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REFLECTION OF LIGHT

INTRODUCTION:

Geometrical optics, or ray optics, describes light propagation in terms of "rays". The "ray" in

geometrical optics is an abstraction, or "instrument", which can be used to approximately

model how light will propagate simply put, a ray of light gives the direction of propagation

of light.Light rays are defined to propagate in a rectilinear path as far as they travel in a

homogeneous medium. Rays bend (and may split in two) at the interface between two

dissimilar media, may curve in a medium where the refractive index changes, and may be

absorbed and reflected. Geometrical optics provides rules, which may depend on the color

(wavelength) of the ray, for propagation of these rays through an optical system.

SECTION I

SOME DEFINITIONS:

(i) Ray: The path of light, as determined within the approximations of geometric optics,

is a ray. In a homogeneous medium, it is a straight line.

(ii) Beam: A collection of rays, usually referred to as a bundle of rays, forms a beam. One

may have a convergent, divergent or, a parallel beam. A convergent beam may converge to

a point or, a line, a divergent beam may diverge from a point or, a line. A parallel beam

consists of parallel rays.

(iii) Collimation: A process whereby a divergent (or, convergent) beam is rendered

parallel usually through the use of lenses and/or mirrors.

(iv) Object & Image: The term object is used to refer to any object (being photographed

or observed) that is a source of light, and its likeness (usually two dimensional) formed or

observed by an optical system is the image.

(v) Optical System: An optical system consists of elements like lenses, mirrors, prisms, etc.

http://en.wikipedia.org/wiki/Light

http://en.wikipedia.org/wiki/Wave_propagation

http://en.wikipedia.org/wiki/Ray_%28optics%29

http://en.wikipedia.org/wiki/Abstract_object

http://en.wikipedia.org/wiki/Instrumentalism

http://en.wiktionary.org/wiki/interface

http://en.wikipedia.org/wiki/Optical_medium

http://en.wikipedia.org/wiki/Refractive_index



(vi) Axis: The axis of an optical system is frequently an axis of symmetry such that a ray

directed along the axis continues in the same direction or, returns backwards (if reflected

within the system)

(vii) Centre of Curvature: Most lenses and curved mirrors being manufactured spherical

(i.e., their surfaces are spherical), the center of curvature of the curved mirror or, the

curved surface of a lens is important and is frequently denoted by the letter C. The radius of

curvature is also equally important in the analysis.

(viii) Pole: The pole of a spherical surface (refracting or, reflecting) is the central point of

the surface involved in the formation of the image. It is denoted by O or, P. The axis, for a

single spherical surface, is the join of the pole with the center of curvature; it is known as

the principal axis.

(ix) Optical Centre: The optical center of a thin lens is a point on the axis of the lens such

that a ray directed towards that point emerges parallel to itself after passing through the

lens.

(x) Paraxial Rays: It is observed that the formation of clear images by spherical surfaces

takes place only with rays which are close to the principal axis and make very small angles

with it. These rays are called paraxial rays.

(xi) Wave speed: It is the distance travelled by the wave disturbance in a unit time. It is

denoted by the letter

(xii) Frequency: It is the number of vibrations made by the medium particle in 1 s. In

other words, it is number of waves passing through a point of the medium in 1 second. It is

generally represented by the letter n or . Its unit is hertz and it is represented as Hz or s–1.

(xiii) Wavelength: It is the distance travelled by the wave in one complete period of a

medium particle. In other words, distance between two consecutive crest or trough. It is

generally denoted by the letter



Relationship between the wavelength, wave speed and frequency:

Wave speed Frequency X Wavelength.

1. REFLECTION OF LIGHT BY PLANE MIRROR

When light rays strike the boundary of two media such as air and glass, a part of light is

turned back into the same medium. This is called Reflection of Light. The wavelength and

the velocity of the light wave remains the same.

N

i

Incident

Ray

Reflected

Ray

r

ir

N

ri

N

1.1 Laws of reflection:

(a) The incident ray (AB), the reflected ray (BC) and normal

(BN) 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 (or

plane of reflection).

