Refraction of Li ght

REFRACTION OF LIGHT (RER)

(RER–1)
1.0 INTRODUCTION
Light seems to travel along straight-line paths in a transparent medium. When light enters from one
transparent medium to another, it changes its direction. This we can recall from our day-to-day
experiences. You might have observed that the bottom of a tank or a pond containing water appears
to be raised. Similarly, when a thick glass slab is placed over some printed matter, the letters
appear raised when viewed through the glass slab. You might have seen a pencil partly immersed
in water in a glass tumbler. It appears to be bent at the interface of air and water. You might have
observed that a lemon kept in water in a glass tumbler appears to be bigger than its actual size,
when viewed from the sides. All these day-to-day experiences are based on a phenomenon called
‘refraction’.
2.0 REFRACTION OF LIGHT
Concept of Refraction of Light
When light travels in the same homogeneous medium, it travels along a straight path. However,
when it passes from one transparent medium to another, the direction of its path changes at the
interface of the two media. This is called Refraction of light.
The phenomenon of bending of light or the change in the path of the light as it passes from one
transparent medium to another is called Refraction of light. The path along which the light travels
in the first medium is called incident ray and that in the second medium is called Refracted ray.
The angles which the incident ray and the refracted ray make with the normal at the surface of
separation are called angle of incidence (i) and angle of refraction (r) respectively.

2.1 Laws of Refraction

Refraction of light follows the following two laws
(i) The incident ray, the refracted ray and the normal to the surface separating the two media,
all lie in the same plane.
(ii) The ratio of the sine of the incident angle ( i) to the sine of the refracted angle ( r) is
constant for a pair of two media and for given wave length of light.
A
Incident
ray i
Rarer medium
O Denser medium
Refracted
r
ray
B
(a) Rarer to denser medium
Fig. 1 Showing refraction of light
sin i
i.e. = constant
sin r
This constant is known as the refractive index of the medium in which refracted ray travels with
respect to the medium in which incident ray travels. You will study refractive index later on in this
chapter.
Refractive index of medium is denoted by ‘ ’
Thus above equation can be written as
sin i
µ=
sin r
This law is also known as Snell’s law as it was stated by Prof. Willebrord Snell (Dutch mathema-
tician and astronomer).
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Class X - Physics

2.2 Cause of Refraction

Refraction is caused due to change in speed of the light as it moves from one medium to another.

2.3 Optical Density

We come across many media like air, glass, water etc. Every transparent medium has a property
known as optical density. The optical density of a transparent medium is closely related to the
speed of light in the medium. Optical density of a medium is the quantity which tells us whether a
light wave will travel slower or faster in that medium or speed of a wave in any medium will depend
on the optical density of that material. If the optical density of a transparent medium is low then
the speed of light in that medium is high. Such a medium is known as optically rarer medium.
Thus, optically rarer medium is that medium through which light travels fast. In other words, a
medium in which speed of light is more is known as optically rarer medium.
On the other hand, if the optical density of a transparent medium is high then the speed of light in
that medium is low. Such a medium is known as optically denser medium. Thus, optically denser
medium is that medium through which light travels slow. In other words, a medium in which speed
of light is less is known as optically denser medium.
Speed of light in air is more than the speed of light in water, so air is optically rarer medium as
compared to the water. In other words, water is optically denser medium as compared to air.
Similarly, speed of light in water is more than the speed of light in glass, so water is optically rarer
medium as compared to the glass. In other words, glass is optically denser medium as compared to
water.
When light goes from air (optically rarer medium) to glass (optically denser medium) such that the
light in air makes an angle with the normal to the interface separating air and glass, then it bends
from its original direction of propagation. Similarly, if light goes from glass to air, again it bends
from its original direction of propagation. The phenomenon of bending of light from its path when
it goes from one optical medium to another optical medium is known as refraction. We have seen
that the speed of light in different media is different, so we can say that refraction of light takes
place because the speed of light is different in different media.

Incident ray
Normal

Air
Glass

(C)
Refracted
ray

Fig. 2 Cases of Refraction

It is observed that
(i) When a ray of light passes from an optically rarer medium to a denser medium, it bends
towards the normal
( r < i), as shown in figure 2(A).
(ii) When a ray of light passes from an optically denser to a rarer medium, it bends away from
the normal ( r > i) as shown in Figure 2(B).
(iii) A ray of light travelling along the normal passes undeflected, as shown in figure 2 (C).
Here i = r = 00.
(iv) The intensity of the refracted ray is less than that of the incident ray. It is because there is
partial reflection and absorption of light at the interface.
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 Refraction of Li ght

3.0 REFRACTIVE INDEX

The refractive index of a medium for a light of given wavelength may be defined as the ratio of the
speed of light in vacuum to its speed in that medium.
Speed of light in vacuum c
Refractive index = or
Speed of light in medium v
Refractive index of a medium with respect to vacuum is also called absolute refractive index.

3.1 Relative Refractive Index

The relative refractive index of medium 2 with respect to medium 1 is defined as the ratio of speed
of light (v1) in the medium 1 to the speed of light (v2) in medium 2 and is denoted by 1µ2.
v1
Thus µ = v
1 2
2

As refractive index is the ratio of two similar physical quantities, so it has no units and dimensions.
It may be noted that refractive index depends on the wavelength of light but is independent of the
angle of incidence.
Important Information
We know that speed greater than speed of light is not possible, So c > v
[v = Velocity of light in given medium]
[c = Velocity of light in vacuum]
c
Now as = , it should be greater than one.
v
Physical Significance of Refractive Index
The refractive index of a medium gives the following two informations :
(i) The value of refractive index gives information about the direction of bending of refracted
ray. It tells whether the ray will bend towards or away from the normal.
(ii) The refractive index of a medium is related to the speed of light. It is the ratio of the speed of
light in vacuum to that in the given medium. For example, refractive index of glass is 3/2.
This indicates that the ratio of the speed of light in glass to that in vacuum is 2 : 3 or the
speed of light in glass is two-third of its speed in vacuum.

Illustration 1 Calculate the refractive index of a diamond if the speed of light in a diamond is
1.24 × 108 m/s. Speed of light in vacuum is 3 × 108 m/s.
Solution. Given, speed of light in vacuum, c = 3 × 108 m/s ;
speed of light in medium, v = 1.24 × 108 m/s ; refractive index, n = ?
c 3 108
By definition, n = 2.42
v 1.24 108

Illustration 2 Calculate the index of refraction for a substance where the angle of incidence is 30°,
the angle of refraction is 60.0°, and the refractive index of the second substance is 1.5
(Take 3 = 1.73).
Solution. Given, i = 30° ; r = 60° ; n2 = 1.5 ; n1 = ?
By Snell’s law,
n1 sin i = n2 sin r
sin r sin 60 3 /2
n1 = n2 = 1.5 = 1.5 = 3 1.5 = 1.73 1.5 = 2.595 2.6
sin i sin 30 1/2

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Class X - Physics

QUICK CHECK-1

Objective Questions
1. A ray of light travelling in air have wavelength , frequency n, velocity V and intensity I. If this ray
enters into water than these parameters are ' , n', v' and I' respectively. Which relation is correct
from following-
(A) ' (B) n = n' (C) v = v' (D) I = I'

2. Light travels through a glass plate of thickness t and having refractive index n. If c is the velocity of
light in vacuum. the time taken by the light to travel this thickness of glass is
t nt tc
(A) (B) tnc (C) (D)
nc c n

3. The frequency of a light wave in a material is 2 × 1014 Hz and wavelength is 5000 Å. The refractive
index of material will be:
(A) 1.33 (B) 1.40 (C) 1.50 (D) 3.00

4. Velocity of light in glass, whose refractive index w.r.t. air is 1.5, is 2x108 m/Sec. In a certain liquid
the velocity of light is found to be 2.5x108 m/Sec. The refractive index of liquid w.r.t. air is
(A) 0.64 (B) 0.80 (C) 1.20 (D) 1.44

5. Relative Refractive Index of medium 2 w.r.t. medium 1 is :

v1 v2 C
(A) 1µ2 = v (B) 1µ2 = v (C) 1µ2 = (D) None of these
2 1 v

Subjective Questions

6. Red light of wavelength 633 nm from a helium–neon laser is incident on a container containing
water. Find the change in wavelength of light in the container, given that the refractive index of
water is 1.33.

