEE-2004, 4/300](1) sin�1(n) (2) sin�1(1/n) (3) tan�1(1/n) (4) tan�1(n)



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10. The refractive index of glass is 1.520 for red light and 1.525 for blue light. Let D1 and D

2 be angles of minimum

deviation for red and blue light respectively in a prism of this glass. Then, [AIEEE-2006, 3/180]

(1) D1 can be less than or greater than D

2 depending upon the angle of prism

(2) D1 > D

2

(3) D1 < D

2

(4) D1 = D

2

11. An experiment is performed to find the refractive index of glass using a travelling microscope. In thisexperiment distances are measured by - [AIEEE-2008, 3/105]

(1) a standard laboratory scale (2) a meter scale provided on the microscope

(3) a screw gauge provided on the microscope (4) a vernier scale provided on the microscope

12. A student measures the focal length of a convex lens by putting an object pin at a distance |u| from the lensand measuring the distance �v� of the image pin. The graph between �u� and �v� plotted by the student should

look like - [AIEEE-2008, 3/105]

(1)

v(cm)

O u(cm)

(2)

v(cm)

O u(cm)

(3)

v(cm)

O u(cm)

(4)

v(cm)

O u(cm)

13. A transparent solid cylindrical rod has a refractive index of3

2. It is surrounded by air. A light ray is incident

at the mid-point of one end of the rod as shown in the figure. [AIEEE-2009, 4/144]

The incident angle for which the light ray grazes along th wall of the rod is:

(1) sin-1

23

(2) sin-1

3

2(3) sin-1

3

1(4) sin-1

21

14. In an optics experiment, with the position of the object fixed, a student varies the position of a convex lensand for each position, the screen is adjusted to get a clear image of the object. A graph between the objectdistance u and the image distance v, from the lens, is plotted using the same scale for the two axes. Astraight line passing through the origin and making an angle of 45° with the x-axis meets the experimental

curve at P. The coordinates of P will be: [AIEEE-2009, 4/144]

(1)

2f

,2f

(2) (f, f) (3) (4f, 4f) (4) (2f, 2f)



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Direction :Questions number 15 � 17 are based on the following paragraph.

An initially parallel cylindrical beam travels in a medium of refractive index () = 0 + 2, where 0 and 2

are positive constants and is the intensity of the light beam. The intensity of the beam is decreasing withincreasing radius. [AIEEE-2010, 4/144, � 1]

15. As the beam enters the medium, it will(1) diverge(2) converge(3) diverge near the axis and converge near the periphery(4) travel as a cylindrical beam

16. The initial shape of the wavefront of the beam is :(1) convex(2) concave(3) convex near the axis and concave near the periphery(4) planar

17. The speed of light in the medium is(1) minimum on the axis of the beam (2) the same everywhere in the beam(3) directly proportional to the intensity (4) maximum on the axis of the beam

18. A car is fitted with a convex side-view mirror of focal length 20 cm. A second car 2.8 m behind the first caris overtaking the first car at a relative speed of 15m/s. the speed of the image of the second car as seen inthe mirror of the first one is : [AIEEE-2011, 4/120]

(1) s/m101

(2) s/m151

(3) 10 m/s (4) 15 m/s

19. Let the x�z plane be the boundary between two transparent media. Medium 1 in z 0 has a

refractive index of 2 and medium 2 with z=0 has a refractive index of 3 . A ray of light in medium

1 given by the vector k�10j�38i�36A

is incident on the plane of separation. The angle of

refraction in medium 2 is : [AIEEE-2011, 4/120]

(1) 30° (2) 45° (3) 60° (4) 75°

20. An object 2.4 m in front of a lens forms a sharp image on a film 12 cm behind the lens. A glass plate 1 cmthick,of refractive index 1.50 is interposed between lens and film with its plane faces parallel to film.At what distance(from lens) should object shifted to be in sharp focus on film ? [AIEEE-2012 4/120]

(1) 7.2 m (2) 2.4 m (3) 3.2 m (4) 5.6 m

21. Diameter of a plano-convex lens is 6 cm and thickness at the centre is 3 mm. If speed of light in material oflens is 2 × 108 m/s, the focal length of the lens is : [JEE Mains 2013](1) 15 cm (2) 20 cm (3) 30 cm (4) 10 cm

22. The graph between angle of deviation () and angle of incidence (i) for a triangular prism is represented by:[JEE Mains 2013]

(1) (2) (3) (4)



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PART-I NCERT QUESTIONS

1. A small candle 2.5 cm in size is placed 27 cm in front of a concave mirror of radius of curvature 36

cm. At what distance from the mirror should a screen be placed in order to receive a sharp image?