(b) The angle of incidence (the angle between normal and the

incident ray) and the angle of reflection are equal. ( i r )

Example: A plane mirror makes an angle of 30o with horizontal. If a vertical ray strikes the

mirror, find the angle between mirror and reflected ray [RPET 1997]

(a)30o (b) 45o (c) 60o (d) 90o

Solution: Since angle between mirror and normal is 90o and reflected ray (RR)

makes an angle of 30o with the normal so required angle will be o60 .

1.2 Reflection at plane surfaces

The point I is called the image of the object A

The image formed by reflection at plane surfaces has the following characteristics:

30o

30o

30o

= 60o

IR

RR



(i) Distance of object from mirror = Distance of image from the mirror.

(ii) The line joining the object point with its image is normal to the reflecting surface.

(iii) The image is laterally inverted (left right inversion).

The ray AB gets reflected at B and goes along BC. The ray AD that falls normally on the

mirror is reflected back along DA. Let us produce BC and AD behind the mirror where they

meet at I. it is simple to prove that triangles ABD and BDI are congruent and AD=DI. Thus,

all reflected rays meet at I when produced behind the mirror. An eye receiving the reflected

rays are diverging from the point I.

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

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

(vi) The laws of reflection holds good for all kinds of reflection. Be it at plane or curved

surfaces

(vii) Image of an object is the point at which rays after reflection (or reflection) actually

converge or appear to diverge from that point

Example: You are standing in front of a mirror 3m from you. There is a painting 2m behind

you on the wall. How far from you is the image of the painting.

Solution: Since image distance= object distance, the image distance of painting from the

mirror ( )

The distance of the image from me ( )

1.3 Real and virtual images

If light rays, after reflection or refraction, actually meets at a point then real image is

formed and if they appears to meet, virtual image is formed.

O I

(Real image) (Virtual object)

Real image (Real image)

(Virtual object) I



1.4 Deviation by reflection

Deviation is the angle between the original direction of the ray and the direction it goes

along after reflection or refraction.

Deviation produced by a plane mirror and by two inclined plane mirrors.

Example: Two vertical plane mirrors are inclined at an angle of 60o with each other. A ray of

light travelling horizontally is reflected first from one mirror and then from the other. The

resultant deviation is

(a)60o (b) 120o (c) 180o (d) 240o

Solution : (d)By using )2360( o240602360

Note : If two plane mirrors are inclined to each other at , the emergent ray is anti-parallel to

incident ray, if it suffers one reflection from each. Whatever be the angle to incidence.

(1) Rotation : If a plane mirror is rotated in the plane of incidence through angle , by

keeping the incident ray fixed, the reflected ray turned through an angle 2.

Example: What should be the height of transmitting antenna if the T.V. telecast is to cover a

radius of 128 Km

I O

(Real object) (Virtual image)

(Virtual image)

(Real object)

(Virtual image)

i r

= (180 – 2i) = (360 – 2)

Final path

Original path

2

IR

RR

IR RR



(a)1560 m (b) 1280 m (c) 1050 m (d) 79 m

Solution : (b) Height of transmitting antenna md

h 1280104.62

)10128(

Re2 6

232

(2) Images by two inclined plane mirrors : When two plane mirrors are inclined to each

other at an angle , then number of images (n) formed of an object which is kept between

them.

(i)

1

360

n ; If

360even integer

(ii) If

360 odd integer then there are two possibilities

(a) Object is placed symmetrically (b) Object is placed

asymmetrically

(a)

1

360

n (b)

360n

Note : If θ = 0o i.e. mirrors are parallel to each other so n i.e. infinite images will be

formed.

If θ = 90o, 3190

360n

If θ = 72o, 4172

360n (If nothing is said object is supposed to be

symmetrically placed).

Example: A ray reflected successively from two plane mirrors inclined at a certain angle

undergoes a deviation of 300o. The number of images observable are

(a)10 (b) 11 (c) 12 (d) 13

Solution : (b)By using 2360300)2360(

/2

/2

Object

Object



o30 . Hence number of images 11130

360

1.5 Additional Information

1. When two plane mirror, inclined to each other at an angle , and

If

360 is a fraction, then the number of image formed will be equal to its integral

part.

2. (i) When the object moves with speed u towards (or away) from the plane mirror then

image also moves toward (or away) with speed u. But relative speed of image w.r.t. object is 2u.

(ii) When mirror moves towards the stationary object with speed u, the image will move with

speed 2u.