7. A ray of light travelling in air falls on the surface of a transparent slab. The ray makes an angle of
45° with the normal to the surface. Find the angle made by the refracted ray with the normal within
the slab. Refractive index of the material of the slab is 2.

8. Which colour has maximum speed in glass?

9. Define refractive index in terms of speed of light and in terms of wavelength. State the factors on
which refractive index of a material depends.

10. Discuss the concept of refraction of light in detail with figure.

40
 Refraction of Li ght

REFRACTION OF LIGHT
(RER–2)

4.0 REFRACTION THROUGH GLASS SLAB

Consider a rectangular glass slab, as shown in figure 3 A ray AB is incident on the face PQ at an
angle of incidence i1. On entering the glass slab, it bends towards normal and travels along BC at
an angle of refraction r1. The refracted ray BC is incident on face SR at an angle of incidence i2.
The emergent ray CD bends away from the normal at an angle of refraction r2.
A

i1
B
P Q
r1

i2
Glass
S R
Air C
r2

lateral displacement
D
Fig. 3 Refraction through glass slab

Using Snell’s law for refraction at face PQ,

sin i1
sin r1 = a g … (1)

For refraction at face SR,

sin i 2 1
sin r2
= g a = a g
… (2)

Multiplying (1) and (2), we get

sin i1 sin i 2
sin r1
× sin r2
=1 … (3)

Now from Figure 3 we can say that r1 = i2 [ r1 and i2 are alternate opposite angles]
So equation (3) can be written as
sin i1 sin r1
sin r1
× sin r2
=1

sin i1 = sin r2
i1 = r2
Thus the emergent ray CD is parallel to the incident ray AB, but it has been laterally (sidewise)
displaced with respect to the incident ray. This shift in the path of light on emerging from a refract-
ing medium with parallel faces is called lateral displacement. Hence lateral shift is the perpendicu-
lar distance between the incident and emergent rays, when light is incident obliquely on a refract-
ing slab with parallel faces.
Factors on which lateral shift depends
(i) Lateral shift varies directly with the thickness of glass slab.
(ii) Lateral shift varies directly with the incident angle.
(iii) Lateral shift varies directly with the refractive index of glass slab.

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Class X - Physics

5.0 REAL AND APPARENT DEPTH

It is on account of refraction of light that the apparent depth of an object placed in denser medium
is less than the real depth when viewed from rarer medium. Figure 4 shows a point object O placed
at the bottom of a beaker filled with water. The rays OA and OB starting from O are refracted
along AD and BC, respectively. These rays appear to diverge from point I.

Eye C
D
r rarer medium
B (medium 1)
A
apparent
depth h' r i
I
Th real depth denser medium
i (medium 2)

O
Fig. 4 real and apparent depths

So, I is the virtual image of O. Clearly, the apparent depth AI is smaller than the real depth AO.
That is why a water tank appears shallower or an object placed at the bottom appears to be raised.
h
h'
nrelative

ni (R.I.of medium of incidence)

where nrelative nr (R.I.of medium of refraction)
h = distance of object from the interface = real depth
h’ = distance of image from the interface = apparent depth

6.0 EFFECTS OF REFRACTION OF LIGHT

The refraction of light leads to some optical illusions. These are
(i) A pencil or a stick immersed in water appears bent and short in length.
(ii) A water tank appears shallow i.e., less deep than its actual depth,
(iii) An ink dot on a paper appears to be raised up when a glass slab is placed over it.
(iv) A fisherman fails to catch a fish if he aims the spear at the head of the fish.
(v) Apparent flattening of the sun at sunrise and at sunset.
Now we shall discuss all these effects in detail.

A pencil Appears Bent and Short in Water

eye

air

B
water

Q
Fig. 5

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 Refraction of Li ght
Consider a pencil PQ. Let AQ portion of the pencil be dipped in water as shown in figure 5. Rays
of light from the tip (Q) of the pencil bend away from the normal as they go from water to air i.e.
denser to rarer medium. These rays appear to come from a point B. Thus, the dipped portion of
the pencil appears as AB. Hence a pencil appears bent and short when immersed in water.

A Water Tank Appears Shallow i.e. Less Deep Than its Actual Depth

A B

O
Fig. 6

Consider an object O say a stone lying on the bed of a water tank as shown in figure 6. A ray (OB)
of light from the object suffers refraction at the free surface of water in the tank and bends away
from the normal along BC. The refracted ray BC appears to come from point I which is above the
object O. Thus, the bed of the tank appears at the level of point I. In other words, water tank
appears shallow.

An Ink Dot on A Paper Appears to Be Raised up When a Glass Slab is Placed Over it

eye

air

glass
slab

ink dot

Fig. 7

The rays of light from the ink dot bend away from the normal as they go from the glass slab to air.
The refracted rays AC and BD appear to come from point I. The point I is the virtual image of the
ink dot and its position is above the ink dot O. Hence, an ink dot on a paper appears to be raised
up when a glass slab is placed over it, as shown in figure 7.

A Fisherman Fails to Catch a Fish If He Aims The Spear at The Head of Fish.

Fig. 8

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Class X - Physics

This is also due to refraction of light. When a fish in water is seen from some angle, then due to
refraction of light, the fish appears to be raised up and moreover the image of the fish is a little
ahead of the actual position of the fish (see figure 8). As a result of this, the spear falls ahead of the
actual position of the head of the fish. Thus, the fisherman is unable to catch the fish. However, a
skilled fisherman always aims at the tail of the fish to catch the fish.

Apparent Flattening of The Sun at Sunrise and Sunset

The sun near the horizon appears flattened. This is due to atmospheric refraction. The density and
the refractive index of atmosphere decreases with altitude, so the rays from the top and bottom
portions of the sun on the horizon are refracted by different degrees. This cause the apparent
flattening of the sun. But the rays from the sides of the sun on a horizontal plane are generally
refracted by the same amount, so the sun still appears circular along its sides.
Apparent Shift in The Position of The Sun at Sunrise And Sunset

Due to the atmospheric refraction, the sun is visible before actual sunrise and after actual sunset.

Apparent
Position
S' of Sun

Atmosphere
Horizon

Observer

Actual
S Position
Earth
of Sun

Fig. 9 Refraction effect at sunset and sunrise

With altitude, the density and hence refractive index of air-layers decreases. The light rays starting
from the sun S travel from rarer to denser layers. They bend more and more towards the normal.
However, an observer sees an object in the direction of the rays reaching his eyes. So to an
observer standing on the earth, the sun which is actually in a position below the horizon, appears
in the position S’, above the horizon. The apparent shift in the position of the sun is by about 0.5 0.
Thus the sun appears to rise early by about 2 minutes and for the same reason, it appears to set
late by about 2 minutes. This increases the length of the day by about 4 minutes.