Describe the nature and size of the image .If the candle is moved closer to the mirror, how would the

screen have to be moved ?

2. A prism is made of glass of unknown refractive index. A parallel beam of light is incident on a face of

the prism. By rotating the prism. The angle of minimum deviation is measured to be 40º. What is the

refractive index of the material of the prism ? If the prism is placed in water ( refractive index 1.33 )

predict the new angle of minimum deviation of a parallel beam of light . The refracting angle of the

prism is 60º.

3. Double-convex lenses are to be manufactured from a glass of refractive index 1.55, with both faces

of the same radius of curvature. What is the radius of curvature required if the focal length is to be 20

cm?

4. An object of size 3.0 cm is placed 14 cm in front of a concave lens of focal length 21 cm. Describe the

image produced by the lens. What happens if the object is moved farther from the lens?

5. A compound microscope consists of an objective lens of focal 2.0 cm and an eye-piece of focal

length 6.25 cm separated by a distance of 15 cm. How far from the objective should an object be

placed in order to obtain the final image at (a) least distance of distinct vision ( 25 cm), (b) infinity?

What is the magnifying power of the microscope in each case ?

6. A small telescope has an objective lens of focal length 144 cm and an eye-piece of focal length 6.0

cm. What is the magnifying power of the telescope? What is the separation between the objective

and the eye-piece ?

7. Does short-sightendness (myopia) or long-sightedness (hypermetropia) imply necessarily) that the

eye has partially lost its ability of accommodation? If not, what might cause these defects of vision?

8. A myopic person has been using spectacles to power-1.0 diopter for distant vision. During old age he

also needs to use separate reading glass of power + 2.0 diopters. Explain what may have happened.

9. A person looking at a mesh of crossed wires is able to see the vertical wires more distinctly than the

horizontal wires. What is this defect due to? How is this defect due to? How is such a defect of vision

corrected?



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Exercise # 1PART - I

A-1. (C) A-2. (B) A-3. (C) A-4. (A) A-5. (C) A-6. (B) A-7. (D)

A-8. (B) A-9. (C) A-10. (B) A-11. (B) A-12. (B) A-13. (C) B-1. (A)

B-2. (B) B-3. (B) B-4. (A) B-5. (D) B-6. (B) B-7. (B) B-8.* (AB)

B-9. (B) B-10. (A) B-11. (C) B-12. (C) B-13. (C) B-14. (A) B-15. (B)

B-16. (C) B-17. (A) B-18. (D) C-1. (B) C-2. (C) C-3. (A) C-4. (A)

C-5. (A) C-6. (D) C-7. (A) C-8.* (BD) C-9. (A) D-1. (B) D-2. (D)

D-3. (D) D-4. (B) D-5. (B) D-6. (C) E-1. (C) E-2. (A) E-3. (A)

E-4. (C) E-5. (D) E-6. (A) F-1. (B) F-2. (C) F-3. (B) F-4. (C)

F-5. (A) F-6. (C) F-7.* (ABC) F-8.* (BC) F-9. (A) F-10. (A) F-11. (D)

G-1. (A) G-2.* (AC) G-3.* (AC) G-4. (C) H-1. (C) H-2. (B) H-3. (B)

H-4. (B) H-5. (D) H-6. (D) H-7.* (ABC) H-8. (C) H-9. (D)

PART - II

1. (A) � p ;(B) � r ; (C) � q ; (D) � s 2. (A) � p, r ; (B) � q, r ; (C) � q, r ; (D) � q, r

3. (A) � p ;(B) � p ; (C) � q ; (D) � s

Exercise # 2PART - I

1. (B) 2. (A) 3. (A) 4. (B) 5. (B) 6. (D) 7. (B)

8. (B) 9. (B) 10. (A) 11. (A) 12. (A) 13. (A) 14. (C)

15. (B) 16. (B) 17. (B) 18. (C) 19. (BD) 20. (AD) 21. (ABD)

22. (AB)