Example:A cube falls down from the back of a truck moving at a speed of

10 km/hr. there is a mirror in the truck facing backward. Considering the

cube to be at rest on the road, what will be the speed of its image in the

mirror

Solution: as the mirror is moving at 10 km/hr the image will move at

double the speed as distance of image from is twice the distance from mirror.

Speed of image =20 km/hr.

3. A man of height h requires a mirror of length at least equal to h/2, to see his own complete

image.

2u

O I

Rest

u

Mirror is moving

O I

Mirror at rest

u u



4. To see complete wall behind himself a person requires a plane mirror of at least one third the

height of wall. It should be noted that person is standing in the middle of the room.

SECTION II

2. REFLECTION OF LIGHT BY CURVED SUFACES

A spherical mirror is a reflecting surface which forms a part of a sphere (as shown in

following a and b diagram). When the reflection takes place from the inner surface and

outer surface is polished or silvered the mirror is known as concave mirror. Vice- versa, it

is convex.

(a) concave mirror (b) convex mirror

Concave Mirror

C F P

Convex Mirror

CFP

2.1 Key terms

(i) Pole (P) is generally taken as the midpoint of reflecting surface.

(ii) Centre of curvature (C) is the center of the sphere of which the mirror is a part.

(iii) Radius of curvature is the radius of the sphere of which the mirror is a part. Distance

between P and C.

(iv) Principal Axis is the straight line connecting pole P and center of curvature C.

(v) Principal focus (F) is the point of intersection of all the reflected rays which strike

the mirror (with small aperture) parallel to the principal axis. In concave mirror it is real

and in the convex mirror it is virtual.

(vi) Focal length (f) is the distance from pole to focus.



(vii) Focal plane is the plane through the focus and perpendicular to the principal axis. If a

parallel beam of light not parallel to the principal axis falls on a concave mirror. It gets

reflected to converge at a point on the focal plane.

(viii) Aperture is the diameter of the mirror.

2.2. Image Tracing

When a point object is placed before a spherical mirror of small aperture, a point image is

formed. To locate the position of the image, we draw two rays from the point object, make

them incident on the mirror and trace the reflected rays. The line joining the point of

incidence and the center of curvature is the normal. A reflected ray is traced by applying

the laws of reflection. If the reflected rays intersect, the point of intersection is the real

image. If the rays diverge after reflection, a virtual image is formed at the point from where

the rays seem to diverge. Figure shows some examples

If the incident rays diverge from a point object, the object is called a real object. Sometimes

the rays incident on the mirror do not diverge from a point rather they converge towards

the mirror. In this case, the point where these rays would meet if there was no mirror is

treated as the object. Such a point is called a virtual object

Thus the point of intersection of the incident rays is called the object and the point of

intersection of the corresponding reflected rays is called its image.

2.3. Sign convention

(i) All distances are measured from the pole.

(ii) Distances measured in the direction of incident rays are taken as positive while in the

direction opposite of incident rays are taken negative.

(iii) Distances above the principle axis are taken positive and below the principle axis are

taken negative.



Note : Same sign convention are also valid for lenses.

Use following sign while solving the problem :

Concave mirror

Convex mirror

Real image (u ≥ f) Virtual image (u< f)

Distance of object u –

Distance of image v –

Focal length f –

Height of object O +

Height of image I –

Radius of curvature R –

Magnification m –

u –

v +

f –

O +

I +

R –

m +

u –

v +

f +

O +

I +

R +

m +

2.4 Mirror formula and Magnification

If u = Distance of object from pole, v = distance of image from pole, f = Focal length, R =

Radius of curvature, m = magnification (or linear magnification)

Mirror formula : uvf

111 ; (use sign convention while solving the problems).

Example: A lighted candle is placed at a distance 40 cm from the vertical wall. Where a

concave mirror of radius of curvature 30cm should be placed so that an image of the flame

is obtained on the wall

Solution:

+ –

+

– Mirror or Lens

Incident ray

Principle

axis



Let the mirror be placed at a distance from the candle

The distance of the wall from the mirror ( )

As the object and the image are both real,

( )

( )

( )

The relevant answer is

So the mirror should be placed at 20 cm from the candle.