7.0 TOTAL INTERNAL REFLECTION

When light ray travel from denser to rare medium it bend away from the normal if the angle of
incident is increased angle of refraction will also increased. At a perticular value of angle the
refracted ray subtend 900 angle with the normal, this angle of incident is known as crtical angle
( C). If angle of incident further increase the ray come back in the same medium this phenomenon
is known as total internal reflection.
Conditions -
1. Angle of incident > Critical angle [i > c]
2. Light should travel from denser to rare medium Glass to air, water to air, Glass to water

44
 Refraction of Li ght

90°
R R R

D D
D C I> C

Fig. 10
Snell Law at boundry
D
sin C = R sin 90

R
sin C
D

When light ray travel from refractive index medium to air then R
, =1, D
=
1
Sin =1/ , sin C C (Red) C (violet)
C

For TIR
1
i > sin i > sin sin i > 1/ >
C C sini

7.1 Some Illustrations of Total Internal Reflection

Sparkling of Diamond
The sparkling of diamond is due to total internal reflection inside it. as refractive index for dia-
mond is 2.5 so C = 24°. Now the cutting of diamond are such that i > iC. so TIR will take place
again and again inside it. The light which beams out from a few places in some specific directions
makes it sparkle.

Optical Fibre
In it light through multiple total internal reflections is
propagated along the axis of a glass fibre of radius of few
microns in which index of refraction of core is greater than
that of surroundings.

Fig. 11

Mirage and Looming

Mirage is caused by total internal reflection in deserts where
due to heating of the earth, refractive index of air near the
surface of earth becomes lesser than above it. Light from distant
objects reaches the surface of earth with i.> C so that TIR
will take place and we see the image of an object along with
the object as shown in Fig 12.
Similar to 'mirage' in deserts, in polar regions 'looming' takes
place due to TIR. Here decreases with height and so the
image of an object is formed in air if (i> C ) as shown in Fig.
Fig. 12

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Class X - Physics

Illustration 1. Prove using formulae of relative refractive index and absolute refractive index,
1 n2
(a) n 21 (b) n21
n12 n1

v1
Solution (a) By definition, n21 ....(1)
v2
Where, v1 and v2 are speeds of light in medium 1 and 2 respectively.
v2
Similarly, n12 ....(2)
v1

v1 v2
(1) × (2) n 21 n12 1 or n12 × n21 = 1
v2 v1

1
or n21
n12

c
(b) By definition, absolute refractive index (n) is given by, n
v
Where, c = speed of light in vacuum ; v = speed of light in medium
c c
n2 ....(1) and n1 ....(2)
v2 v1

1 n2 c / v2 n2 v1
or ....(3)
2 n1 c / v1 n1 v2

v1
Now, n21 ....(4)
v2

n2
From (3) & (4) , we get, n21
n1

QUICK CHECK-2

Objective Questions

1. Optical fibre are based on -

(A) Total internal reflection (B) Less scattering
(C) Refraction (D) Less absorption coefficient

2. A ray of light propagates from glass (refractive index = 3/2) to water ( refractive index = 4/3). The
value of the critical angle

8
(A) sin–1 (1/2) (B) sin–1 9 (C) sin–1 (8/9) (D) sin–1 (5/7)

46
 Refraction of Li ght
3. 'Mirage' is a phenomenon due to
(A) Reflection of light (B) Refraction of light
(C) Total internal reflection of light (D) Diffraction of light

4. In the formation of a rainbow light from the sun on water droplets undergoes
(A) Dispersion only (B) Only total internal reflection
(C) Dispersion and total internal reflection (D) None of these

5. The wavelength of light in two liquids 'x' and 'y' is 3500 Å and 7000Å , then the critical angle will
be
(A) 60° (B) 45° (C) 30° (D) 15°

Subjective Questions
3 4
6. Absolute refractive index of glass is & Absolute refractive index of water is . Then the relative
2 3
refractive index of glass with respect to water and also speed of light in water is respectively :

7. How much height of water should be filled in a container 21 cm in height, so that it appears half
4
filled when viewed from the top of the container (given that = ):
w 3

8. State and explain Snell’s law.

9. Relative refractive index of a optical medium can be:

10. When a ray of light enters from one medium to another, then its velocity in second medium be-
comes double. Then the maximum value of angle of incidence so that total internal reflection may
not take place will be :

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Class X - Physics

REFRACTION OF LIGHT
(RER–3)

8.0 SPHERICAL LENSES

Definition
A lens is a piece of transparent refracting material bound by two spherical surfaces or one spherical
and other plane surface.
A lens is the most important optical component used in microscopes, telescopes, cameras, projectors,
etc.
Basically lenses are of two types :
(i) Convex lens or converging lens
(ii) Concave lens or diverging lens

Convex Lens And Their Types

A lens which is thick at the centre and thin at the edges is called a convex lens. The most common
form of a convex lens has both the surfaces bulging out at the middle. Some forms of convex lenses
are shown in the figure

double plano concavo

convex convex convex

(a) (b) (c)

Fig. 13 : Types of convex lens

Concave Lens And Their Types

A lens which is thin at the middle and thick at the edges is called a concave lens. The most
common form of a concave lens has both the surfaces depressed inward at the middle. Some
forms of concave lenses are shown in the figure.

double plano convexo

concave concave concave

(a) (b) (c)

Fig. 14 : Types of concave lens

48
 Refraction of Li ght

8.1 Terms
(i) Centre of curvature (C)
The centre of curvature of the surface of a lens is the centre of the sphere of which it forms a part.
Because a lens has two surfaces, so it has two centres of curvature. Points C1 and C2 of figure 15
(a) and shows centre of curvatures.
(ii) Radius of curvature (R)
The radius of curvature of the surface of a lens is the radius of the sphere of which the surface
forms a part. R1 and R2 in figure 15 (a) and (b) are the radius of curvatures of two spheres.
( i i i ) P ri nc i pa l ax i s (C 1 C 2 )
It is the line passing through the two centres of curvature of the lens.

Fig. 15

(iv) Optical center

If a ray of light is incident such that it goes undeviated through the lens (Figure 16) then the point
of intersection of principle axis and the incident ray inside the lens is the optical center. It is taken at the
center of lens for thin lenses

Fig. 16

(v) Principal foci and focal length

The point on the principal axis of a lens where all the rays parallel to principal axis converge or
appear to diverge after refraction is called ‘principal focus’.
Focal length - The distance between the focus and the optical centre of a lens is called its ‘focal
length’.
A convex / concave lens has two principal foci F 1 and F2. F1 is towards left of the lens and from this
region, light rays are incident on the lens. F2 is towards right of the lens and in this region, light rays
are emergent after refraction.

2F1 F1 F2 2F2 2F1 F1 F2 2F2

(a) A convex lens (b) A concave lens

Fig. 17

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Class X - Physics

(vi) Aperture-
It is the diameter of the circular boundary of the lens. In figure 18 (a) and (b), AB is the aperature
of lens.

Fig. 18

9.0 RULES FOR IMAGE FORMATION BY A CONVEX LENS

The position of the image formed by a convex lens can be found by considering two of the following
rays

(i) A ray of light coming parallel to principal axis, after refraction

through the lens, passes through the principal focus (F)
O
as shown in the figure 19 F

Fig. 19

(ii) A ray of light passing through the optical centre O of the

lens goes straight without suffering any deviation as O
shown in the figure 20

Fig. 20
(iii) A ray of light coming from the object and passing through the principal focus of the lens after
refraction through the lens, becomes parallel to the principal axis. This is shown in figure

F O

Fig. 21

10.0 IMAGE FORMED BY CONVEX LENS

The position, size and nature of the image formed by a convex lens depends upon the distance of
the object from the optical centre of the lens. For a thin convex lens, the various cases of image
formation are explained below:

(i) When object lies at infinity

When an object lies at infinity, the rays of light coming from the object may be regarded as a
parallel beam of light. The ray of light BO passing through the optical centre O goes straight
without any deviation. Another parallel ray AE coming from the object, after refraction, goes along
EA'. Both the reflected rays meet at A' in the focal plane of the lens. Hence, a real, inverted and
highly diminished image is formed on the other side of the lens in its focal plane.