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PART - II

1. 2 2. 1 3. 5 4. 5

Exercise # 3

PART - I

1. (a) B, (b) A, (c) D, (d) D

2. A B at 15 cm to the right of mirror. B is 0.3 cm above RS & A is 1.5 cm below RS. Magnification is �1.5

3. (i) C, (ii) D

4. (i) A = 4º, = 0.04, (ii) n = 8/5 = 1.6

5. (i) (B), (ii) (B), (iii) (C) 6. (i) (B), (ii) (D) 7. f =)(

R

13

3

8. (B) 9. (C) 10. (A) 11. OE = 6.06 m 12.dtdv

= 0.09 m/s; dtdm

= � 0.3 sec�1

13. (a) i = 60° (b) 60° 14. (C) 15. (B) 16. (B) 17. (C) 18. (C)

19. (A) 20. (B) 21. (A) � p,q,r,s; (B) � q ; (C) � p,q,r,s ; (D) � p,q,r,s 22. (C)

23. (CD) 24. (ABC) 25. 6 26. (B) 27. 3 28. 6

29. (A) � p,r ; (B) � q,s,t ; (C) � p,r,t ; (D) � q, s 30. (C) 31. 2 32. (B)

33. (B) 34. (C) 35. (C) 36. (D)

PART - II

1. (2) 2. (1) 3. (4) 4. (1) 5. (3) 6. (2) 7. (2)

8. (1) 9. (4) 10. (3) 11. (4) 12. (2) 13. (3) 14. (4)

15. (4) 16. (4) 17. (1) 18. (2) 19. (2) 20. (4) 21. (3)

22. (3)

Exercise # 4

1. The screen should be placed 54 cm from the mirror. The image is real, inverted and magnified. Thesize of the image is 5.0 cm. If the candle is moved closer, the screen would have to be moved fartherand farther. Closer than 18 cm from the mirror, the image gets virtual and cannot be collected on thescreen.

2. n = ]2/A[sin]2/)DA([sin m

=

30sin50sin

= 2 × 0.766 = 1.532 ~ = 1.53

=

30sin]2/)D30[(sin m =

33.153.1

which gives mD = 10°.



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3. Use the lens maker�s formula to obtain R = 22 cm.

4. Image is erect, virtual and located 8.4 cm from the lens on the same side as the object. It is dimin-ished to a size = (8.4/14) × 3 cm = 1.8 cm. As the object is moved away from the lens, the virtual

image moves towards the focus of thelens (but never beyond), and progressively diminishes in size.Note that when the object is placed at the focus of the concave lens (21 cm), the image is located at10.5 cm (not at infinity as one might wrongly think). A virtual object at the focus of a concave lensproduces an image at infinity.

5. (a) ve = � 2.5 cm and f

e = 6.25 cm give u

e = � 5 cm ; v

0 = (15 � 5) cm = 10 cm.

f0 = u

0 = � 2.5 cm; Magnifying power =

525

5.210

= 20

(b) ue = � 6.25 cm, v

0 = (15 � 6.25) cm = 8.75, f

0 = 2.0 cm. Therefore,

u0 = � (70/27) = � 2.59 cm.

Magnifying power = |u|

v

0

0× (25/6.25) =

827

× 4 = 13.5

6. 24 ; 150 cm

7. No, a person may have normal ability of accommodation of the eye-lens and yet may be myopic orhypermetropic. Myopia arises when the eye-ball from front to back gets too shortened. In practice, inaddition, the eye-lens may also lose some of its ability of accommodation. When the eyeball has thenormal length but the eye-lens loses partially its ability of accommodation (as happens with increas-ing age for any normal eye) the �defect� is called presbyopia and is corrected in the same manner as

hypermetropia.

8. The far point of the person is 100 cm, while his near poin may have been normal (about 25 cm).Objects at infinity produce virtual image at 100 cm (using spectacles). To view closer objects i.e.,those which are (or whose images using the spectacles are) between 100 cm and 25 cm, the personuses the ability of accommodationof his eye-lens. This ability usually gets partially lost inold age(presbyopia). The near point of the person recedes to 50 cm. to view objects at 25 cm clearly, theperson needs converging lens of power + 2 dioptres.

9. The defect (called astigmatism) arises because the curvature of the cornea plus eye-lens refractingsystem is not the same in different planes. The eye-lens is usually spherical i.e., has the same curva-ture on different planes but the curvature in the vertical plane is enough, so sharp images of verticalwires can be formed on the retina. But the curvature is insufficient in the horizontal planes, so hori-zontal wires appear blurred. The defect can be corrected by using a cylindrical lens with its axis alongthe vertical. Clearly, parallel rays in the vertical plane will sufer no extra refraction, but those in thehorizontal plane can get the required extra convergence due to refraction byt he curved surface ofthe cylindrical lens if the curvature o the cylindrical surface is chosen appropriately.



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Geometrical Optics

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