Magnification : m = Size of image/ Size of object = -v/u

Question to upload

More Solved Examples

Example: A convex lens in air produces a real image having the same size as object. When

the object and the lens immersed in a liquid, the real image formed is enlarged two times

the object size. Find the refractive image of the liquid. ( )

Solution:Combining the lens equation and the lens maker’s formula we have

(

) (

)

In air:

(

) (

) ( )

In liquid:

(

) (

) ( )

Dividing (i) and (ii), we get:

( )



Hence the refractive index of liquid is

Example:Photographs of the ground are taken, from an altitude of 2000 m, by a camera

with a lens of focal length 50 cm. the size of the film in the camera is what

area of the ground can be photographed by this camera at any one time?

Solution:We will take ground to be photographed as object and the image will be formed on

the camera film.

Thus u = 2000 cm. f= 50 cm

Let the area to photographed be x meters long x meters wide.

(size of real inverted image is taken negative)

The area photographed =

Note:

Area magnification =

Example: An object is imaged by a lens on a screen placed 12 cm from the lens. When the

lens is moved 20 cm away from the object, the screen must be moved 20cm closer to the

object to reform it. Find the focal length of the lens.



Solution:

Let x = magnitude of initial object distance,

( )

After shifting the lens and the screen

( )

( )

( )

Solving (i) and (ii), we get

( )( ) ( )

( (( )

Hence, the focal length of the lens is 4 cm.

Example: One surface of biconvex lens having focal length 40cm is silvered. The radius of

the curvature of the other surface is 60 cm. at what distance from the silvered lens should

an object be placed to obtain a real image magnified three times?

Solution:Let x= magnitude of radius of the curvature of the silvered surface.



From lens maker’s formula

(

) (

)

(

) (

)

(

)

The silvered lens will behave like a converging mirror with focal length F because it is a

combination of a converging lens and a converging (concave) mirror.

Focal length of mirror

For the concave mirror:

⁄

Example-When the flat surface of the piano convex lens is silvered, an object coincides with

its image at a distance of 15 cm from the lens. If the curved surface is silvered, the object

coincides with its image at a distance of 5 cm from the lens. Calculate the refractive index of

glass.

Solution:In both the situations, the silvered lens will act like a concave mirror. Let be

the equivalent focal lengths of the silvered lens when the flat and the curved surfaces are

silvered respectively. Let be the focal length of the unsilvered lens.



If flat surface is silvered:

As the object coincides with image, it must be at the center of curvature.

Is curved surface is silvered:

The radius of curvature of the curved side

Now applying Lens maker’s formula we can calculate the refractive index

(

) (

)

( ) (

)

( ) (

)

⁄



Example-A converging beam of light falls on one surface of a biconvex lens whose other

surface is silvered. After reflection from the silvered lens, the beam converges to a point 24

cm in front of the lens. The focal length of the lens is 30 cm and the silvered surface has a

radius of the curvature equal to 50 cm. where wills the beam of light coverage if the lens is

removed from its path?

Solution:The silvered lens is a combination of diverging lens and a diverging mirror. Hence

it will behave like a convex mirror of focal length F.

For equivalent convex mirror:

For equivalent convex mirror:

⁄

( )

( )⁄

Hence the beam will coverage at a point +6.74 cm behind the lens if it is removed.

Example: 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



Solution: The walls will act as two mirrors inclined to each other at 90o and so sill form

3190

360 images of the person. Now these images with object (Person) will act as objects

for the ceiling mirror and so ceiling will form 4 images as shown. Therefore total number of

images formed = 3 + 4 = 7

Note : The person will see only six images of himself ),,,,,( '3

'2

'1321 IIIIII

Example: A ray of light incident on the first mirror parallel to the second and is reflected

from the second mirror parallel to first mirror. The angle between two mirrors is

(a) 30o (b) 60o (c) 75o (d) 90o

Solution : (b) From geometry of figure

o180

o60

Example: A point object is placed mid-way between two plane mirrors distance 'a' apart.