50
 Refraction of Li ght

A
Object at
Infinity B

E
B'
O F
F

A'
Real, inverted
And highly
Diminished image
Fig. 22

(ii) When object lies beyond 2F

When an object lies beyond 2F, its real, inverted and diminished image is formed between F and
2F on the other side of the lens as explained below
A ray of light AE coming parallel to the principal axis, after refraction, passes through the principal
focus F and goes along EF. Another ray AO passing through the optical centre O goes straight
without suffering any deviation. Both the refracted rays meet at A . Hence a real, inverted and
diminished image is formed between F and 2F on the other side of the convex lens.

A
E

F
B'
B O
2F F 2F

A'
Real, inverted
and diminished image

Fig. 23

(iii) When object lies at 2F

When an object lies at 2F in front of a convex lens, its real inverted image having same size as that
of the object is formed on the other side of the convex lens as explained below :
A ray of light AE coming parallel to the principal axis, after refraction, passes through the principal
focus F and goes along EF. Another ray AO passing through the optical centre O goes straight
without suffering any deviation. Both the refracted rays meet at A Hence a real, inverted image
having the same size as that of the object is formed at 2F on the other side of the lens.

A
E

F 2F
B
O B'
2F F
Real, inverted
and same size
A'

Fig. 24

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Class X - Physics

(iv) When object lies between F and 2F

When an objects lies between F and 2F in front of a convex lens, its real, inverted and magnified
image is formed beyond 2F on the other side of the lens as explained below :
A ray of light AE coming parallel to the principal axis, after refraction, passes through the principal
focus F and goes along EF. Another ray of light AO passing through the optical centre goes straight
without any deviation. Both these refracted rays meet at A'. Hence a real, inverted and magnified
image is formed beyond 2F on the other hand side of the lens.
A E

B'
2F B F O
F 2F

Real, inverted
and magnified

A'
Fig. 25

(v) When object lies at F

When an object lies at the principal focus F of a convex lens, then its real, inverted and highly
magnified image is formed at infinity on the other side of the lens as explained below
A ray of light AE coming parallel to the principal axis, after refraction, passes through the principal
focus F and goes along EF. Another ray of light AO passing through the optical centre O goes
straight without any deviation. Both these refracted rays are parallel to each other and meet at
infinity. Hence a real, inverted, highly magnified image is formed at infinity on the other side of the
lens.

Fig. 26
(vi) When object lies between O and F
When an object lies between the optical centre O and the principal focus F of a convex lens, then
its virtual, erect and magnified image is formed on the same side as that of the object as explained
below :
A ray of light AE coming parallel to the principal axis, after refraction, passes through the principal
focus F and goes along EF. Another ray of light AO passing through the optical centre goes straight
without any deviation. Both these refracted rays appear to meet at A', when produced backwards.
Hence a virtual, erect and enlarged image is obtained on the same side as the object.
A'

Virtual erect
A E
and magnified

B' F B O F

Fig. 27

52
 Refraction of Li ght
The results of image formation by a convex lens are summarised in the Table

Position of the Position of the

Size of the image Nature of the image
object image

At infinity At the focus F Highly diminished Real and inverted

Beyond 2F Between F and 2F Diminished Real and inverted

At 2F At 2F Same size Real and inverted

Between F and 2F Beyond 2F Magnified Real and inverted

At F At infinity Highly magnified Real and inverted

On the same side as

Between O and F Magnified Virtual and erect
that of the object

11.0 RULES FOR IMAGE FORMATION BY A CONCAVE LENS

The position of the image formed by a concave lens can be found by considering following two
rays coming from a point object (as explained below).
(i) A ray of light coming parallel to the principal axis, after refraction, appears to pass through
the principal focus F of the lens, when produced backwards (See figure)
(ii) A ray of light passing through the optical centre O of the lens goes straight without suffering
any deviation (See figure)

Fig. 28
12.0 IMAGE FORMED BY CONCAVE LENS
The image formed by a concave lens is always virtual, erect and diminshed and is formed between
the optical centre O and the principal focus F of the lens. For a thin concave lens of small aperature,
the cases of image formation are discussed below :
(i) When the object lies at infinity
When object lies at infinity in front of a concave lens, a virtual, erect, highly diminished image is
formed at the principal focus F as explained below. The rays of light AE and BD coming parallel to
the principal axis of the concave lens, after refraction, go along EG and DH respectively. When
extended in the backward direction, these refracted rays appears to be coming from the principal
focus F. Hence a virtual, erect and highly diminished image is formed at the principal focus F. (See
figure )
G

E
A

F O F

B
D

H
Fig. 29

53
Class X - Physics

(ii) When obj ect l i es bet ween O and

When an object lies at any position between the optical centre O and infinity in front of a concave
lens, the image formed is virtual erect and diminished and is formed between the optical centre O
and the principal focus F as explained below :

A ray of light AE coming parallel to the principal axis, after refraction, goes along EG and appears
to pass through the principal focus F when produced backwards, another ray of light AO passing
through optical center O goes straight without any deviation. Both these refracted rays appear to
meet at A’. Hence, a virtual, erect & diminished image is formed between O and F. (See figure )

A E

A'

2F B F B' O F
Virtual erect
and diminished

Fig. 30

The summary of image formation by a concave lens for different positions of the object is given in
Table

Table
Position of the object Position of the image Size of the image Nature of the image
At infinity At F Highly diminished Virtual and erect
Between O and Between O and F Diminished Virtual and erect

QUICK CHECK-3

Objective Questions
1. A convex lens forms an image of a distant object on a screen. If the upper half of the lens is blocked
by a piece of black paper, then :
(A) The lower half of the image will be cut out
(B) The upper half of the image will be cut out
(C) The image will be full but its intensity will be reduced
(D) Nothing will happen to the image

2. A lens has :
(A) Only one focus (B) Two focus (C) Three focus (D) Four focus

3 4
3. Absolute refractive index of glass is and absolute refractive index of water is . If the wavelength
2 3
–7
of light ray is 2 × 10 m in glass, then its wavelength in water is :
9 4 –7 1
(A) 10 –7 m (B) 10 –7 m (C) 2 × 10 m (D) 10 –7 m
4 9 2

54
 Refraction of Li ght

4. A bulb is placed at a depth of 2 7 m in water and a floating opaque disc is placed on the surface
of water, so that the bulb is not visible from the surface. Then the minimum diameter of the disc is
4
w :
3

(A) 42 m (B) 6 m (C) 2 7 m (D) 12 m

5. A ray of light from a denser medium strikes a rarer medium at an angle of incidence i. If the
reflected and refracted rays make an angle of 90° with each other and the angle of refraction is r,
then the critical angle for the pair of media is :
–1 –1 –1 –1
(A) sin (tan i) (B) cos (tan r) (C) tan (sin r) (D) tan (sin i)

Subjective Questions

6. You are given a circular plane glass sheet, a convex lens and a concave lens. How will you differ-
entiate them?

7. At critical angle of incidence, the angle of refraction is :

8. A ray of light strikes at the face AB of prism ABC as shown in the figure. If face AC is silvered then
the value of refractive index of glass prism for which the incident light retraces its path is :
A

30°
60°

B C

9. Explain why the refractive index of a medium is less for a light having higher wavelength, thereby
explain why refractive index for red light in a medium is less than the blue light.

10. A ray R1 is incident on the plane surface of the glass slab (kept in air) of
refractive index 2 at an angle of incidence equal to the critical
angle for this air glass system. The refracted ray R2 undergoes partial
reflection and refraction at the other surface. The angle between
reflected ray R3 and the refracted ray R4 at that surface is :–

55
Class X - Physics

REFRACTION OF LIGHT
(RER–4)

13.0 NEW CARTESIAN SIGN CONVENTION

(i) All distances are measured from the optical centre of the lens.
(ii) The distances measured from optical centre in the same direction as the incident light are
taken as positive.
(iii) The distances measured from optical centre in the direction opposite to the direction of the
incident light are taken as negative.
(iv) Heights measured upwards and perpendicular to the principal axis are taken as positive.
(v) Heights measured downwards and perpendicular to the principal axis are taken as nega-
tive.

Figure shows the above given points.

Fig. 31 Sign convention

Consequences of the sign convention

(i) The focal length (f) of a converging (convex) lens is positive and that of a diverging (con-
cave) lens is negative.
(ii) Object distance (u) is always negative.
(iii) The distance of real image (v) is positive and that of virtual image is negative.
(iv) The object height h1 is always positive. Height h2 of virtual erect image is positive and that of
real inverted image is negative.
(v) The linear magnification m = h2/h1 is positive for a virtual image and negative for a real
image.

14.0 LENS FORMULA

(i) Object distance (u)

Distance of object from the optical centre of a lens is known as object distance. It is denoted
by u.
(ii) Image distance (v)
Distance of image from the optical centre of a lens is known as image distance. It is denoted
by v.
(iii) The relation between object distance (u), image distance (v) and focal length (f) of a lens is
called lens formula. The lens formula is given by
1 1 1
– =
v u f
1 1 1
or – =
distance of image from lens distance of object from lens focal length of lens

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 Refraction of Li ght

15.0 MAGNIFICATION
The size or height of image formed by a lens depends upon the position of the object from the
optical centre of the lens. It means a lens can produce images of different sizes depending upon
the position of a given object.
The ratio of the size (or height) of the image to the size (or height) of the object is known as the
magnification (m) produced by the lens.
size (or height) of image h'
i.e. m= =
size (or height) of object h

image distance
It can also be shown that magnification of a lens =
object distance
v
m=
u
h' v
Therefore m= =
h u
(i) Magnification (m) is positive if the image produced by a lens is virtual.

(ii) Magnification in case of a concave lens is always positive as it always forms a virtual image.

(iii) Magnification in case of a convex lens is positive when it forms a virtual image but magnifi-
cation in case of a convex lens is negative when it forms a real image.

Illustration 1. A concave lens has focal length of 15 cm. At what distance should the object from the
lens be placed so that it forms an image at 10 cm from the lens ? Also, find the
magnification produced by the lens.
Solution A concave lens always forms a virtual, erect image on the same side of the object.
Image distance v = –10 cm ; focal length f = –15 cm ; object distance u = ?
Lens equation,
1 1 1 1 1 1 1 1 1 2–3 –1
– or – or – or u = – 30 cm
v u f (–10) u (–15) u 15 10 30 30
v (–10) 1
Magnification, m = +0.33
u (–30) 3
The positive sign shows that the image is erect and virtual. The image is one-third of
the size of the object.

Illustration 2. A 2.0 cm tall object is placed perpendicular to the principal axis of a convex lens of
focal length 10 cm. The distance of the object from the lens is 15 cm. Find the nature,
position and size of the image. Also find its magnification.
Solution Given, height of the object h1 = + 2.0 cm ; focal length f = + 10 cm ; object distance
u = –15 cm ; image distance v = ? ; height of the image h2 = ?
Lens equation,
1 1 1 1 1 1 1 1 1 3–2 1
– or – or – or v = + 30 cm
v u f v (–15) ( 10) v 10 15 30 30

h2 v v 30
Magnification, m or h2 h1 ( 2) = – 4 cm
h1 u u –15
The negative sign of h2 shows that the image is inverted and real. A real, inverted
image, 4 cm tall, is formed at a distance of 30 cm on the other side of the lens.

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Class X - Physics

16.0 POWER
Power of a lens is defined as the reciprocal of the focal length of the lens (expressed in meters). It is denoted
by P.
1 100
i.e. P= or P=
f (in m) f (in cm)
Thus, we can say that a lens of small focal length has large power of converging or diverging a
parallel beam of light. On the other hand, a lens of large focal length has small power of converging
or diverging a parallel beam of light. Since a convex lens converges a parallel beam of light, so it
has a power of converging the beam. When a convex lens has a large power, it means, this convex
lens strongly converges the parallel beam of light and near to its optical centre. On the other hand,
when a convex lens has a small power, then this lens converges the parallel beam of light but away
from its optical centre.
Unit of power of a lens is diopter (D).
Definition of diopter (D)
Power of a lens is 1 diopter if its focal length is 1 metre.
Power of convex lens is positive.
Power of concave lens is negative.

17.0 COMBINATION OF TWO LENSES

Consider two lenses of focal lengths f1 and f2 respectively. When these lens are in contact, the
combination behaves as a single lens of focal length f. This focal length (f) is known as equivalent
focal length and is given by
1 1 1
= f +f
f 1 2

1
Since = P, power of lens, so the power of the combination of two lenses is given by
f
P = P1 + P2

1 1 1
Where, P= , P1 = f and P2 = f
f 1 2

If number of lenses of powers P1, P2, P3,...............etc. are placed in contact with each other, then
the power of this combination of lenses is given by
P = P1 + P2 + P3 + ........
Note
(i) If a convex lens is placed in contact with a concave lens and a power of this combination is
positive, then combination of these lenses behaves as a convex lens.
(ii) If a convex lens is placed in contact with a concave lens and the power of this combination
is negative, the combination of these lenses behaves as a concave lens.

58
 Refraction of Li ght

Illustration 3. A magnifying lens has a focal length of 10 cm. (a) Where should the object be placed
if the image is to be 30 cm from the lens ? (b) What will be the magnification ?
Solution (a) In case of magnifying lens, the lens is a converging lens i.e. a convex lens. While
using it as a magnifying lens, the image is virtual, erect, and magnified.
Here, f = + 10 cm ; v = – 30 cm
(negative sign of v is taken because in case of lens, virtual image is formed on the left
side)
By lens formula,
1 1 1 1 1 1 1 1 1 –1 – 3 –4 –2
or or – –
v u f (–30) u ( 10) u 30 10 30 30 15
or u = –7.5 cm
So the object must be placed in front of lens at a distance of 7.5 cm from it.
(b) v 30 = +4
m
u 7.5
Thus, image is virtual, erect and four times the size of object.

Illustration 4. An object 25 cm high is placed in front of a convex lens of focal length 30 cm. If the
height of real image formed is 50 cm, find the distance between the object and the
image ?
Solution h1 = 25 cm, f = + 30 cm, h2 = – 50 cm
h2 50
m 2
h1 25
v v
Also, m or –2 or v = – 2u
u u
1 1 1 1 1 1 –3 1
Now, – or – or or u = – 45 cm
v u f (–2u) u ( 30) 2u 30
v = – 2u = – 2(–45) = 90 cm
Since object and image are on opposite sides of lens, the distance between object and
image
d = IuI + IvI = 45 + 90 = 135 cm

Illustration 5. A converging lens of focal length 6.25 cm is used as a magnifying glass. If near point of
the observer is 25 cm from the eye and lens is held close to eye, calculate (i) the
distance of the object from the lens (ii) the magnification (iii) Also, find the magnification
when the final image is formed at infinity.
Solution (i) f = + 6.25 cm, v = – 25 cm, u = ?
Lens formula,
1 1 1 1 1 1 1 1 1 –1 – 4 –5 1
or – or – – –
v u f (–25) u ( 6.25) u 25 6.25 25 25 5
or u = – 5 cm
D 25
(ii) m 1 1 =5
f 6.25
(iii) When the image is formed at the infinity,
D 25
m =4
f 6.25

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Class X - Physics

QUICK CHECK-4

Objective Questions

1. What is the power of a diverging lens of focal length 40 cm :

(A) 2.5 dioptre (B) – 2.5 dioptre (C) – 3.5 dioptre (D) 4 dioptre

2. An object is located at a distance of 10 cm in front of a convex lens of focal length 12 cm. Then the
image is located at :
(A) +60 cm (B) –60 cm (C) +30 cm (D) –30 cm