The plane mirror forms an infinite number of images due to multiple reflection. The

distance between the nth order image formed in the two mirrors is

(a)na (b) 2na (c) na/2 (d) n2 a

solution (b)

From above figure it can be proved that separation between nth order image formed in the

two mirrors = 2na

Example: Two plane mirrors P and Q are aligned parallel to each other, as shown in the

figure. A light ray is incident at an angle of 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

I1

I2 I3

O

Three images by walls

I1

I2 I3

O

Four images by ceiling

I1' a/2 a/2 a

M ' M

I order

image

II order

image

III order

image

III order

image

II order

image

I order

image

I1 I2 I3 I2' I3' a/2

3a/2 a/2

3a/2

5a/2 5a/2

O



(a)tand

l (b)

tanl

d

(c) tanld (d)None of these

solution (a)Suppose n = Total number of reflection light ray undergoes before exist out.x =

Horizontal distance travelled by light ray in one reflection.

So nx = l also d

xtan

tand

ln

Example: Two objects A and B when placed one after another infront of a concave mirror of

focal length 10 cm from images of same size. Size of object A is four times that of B. If object

A is placed at a distance of 50 cm from the mirror, what should be the distance of B from

the mirror

(a)10 cm (b) 20 cm (c) 30 cm (d) 40 cm

Solution : (b) By using A

B

A

B

B

A

uf

uf

O

O

I

I

uf

f

O

I

5010

10

4

1

1

1

Bu

cmuB 20 .

Example: A square of side 3 cm is placed at a distance of 25 cm from a concave mirror of

focal length 10 cm. The center of the square is at the axis of the mirror and the plane is

normal to the axis. The area enclosed by the image of the wire is

(a)4 cm2 (b) 6 cm2 (c) 16 cm2 (d) 36 cm2

Solution: (a) By using o

i

A

Am 2 ; where

uf

fm

Hence from given values 3

2

2510

10

m and 29 cmAo 2

2

493

2cmAi

Example: A concave mirror of focal length 100 cm is used to obtain the image of the sun

which subtends an angle of 30'. The diameter of the image of the sun will be

(a)1.74 cm (b) 0.87 cm (c) 0.435 cm (d) 100 cm

solution: Diameter of image of sun fd

18060

30100

d

cmd 87.0 .

Example:A thin rod of length f / 3 lies along the axis of a concave mirror of focal length f.

One end of its magnified image touches an end of the rod. The length of the image is [MP PET 1995]

(a)f (b) f2

1 (c) 2 f (d) f

4

1

d

l

d

l

x

Image of

sun

d

F



Solution : (b) If end A of rod acts an object for mirror then it's image will be A' and

3

5

32

fffu

So by using uvf

111

3

5

111

fvf

fv

2

5

Length of image 2

22

5 fff

Example: 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. 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

Solution : (d)

Example: A small plane mirror placed at the center of a spherical screen of radius R. A

beam of light is falling on the mirror. If the mirror makes n revolution. per second, the

speed of light on the screen after reflection from the mirror will be

(a)4nR (b) 2nR (c) 2

nR (d)

4

nR

Solution : (a) When plane mirror rotates through an angle , the reflected ray rotates

through an angle 2. So spot on the screen will make 2n revolution per second

Speed of light on screen nRRnRv 4)2(2

Position, size and nature of image formed by the spherical mirror

C A' F

A

2f f / 3

v

u = 2f – (f/3)

Object

image

O Initially

C Object

O Finally

Image

C



EXERCISES

Level 1

1. An object is initially at a distance of 100 cm from a plane mirror. If the mirror approaches

the object at a speed of 5 cm/s, then after 6 s the distance between the object and its image

will be

(a) 60 cm (b) 140 cm (c) 170 cm (d) 150 cm

2. An object placed in front of a plane mirror is displaced by 0.4 m along a straight line at an

angle of 30o to mirror plane. The change in the distance between the object and its image is

(a) 0.20 m (b) 0.40 m (c) 0.25 m (d) 0.80 m

3. A convex mirror of focal length 10 cm is placed in water. The refractive index of water is

4/3. What will be the focal length of the mirror in water

(a)10 cm (b) 40/3 cm (c) 30/4 cm (d) None of these

Mirror Location of the object

Location of the image

Magnification,

Size of the image

Nature

Real

virtual

Erect

inverted

(a) Concave

At infinity

i.e. u = ∞

At focus i.e. v = f m << 1, diminished Real inverted

Away from centre of

curvature (u > 2f)

Between f and 2f i.e.