3. An object placed 10 cm in front of a lens has an image 20cm behind the lens. Then the power of
the lens (in dioptre) is :
(A) +1.5 (B) +3.0 (C) –5.0 (D) 15

4. The lens formula is given by :

1 1 2 1 1 2 1 1 2
(A) + = (B) – = (C) + =– (D) None of these
v u R v u R v u R

5. A concave lens of focal length f 0=15 cm forms an image at a distance of 10 cm from the lens. Then
the distance of object from the lens is :
(A) 15 cm (B) 20 cm (C) 25 cm (D) 30 cm

Subjective Questions

6. Two thin lenses of focal length f 1 and f 2 are placed in contact. Then the focal length of the
composite lens will be:

7. Unit of power of lens is :

8. Two convex lens of power 2.5 D are put in close contact with each other. Find power of combina-
tion.

9. Magnification in case of lens is given by :

10. A 2 cm long pin is placed perpendicular to the principal axis of a convex lens of focal length 12
cm. The distance of the pin from the lens is 15 cm. Then the size of the image is :

60
 Refraction of Li ght

Objects can absorb light, reflect light, and transmit light. Transparent materials transmit almost all
the light striking them, so you can see objects clearly through them. Only a small amount of light is
absorbed and reflected by transparent materials.
If the two radii of curvatures of a lens are not equal, the focal length remains unchanged whether the
light is incident on first face or the second face.
Speed of light is maximum in vacuum, it is about 3 × 108 m/s. Speed of light in air is almost equal
to the speed of light in vacuum. Speed of light in water is 2.25 × 108 m/s. Speed of light in ordinary
glass is 2.0 ×108 m/s.
An optically denser medium may not possess greater mass density. For example, kerosene having
higher refractive index, is optically denser than water, although its mass density is less than water.
According to Snell’s law,

sin i n
= n 21 = 2
sin r n1

or n1 sin i = n2 sin r
This is another form of Snell’s law.
Convex lenses are used as magnifiers in simple microscope, compound microscope, telescope,
etc. Convex lenses are also used to correct eye defect ‘hypermetropia’ or ‘long sightedness’.
The minimum distance between a real object and its real image formed by a convex lens is 4f i.e,
when the object is placed at 2F1 and image is formed at 2F2.
A concave lens is used to correct the eye defect ‘myopia’ or ‘short sightedness’ in which a person
cannot see the distant objects clearly.
For both concave mirror as well as concave lens, focal length f is negative. Similarly, for convex
mirror and convex lens, focal length f is positive.
If the two radii of curvatures of a convex lens are equal, then it is called ‘equiconvex lens’. Similarly,
if the two radii of curvatures of a concave lens are equal, then it is called ‘equiconcave lens’.
A negative sign in the value of the magnification indicates that the image is real and inverted. A
positive sign in the value of the magnification indicates that the image is virtual and erect.
For convex lens, ‘m’ can be +ve as well as –ve. Also, |m| can be >1 or <1 or = 1. For concave
lens, ‘m’ is always +ve and |m|<1.

61
Class X - Physics

EXERCISE - 1 PRIMARY CHECK

1. Study the figure given here. How will the incident ray of light I move beyond the point "P" :

R4 R3
R2
Air P
Water
I 30°
R1

(A) R1 (B) R2 (C) R3 (D) R4

2. You are given water, mustard oil, glycerine and kerosene. In which of these media, a ray of light
incident obliquely at same angle would bend the most ? (Given W = 1.33, G = 1.74, K = 1.44,
M.O. = 1.46)
(A) Kerosene (B) Water (C) Mustard oil (D) Glycerine

3. Figure shows a ray of light as it travels from medium A to medium B.

Refractive index of the medium B relative to medium A is
Medium B 45°
(A) 3/2

(B) 2/3 60°

Medium A
(C) 1/ 2
(D) 2

4. A light ray enters from medium A to medium B as shown in figure. The

refractive index of medium B relative to A will be Medium B
(A) greater than unity
(B) less than unity
(C) equal to unity
Medium A
(D) zero

5. Which of the following statements are correct :

(1) Optical density and density of a medium are same
(2) Maximum value of speed of light can be greater than 3 × 10 8 m/sec
(3) More the value of for a medium more is its optical density
(4) More the value of for a medium lesser is the velocity of light for that medium
(A) (1), (2) and (3) are correct (B) Only (1) and (4) are correct
(C) Only (3) and (4) are correct (D) All are wrong

6. A straight line graph is obtained by plotting sine of angle of incidence y

versus sine of angle of refraction. The slope of this graph represents :
(A) Velocity of light
sin i

(B) Critical angle

(C) Refractive index
x
(D) Frequency of light O sin r

62
 Refraction of Li ght

7. A ray of light is incident on one of the parallel faces of rectangular glass slab. It emerges out of the
opposite parallel face making angle of emergence:
(A) equal to angle of incidence (B) greater than angle of incidence
(C) smaller than angle of incidence (D) equal to zero

8. A ray of light incident on one of the parallel faces of rectangular glass slab, emerges out of the
opposite parallel face
(A) inclined to the incident ray
(B) along the same straight line as the incident ray
(C) parallel to the incident ray but laterally displaced
(D) gets absorbed into the body of the glass slab and does not emerge out of it

9. The lateral displacement of an incident ray passing out of a rectangular glass slab, for the same
angle of incidence :
(A) is directly proportional to the thickness of the glass slab
(B) is inversely proportional to the thickness of the glass slab
(C) is independent of the thickness of the glass slab
(D) none of the above options is correct.

10. The path of a ray of light coming from air passing through a rectangular glass slab traced by four
students are shown as A, B, C and D in fig. Which one of them is correct ?

A B

C D

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

11. Beams of light are incident through the holes A and B and emerge out of box through the holes C
and D respectively as shown in the figure. Which of the following could be inside the box ?

A
C

B
D

(A) A concave lens (B) A convex lens

(C) A rectangular glass slab (D) A prism

12. A convex lens

(A) is thicker at the edges than at the middle (B) has uniform thickness all through
(C) is thicker at the middle than at the edges (D) is called a diverging lens.

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Class X - Physics

13. Which of the following can make a parallel beam of light when light from a point source is incident
on it ?
(A) Concave mirror as well as convex lens
(B) Convex mirror as well as concave lens
(C) Two plane mirrors placed at 90° to each other
(D) Concave mirror as well as concave lens

14. A beam of light is incident through the holes on side A and emerges out of the holes on the other
face of the box as shown in the fig. Which of the following could be inside the box ?

10 1
9 2
8 3
7 4
6 5
5 6
4 7
3 8
2 9
10
1

(A) Concave lens (B) Rectangular glass slab

(C) Prism (D) Convex lens

15. Which of the following ray diagrams is correct for the ray of light incident on a lens shown in fig.

F1 O F2 F1 O F2

A B

F1 O F2 F1 O F2

C D

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

16. In the figure given below, there are two convex lens L1 and L2 having focal length of f1 and f2
respectively. The distance between L1 and L2 will be

L1 L2

(A) f1 (B) f2 (C) f1 + f2 (D) f1 – f2

64
 Refraction of Li ght

17. When an object is placed in front of a convex lens , the image formed :
(A) is always virtual (B) is always real
(C) may be real or virtual (D) is always erect

18. An object is placed before a concave lens. The image formed

(A) is always inverted (B) is always erect
(C) is always real (D) may be erect or inverted

19. What should be the value of distance d so that final image is formed on the object itself.(focal length
of the lenses are written on the lenses).
10 cm –20cm

10cm
d
(A) 10 cm (B) 20 cm (C) 5 cm (D) None of these

20. How will be image formed by a convex lens be affected if the

central portion of the lens is wrapped in black paper? Black
Paper
(A) No image is formed by the remaining portion of the lens
(B) The central of the image will be absent
(C) There will be no effect
(D) The full image will be formed but it will be less bright

21. A thin lens and a spherical mirror, each has a focal length of +25 cm. This means
(A) Both are convex
(B) Both are concave
(C) The lens is convex and the mirror is concave
(D) The lens is concave and mirror is convex

22. A convex lens forms a virtual image of an object placed at a distance of 20 cm it. The focal length
of the lens must be :
(A) greater than 20 cm (B) greater than 10 cm, less than 20 cm
(C) less than 20 cm (D) infinite

23. A convex lens forms a virtual image when an object is placed at a distance of 18 cm from it. Then
it’s focal length must be :
(A) Greater than 36 cm (B) Greater than 18 cm
(C) Less than 36 cm (D) Less than 18 cm

24. A 2 cm long pin is placed perpendicular to the principal axis of a convex lens of focal length 12 cm.
The distance of the pin from the lens is 15 cm. Then the size of the image is :
(A) 2 cm (B) 6 cm (C) 3 cm (D) 8 cm

25. Which of the following statements is true ?

(A) A convex lens has 4 dioptre power having a focal length 0.25 m
(B) A convex lens has –4 dioptre power having a focal length 0.25 m
(C) A concave lens has 4 dioptre power having a focal length 0.25 m
(D) Both (B) and (C)

65
Class X - Physics

26. An object placed 10 cm in front of a lens has an image 20 cm behind the lens. Then the power of
the lens (in dioptre) is :
(A) + 1.5 (B) + 3.0 (C) – 5.0 (D) + 15.0

27. Two similar plano-convex lenses are combined together in three different ways as shown in the
adjoining figure. The ratio of the focal lengths in the three cases will be :

(A) 2 : 2 : 1 (B) 1 : 1 : 1 (C) 1 : 2 : 2 (D) 2 : 1 : 1

28. Two thin lenses of focal length f1 and f2 are placed in contact. Then the focal length of the composite
lens will be:

(f1 f2 ) f1 f2 f1.f2
(A) (B) f .f (C) f1 .f2 (D) f f
2 1 2 1 2

29. If critical angle of a light ray for a material-air interface is 30°, then the refractive index of the
material is :
(A) 1.0 (B) 1.5 (C) 2.0 (D) 2.5

30. Total internal reflection occurs when light travels from :

(A) A rarer medium to a denser medium and the angle of incidence is less than the critical angle
(B) A denser medium to a rarer medium and the angle of incidence is less than the critical angle
(C) A rarer medium to denser medium and the angle of incidence is greater than the critical angle
(D) A denser medium to a rarer medium and the angle of incidence is greater than the critical angle

66
 Refraction of Li ght

2
Very short answer type questions
1. What kind of lens can form a (i) Virtual, erect, diminished image ? (ii) virtual, erect, magnified
image ?

2. What is the basic cause of refraction?

3. Does the refraction of light make a swimming pool seem deeper or shallower ?

4. What kind of lens can be used to produce a real image?

5. A red light and blue light enter a rectangular glass block normal to its surface at the same time.
Strictly speaking, after passing through the block, which pulse exits first?

6. Two thin lenses of power +4.5 D and –2.5 D are placed in contact. Find the power and focal length
of the lens combination. [CBSE 2007]

Short answer type questions

7. An object placed on a metre scale at 8 cm mark was focused on a white screen placed at 92 cm
mark, using a converging lens placed on the scale at 50 cm mark. [CBSE 2013]
(i) Find the focal length of the converging lens.
(ii) Find the position of the image formed if the object is shifted towards the lens at a position of
29.0 cm.
(iii) State the nature of the image formed if the object is further shifted towards the lens.

8. To construct a ray diagram we use two light rays which are so chosen that it is easy to know their
directions after refraction from the lens. List these two rays and state and path of these rays after
refraction. Use these two rays to locate the image of an object placed between ‘f’ and ‘2f’ of a
convex lens. [CBSE 2013]

9. Draw the ray diagram to represent the nature, position and relative size of the image formed by a
convex lens for the object placed at 2 F 1.

10. If you place a glass test tube in water, you can see the tube. If you place it in clear soyabean oil, you
may not be able to see it. What does this indicate about the speed of light in the oil and in the glass?
What about their refractive indices ?

11. Prove that n12 × n23 × n31 = 1.

12. “The time difference between the actual sunset and the apparent sunset is about 2 minutes.” What
is the reason for the same? Explain with the help of a diagram. [CBSE 2012]

Long answer type questions

13. Why does a light ray, incident on a rectangular glass slab immersed in any medium, emerges
parallel to itself ? Explain using a diagram. Prove it using Snell's law.

14. The image of a candle flame placed at a distance of 45 cm from a spherical lens is formed on a
screen placed at a distance of 90 cm from the lens. Identify the type of lens and calculate its focal
length. If the height of the flame is 2 cm, find the height of its image. [CBSE 2012]

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Class X - Physics

15. Draw ray diagrams showing the image formation by a convex lens when an object is placed
(a) between optical centre and focus of the lens
(b) between focus and twice the focal length of the lens
(c) at twice the focal length of the lens
(d) at infinity
(e) at the focus of the lens

16. What is meant by ‘refractive index of a transparent medium’? Trace the path of a ray of light of
show that the emergent ray is laterally displaced when it passes through a rectangular slab.
[CBSE 2007]
17. Define power of a lens. What is its unit ? How are power and focal length related ? One student
uses a lens of focal length 50 cm and another of –50 cm. What is the nature of the lens and its
power used by each of them?

Numerical problems
18. An object 5 cm high is held 25 cm away from a converging lens of f = + 10 cm. Find the position
and size of the image formed. Is the image real or virtual ?

19. An object 10 cm long is placed at distance of 15 cm from a convex lens of focal length 10 cm. Find
the position and size of the image .

20. An object placed at 50 cm from a lens produces a virtual image at a distance of 10 cm in front of the
lens. Calculate the focal length of the lens.

21. An object which is placed at 10 cm in front of a lens forms a real image three times magnified.
Where is the image formed ? What is the focal length of the lens ?

22. An object 4 cm high is placed at a distance of 10 cm from a convex lens of focal length 20 cm. Find
the position, nature and size of the image.

23. A thin lens has a focal length of – 25 cm. What is the power of the lens and what is its nature ?

24. An object of size 3 cm is placed at 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 ?

25. An object is placed at 5 cm in front of a lens and an image is formed 10 cm behind the lens. What
type of lens is it, and what is the value of its focal length ?