f < v < 2f

m < 1, diminished Real inverted

At centre of

curvature u = 2f

At centre of

curvature i.e. v = 2f

m = 1, same size as

that of the object

Real inverted

Between centre of curvature and focus :

F < u < 2f

Away from the centre of curvature

v > 2f

m > 1, magnified Real inverted

At focus i.e. u = f At infinity i.e. v = ∞ m = ∞, magnified Real inverted

Between pole and focus u < f

v > u m > 1 magnified Virtual erect

(b) Convex At infinity i.e. u = ∞ At focus i.e., v = f m < 1, diminished Virtual erect

Anywhere between

infinity and pole

Between pole and

focus m < 1, diminished Virtual erect

P F C

C F P



4. A ray of light travels from A to B with uniform speed. On its way it is reflected by the

surface XX'. The path followed by the ray to take least time is

(a) 1

(b) 2

(c) 3

(d) 4

5. Two mirrors, each 1.6m long are facing each other. The distance between the mirrors is

20 cm. a light ray incident on one end of one of the mirrors at an angle of incidence of

How many times is the ray reflected before it reaches the other end?

6. An object is 375 mm from a concave mirror of 250 mm focal length. Find the image

distance. If the object is moved 5 mm farther from the mirror, how far does the image

move?

7. A object 28 mm high is 0.48 m from a convex mirror with a radius of curvature of 0.82m.

locate the image. Is it real or virtual? It is erect or inverted? What is its size?

8. A man runs towards a mirror at a speed 15 m/s. The speed of the image relative to the man is

(a) 15 1ms (b) 30 1ms (c) 35 1ms (d) 20 1ms

9.A man is 180 cm tall and his eyes are 10 cm below the top of his head. In order to see his entire height right from toe to head, he uses a plane mirror kept at a distance of 1 m from him. The minimum length of the plane mirror required is

(a) 180 cm (b) 90 cm (c) 85 cm(d) 170 cm

10.A small object is placed 10 cm infront of a plane mirror. If you stand behind the object 30 cm from the object and look at its image, the distance focused for your eye will be [KCET (Engg.) 2001]

(a) 60 cm (b) 20 cm (c) 40 cm (d) 80 cm

11. A plane mirror produces a magnification of

(a) – 1 (b) + 1 (c) Zero(d)Between 0 and +

12. Two plane mirrors are parallel to each other an spaced 20 cm apart. An object is kept in

between them at 15 cm from A. Out of the following at which point an image is not formed

in mirror A (distance measured from mirror A)

(a) 15 cm (b) 25 cm (c) 45 cm (d) 55 cm

13. A diminished virtual image can be formed only in

(a) Plane mirror (b) A concave mirror (c) A convex mirror (d) Concave-parabolic mirror

14. A diminished virtual image can be formed only in

(a) Plane mirror (b) A concave mirror

(c) A convex mirror (d) Concave-parabolic mirror

X X

B A

1 2 3 4



15. Match List I with List II and select the correct answer using the codes given below the lists [SCRA 1998] List I List II

(Position of the object) (Magnification)

(I) An object is placed at focus before a convex mirror (A) Magnification is – (II) An object is placed at centre of curvature before a concave mirror (B) Magnification is 0.5 (III) An object is placed at focus before a concave mirror (C) Magnification is + 1

(IV) An object is placed at centre of curvature before a convex mirror (D) Magnification is – 1

(E) Magnification is 0.33

Codes :

(a) I-B, II-D, III-A, IV-E (b) I-A, II-D, III-C, IV-B (c) I-C, II-B, III-A, IV-E (d) I-B, II-E, III-D, IV-C

16. All of the following statements are correct except

(a) The magnification produced by a convex mirror is always less than one

(b) A virtual, erect, same-sized image can be obtained 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

17. A convex mirror is used to form the image of an object. Then which of the following statements is wrong

(a) The images lies between the pole and the focus (b) The image is diminished in size

(c) The images is erect (d) The image is real

18. A dice is placed with its one edge parallel to the principal axis between the principal focus and the centre of the curvature of a concave mirror. Then the image has the shape of