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 Refraction of Li ght

1. On immersing a glass lens in water its focal length (Raj./NTSE Stage-l/2005)

(A) will become zero (B) will decrease (C) will increase (D) will become infinite
2. If a ray of light is incident normally on the glass slab, then angle of refraction will be :
(Raj./NTSE Stage-I/2006)
(A) 0° (B) 45° (C) 60° (D) 90°
3. The image of an object is formed at the distance of distinct vision from the lens of a simple microscope
of focal length 2.5 cm. Its magnifying power is (Raj./NTSE Stage-I/2006)
(A) 2.5 (B) 5 (C) 10 (D) 11
4. When a light wave of frequency 5×10 Hz is passed through a medium of refractive index 1.5 then
14

its wavelength will become (Raj./NTSE Stage-I/2007)

(A) 4000Å (B) 4500Å (C) 6000Å (D) 9000Å
5. While obtaining the image of a candle by a convex lens, if lower half portion of the lens is blackened
to make it opaque completely, then the intensity of the image will be (Raj./NTSE Stage-I/2007)
(A) constant (B) decreased (C) incresed (D) zero
6. If a lens has power -2.5D, then it is a : (NTSE/Stage-I/MP 2012)
(A) convex lens, with a focal length of 40 cm (B) concave lens with a focal length of 40 cm
(C) convex lens with a focal length of 0.4 cm (D) concave lens with a focal length of 0.4 cm
7. The instrument that is based on the principle that when an object is placed between first principal
focus and the optic centre of convex lens, an upright, virtual and enlarged image on the same side
of the object is formed, is (NTSE/stage-I/AP 2013)
(A) Telescope (B) Projector (C) Camera (D) Simple microscope
8. A lens of power +3D and another of power-1.5 D are placed in contact. What would be the focal
length of the combination? (NTSE/Stage-I/ODISA 2013)
(A) 1.5 m (B) – 0.67 m (C) 0.67 m (D) – 67.0 m
9. A concaved lens has focal length of 15 cm. At what distance should the object from the lens be
placed so that it forms an erect and virtual image at 10 cm from the lens?
(NTSE/Stage-I/ODISA 2013)
(A) 30 cm (B) 15 cm (C) 60 cm (D) 10 cm
10. The minimum distance between an object and its real image in a convex lens is (f = focal length of
the lens) (West Bengal/ NTSE Stage-I/2013)
(A) 2.5 f (B) 2f (C) 4f (D) f
11. Match the folbwing (Haryana/ NTSE Stage-I/2013)
Column Column II
(a) Convex mirror, real object (p) Real image
(b) Concave mirror real object (q) Virtual image
(c) Concave lens real object (r) Magnified image
(d) Convex lens, real object (s) Diminished image
(A) (a)-q,s (b) p, q, s (c) q, r (d) -p,q,r, s
(B) (a)-q (b) p, q, s (c) q, r (d) -p,q,r
(C) (a)-s (b) p, q, s (c) q, s (d) -p,q,r,s
(D) (a) q,s (b) p,q,r,s (c) q,s (d)-p,q,r,s

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Class X - Physics

12. A student was asked to draw a ray diagram for formation of image by a convex lens for the following
positions of the object: (Raj./NTSE Stage-I/2014)
(a) between F and 2F
(b) at F
(c) at 2F
(d) between F and optical centre.
The position for which virtual image can be formed among these is
(A) b (B) a (C) c (D) d
13. The resultant focal length of the lenses as shown in the figure is : (Delhi/ NTSE Stage-I/2014)

f f
(A) 2f (B) (C) (D) f
2 4
14. The ability of a lens to converge or diverge light rays depends on :
(MAHARASHTRA/ NTSE Stage-I/2014)
(A) principal axis (B) focal length (C) object distance (D) image distance
15. After refraction of light through a glass slab, incident ray and refracted are :
(MAHARASHTRA/ NTSE Stage-I / 2014)
(A) perpendicular (B) parallel (C) in a straight line (D) (A) and (C)
16. If a lens of focal length 'f' is cut in two equal parts shown as :
f

are put in contact as shown in figure (i) and (ii)

fig (i) fig (ii)

the resulting focal length of fig (i) and (ii) will be- (Haryana/ NTSE Stage-I/2014)
(A) f/2,0 (B) 0,f/2 (C) f,f (D) f/2,(infinity)
17. White light is incident on the interface of glass and air as shown in the figure. If green light is just totally
internally reflected then the emerging ray in air contains: (Haryana./NTSE Stage-I/2014)

air
green
glass

white
light
(A) yellow, orange , red (B) violet, indigo, blue
(C) all colours except green (D) all colours
18. A ray of light is incident in medium 1 on a surface that separates medium 1 from medium 2. Let v 1
and v2 represent the velocity of light in medium 1 and medium 2 respectively. Also let n 12 and n21
represent the refractive index of medium 1 with respect to medium 2 and refractive index of me-
dium 2 with respect to medium 1, respectively. If i and r denote the angle of incidence and angle of
refraction, then (NTSE Stage-I/2015)
sin i v1 sin i v2 sin i v1 sin i v2
(A) sin r n 21 (B) sin r n 21 (C) sin r n12 (D) n12
v2 v1 v2 sin r v1
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 Refraction of Li ght

19. A student was asked to draw a ray diagram for formation of image by a convex lens for the following
positions of the object: (Raj./NTSE Stage-1/2015)
(a) between F and 2F (b) at F
(c) at 2F (d) between F and optical centre
The position for which virtual image can be formed among these is
(A) b (B) a (C) c (D) d.
20. When light travels from medium X to medium Y as shown: (Raj./NTSEStage-I/2016)
(A) both the speed and the frequency decrease
(B) both the speed and the frequency increase x
(C) both the speed and the wavelength decrease y
(D) both the wavelength and the frequency are unchanged.
21. If speed of light travelling from air to a medium decreases by 40 %, find the refractive index of the
medium with respect to air. (Maharashtra/ NTSE Stage-I/2016)
(A) 2.5 (B) 1.67 (C) 1.3 (D) 1.25
22. A convex lens has focal length 30 cm. If an object is placed at a distance of 15 cm from it then the
magnification produced by the lens is (Raj./ NTSEStage-I/2017)
(A) 6.66 (B) 0.5 (C) 1 (D) 2
23. Which diagram below illustrates the path of a light ray as it travels from a given point X in air to
another given point Y in glass ? (Raj./ NTSEStage-I/2017)

Y Y Y
(A) glass Y (B) glass (C) glass (D) glass
air air air air
X X X X

CHECK LIST
Suggested Total Doubts Chapter
Total Ques. Time Taken
Exercise Name Time to Solve taken in this completely
Given by Student
All Questions chapter Solved on date

Quick Check -1 10 15 Minutes

CLASS WORK

Quick Check -2 10 15 Minutes

Quick Check -3 10 15 Minutes

Quick Check -4 10 15 Minutes

Primary Check 30 60 Minutes

HOME WORK

Subjective Check 25 80 Minutes

Competitive Check 23 50 Minutes

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Class X - Physics

ANSWERS
QUICK CHEKC-1
1. (B) 2. (C) 3. (D) 4. (C) 5. (A)

QUICK CHEKC-2
1. (A) 2. (C) 3. (C) 4. (C) 5. (C)

QUICK CHEKC-3
1. (C) 2. (B) 3. (A) 4. (D) 5. (A)

QUICK CHEKC-4
1. (B) 2. (B) 3. (D) 4.(B) 5. (D)

EXERCISE-1 : PRIMARY CHECK

Que. 1 2 3 4 5 6 7 8 9 10
Ans. B D A A C C A C A B
Que. 11 12 13 14 15 16 17 18 19 20
Ans. C C A D A C C B A D
Que. 21 22 23 24 25 26 27 28 29 30
Ans. A A B D A D B D C D

EXERCISE-2 : SUBJECTIVE CHECK

18. v = + 50/3 cm = 16.67 cm ; h2 = – 10/3 cm = – 3.33 cm ; real
19. v = + 30 cm ; h2 = – 20 cm 20. f = – 12.5 cm 21. v = + 30 cm ; f = + 7.5 cm
22. v = – 20 cm ; h2 = + 8 cm ; image is virtual, erect & magnified 23. P = – 4 D ; concave
24. v = – 8.4 cm ; h2 =+1.8 cm ; virtual, erect & diminished. As the object is moved away from the lens,
the virtual image moves towards the focus of the lens (but never beyond F) and gradually diminishes
in size.
25. convex ; + 3.33 cm
EXERCISE-3 : COMPETITIVE CHECK
Que. 1 2 3 4 5 6 7 8 9 10
Ans. C A D A B B D C A C
Que. 11 12 13 14 15 16 17 18 19 20
Ans. D D B B B A A A D C
Que. 21 22 23
Ans. B D D
*****

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