(a) Cube (b)Cuboid (c)Barrel shaped (d)Spherical

19. An object of length 6cm is placed on the principal axis of a concave mirror of focal

length f at a distance of 4 f. The length of the image will be

(a) 2 cm (b) 12 cm (c) 4 cm (d) 1.2 cm

20. A point object is placed at a distance of 30 cm from a convex mirror of focal length

30cm. The image will form at

(a) Infinity (b) Focus (c) Pole (d) 15 cm behind the mirror

21. A concave mirror of focal length 15 cm forms an image having twice the linear

dimensions of the object. The position of the object when the image is virtual will be

(a) 22.5 cm (b) 7.5 cm (c) 30 cm (d) 45 cm



Level -2

1. The figure shows two rays A and B being reflected by a mirror and going as A' and B'. The

mirror is

(a) Plane (b) Concave

(c) Convex (d) May be any spherical mirror

2. 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

3. A man having a height of 6 m, want to see his full height in mirror.

He observes an image of 2m height of his whole body erect, then used mirror is

(a) Concave (b) Convex (c) Plane (d) None of these

4. The focal length of a convex mirror is 20 cm its radius of curvature will be

(a) 10 cm (b) 20 cm (c) 30 cm (d) 40 cm

5. Under which of the following conditions will a convex mirror of focal length f produce an

image that is erect, diminished and virtual

(a) Only when 2f > u > f (b) Only when u = f

(c) Only when u < f (d) Always

6. As the position of an object reflected in a concave shell mirror of 0.25m focal length is

varied, the position of the image varies. Plot the image distance as a function of the object

distance, letting the latter change from Where is the image real? Where virtual?

7. If it is possible, under what condition will the image in a concave mirror be (a) real (b)

virtual (c) erect (d) inverted (e) magnified (f) reduced?

8. Repeat question 7 for a convex mirror?

9. A U-shaped wire is placed before a concave mirror having

radius of curvature 20 cm as shown in figure. Find the length

of the image

A

B B

A



10. A point source S is placed midway between two converging

mirrors having equal focal length as shown in figure. Find the values

of d for which only one image is formed

11. A particle is moving at a constant speed V from a large distance towards a concave

mirror of radius R along its principal axis. Find the speed of the image formed by the mirror

as a function of the distance of the particle from the mirror.

12. A small block of mass m and a concave mirror of radius R fitted with a stand lie on a

smooth horizontal table with a separation d between them. The mirror together with its

stand has a mas The block is pushed at towards the mirror so that it starts moving

towards the mirror at a constant speed V and collides with it. The collision is perfectly

elastic. Find the velocity of the image (a) at a time (b) at a time

13. A gun of mass M fires a bullet of mas m with a horizontal speed V. the gum is fitted with

a concave mirror of focal length facing towards the receding bullet. Find the speed of

separation of the bullet and the image just after the gum was fired

14. A mass m=50 g is dropped on a vertical spring of spring constant 500

from a height cm as shown in figure. The mass sticks to the spring and

executes simple harmonic oscillates after that. A concave mirror of focal length

12cm facing the mass is fixed with its principal axis coinciding with the line of

motion of the mass, its pole being at a distance of 30 cm from the free end of the

spring. Find the length in which the image of the mass oscillates.

15. Two concave mirrors of equal radii of curvature R are fixed on a stand facing opposite

directions. The whole system has a mass and is kept on a frictionless horizontal table

Two blocks A and B, each of mass m, are placed on the two sides of the stand. At , the

seperation between A and the mirrors is 2R and also the seperation between B and the

mirrors is 2R. the block B moves towards the mirror at a speed . All collisions which take

place are elastic. Taking the original position of the mirrors-stand system to be and

X-axis along AB, find the position of the image of A and B at



(a)

(b)

(c)

16. consider the situation shown in figure. The elevator is going up with an

acceleration of and the focal length of the mirror is 12.0 cm. all

the surfaces are smooth and the pulley is light. The mass-pulley system is

released from rest (with respect to the elevator) at when the distance

of B from the mirror is 42.0 cm. find the distance between the image of the block B and the

mirror at Take

17. Two plane mirrors are at right angles to each other. A man stands between them and combs his hair with his right hand. In how many of the images will he be seen using his right hand

(a) None (b) 1 (c) 2 (d) 3

18. 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 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 the first one) before it emerges out is [IIT-JEE (Screening) 2002]

(a) 28

(b) 30

(c) 32

(d) 34

19. A point object O is placed between two plan mirrors as shown is fig. The distance of the

first three images formed by mirror 2M from it are

(a) 2 mm, 8 mm, 18 mm

(b) 2 mm, 18 mm, 28 mm

(c) 2 mm, 18 mm, 22 mm

(d) 2 mm, 18 mm, 58 mm

20.A plane mirror is placed at the bottom of the tank containing a liquid of refractive index . P is a small object at a height h above the mirror. An observer O-vertically above P

outside the liquid see P and its image in the mirror. The apparent distance between these two will be

(a) h2

(b)

h2

(c) 1

2

h

(d)

11h

B

30o

A

0.2m

O

P h

2mm 10mm

M1 M2

O



21. In an experiment of find the focal length of a concave mirror a graph is drawn between the magnitudes of u and v. The graph looks like [AIIMS 2003]

(a) (b)

22. A short linear object of length l lies along the axis of a concave mirror of focal length f at

a distance u form the pole of the mirror. The size of the image is approximately equal to [IIT 1988; BHU 2003]

(a) 2/1

f

ful (b)

2

f

ful (c)

2/1

fu

fl (d)

2

fu

fl

23.A point object is moving on the principal axis of a concave mirror of focal length 24 cm

towards the mirror. When it is at a distance of 60 cm from the mirror, its velocity is 9

cm/sec. What is the velocity of the image at that instant

(a) 5 cm/sec towards the mirror

(b)4cm/sec towards the mirror

(c) 4 cm/sec away from the mirror

(d) 9 cm/sec away from the mirror

24. A thin rod of 5 cm length is kept along the axis of a concave mirror of 10 cm focal length

such that its image is real and magnified and one end touches the rod. Its magnification will

be

(a) 1 (b) 2 (c) 3 (d) 4

25.A luminous object is placed 20 cm from surface of a convex mirror and a plane mirror is

set so that virtual images formed in two mirrors coincide. If plane mirror is at a distance of

12 cm from object, then focal length of convex mirror, is

(a) 5 cm (b) 10 cm (c) 20 cm (d) 40 cm

26. A vehicle has a driving mirror of focal length 30 cm. Another vehicle of dimension 375.142 m is 9 m away from the mirror of first vehicle. Position of the second vehicle as

seen in the mirror of first vehicle is

(a) 30 cm

(b) 60 cm

(c) 90 cm

(d) 9 cm

27. A concave mirror of radius of curvature 60 cm is placed at the bottom of tank

containing water upto a height of 20 cm. The mirror faces upwards with its axis vertical.

Solar light falls normally on the surface of water and the image of the sun is formed. If

3

4wa then with the observer in air, the distance of the image from the surface of water is

v

u

v

u

v

u

v

u

9m



(a) 30 cm (b) 10 cm (c) 7.5 cm above (d) 7.5 cm below

28.A concave mirror forms an image of the sun at a distance of 12 cm from it

(a) The radius of curvature of this mirror is 6 cm

(b) To use it as a shaving mirror, it must be held at a distance of 8-10 cm from the face

(c) If an object is kept at a distance of 12 cm from it, the image formed will be of the same size as the object

(d) All the above a alternatives are correct

29. A small piece of wire bent into an L shape with upright and horizontal portions of equal lengths, is placed with the horizontal portion along the axis of the concave mirror whose radius of curvature is 10 cm. If the bend is 20 cm from the pole of the mirror, then the ratio of the lengths of the images of the upright and horizontal portions of the wire is

(a) 1 : 2 (b) 3 : 1 (c) 1 : 3 (d) 2 : 1

30.As the position of an object (u) reflected from a concave mirror is varied, the position of

the image (v) also varies. By letting the u changes from 0 to the graph between v versus

u will be

(a) (b) (c) (d)

31. A concave mirror of focal length 10 cm and a convex mirror of focal length 15 cm are placed facing each other 40 cm apart. A point object is placed between the mirrors, on their common axis and 15 cm from the concave mirror. Find the position and nature of the image produced by the successive reflections, first at concave mirror and then at convex mirror

(a) 2 cm (b) 4 cm (c) 6 cm (d) 8 cm

v

u

v

u

v

u

v

u

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