NCERT Textbook: Light - Reflection & Refraction | Science & Technology for UPSC CSE PDF Download

 Page 1


Science
134
Light – Reflection and
Refraction
9 CHAPTER
W
e see a variety of objects in the world around us. However, we are
unable to see anything in a dark room. On lighting up the room,
things become visible. What makes things visible? During the day, the
sunlight helps us to see objects. An object reflects light that falls on it.
This reflected light, when received by our eyes, enables us to see things.
We are able to see through a transparent medium as light is transmitted
through it. There are a number of common wonderful phenomena
associated with light such as image formation by mirrors, the twinkling
of stars, the beautiful colours of a rainbow, bending of light by a medium
and so on.  A study of the properties of light helps us to explore them.
By observing the common optical phenomena around us, we may
conclude that light seems to travel in straight lines. The fact that a small
source of light casts a sharp shadow of an opaque object points to this
straight-line path of light, usually indicated as a ray of light.
More to Know!
If an opaque object on the path of light becomes very small, light has a tendency to
bend around it and not walk in a straight line – an effect known as the diffraction of
light. Then the straight-line treatment of optics using rays fails. To explain phenomena
such as diffraction, light is thought of as a wave, the details of which you will study
in higher classes. Again, at the beginning of the 20
th
 century, it became known that
the wave theory of light often becomes inadequate for treatment of the interaction of
light with matter, and light often behaves somewhat like a stream of particles. This
confusion about the true nature of light continued for some years till a modern
quantum theory of light emerged in which light is neither a ‘wave’ nor a ‘particle’ –
the new theory reconciles the particle properties of light with the wave nature.
In this Chapter, we shall study the phenomena of reflection and
refraction of light using the straight-line propagation of light. These basic
concepts will help us in the study of some of the optical phenomena in
nature. We shall try to understand in this Chapter the reflection of light
by spherical mirrors and refraction of light and their application in real
life situations.
9.1 REFLECTION OF LIGHT 9.1 REFLECTION OF LIGHT 9.1 REFLECTION OF LIGHT 9.1 REFLECTION OF LIGHT 9.1 REFLECTION OF LIGHT
A highly polished surface, such as a mirror, reflects most of the light
falling on it. You are already familiar with the laws of reflection of light.
2024-25
Page 2


Science
134
Light – Reflection and
Refraction
9 CHAPTER
W
e see a variety of objects in the world around us. However, we are
unable to see anything in a dark room. On lighting up the room,
things become visible. What makes things visible? During the day, the
sunlight helps us to see objects. An object reflects light that falls on it.
This reflected light, when received by our eyes, enables us to see things.
We are able to see through a transparent medium as light is transmitted
through it. There are a number of common wonderful phenomena
associated with light such as image formation by mirrors, the twinkling
of stars, the beautiful colours of a rainbow, bending of light by a medium
and so on.  A study of the properties of light helps us to explore them.
By observing the common optical phenomena around us, we may
conclude that light seems to travel in straight lines. The fact that a small
source of light casts a sharp shadow of an opaque object points to this
straight-line path of light, usually indicated as a ray of light.
More to Know!
If an opaque object on the path of light becomes very small, light has a tendency to
bend around it and not walk in a straight line – an effect known as the diffraction of
light. Then the straight-line treatment of optics using rays fails. To explain phenomena
such as diffraction, light is thought of as a wave, the details of which you will study
in higher classes. Again, at the beginning of the 20
th
 century, it became known that
the wave theory of light often becomes inadequate for treatment of the interaction of
light with matter, and light often behaves somewhat like a stream of particles. This
confusion about the true nature of light continued for some years till a modern
quantum theory of light emerged in which light is neither a ‘wave’ nor a ‘particle’ –
the new theory reconciles the particle properties of light with the wave nature.
In this Chapter, we shall study the phenomena of reflection and
refraction of light using the straight-line propagation of light. These basic
concepts will help us in the study of some of the optical phenomena in
nature. We shall try to understand in this Chapter the reflection of light
by spherical mirrors and refraction of light and their application in real
life situations.
9.1 REFLECTION OF LIGHT 9.1 REFLECTION OF LIGHT 9.1 REFLECTION OF LIGHT 9.1 REFLECTION OF LIGHT 9.1 REFLECTION OF LIGHT
A highly polished surface, such as a mirror, reflects most of the light
falling on it. You are already familiar with the laws of reflection of light.
2024-25
Light – Reflection and Refraction 135
Let us recall these laws –
(i) The angle of incidence is equal to the angle of reflection, and
(ii) The incident ray, the normal to the mirror at the point of incidence
and the reflected ray, all lie in the same plane.
These laws of reflection are applicable to all types of reflecting surfaces
including spherical surfaces. You are familiar with the formation of image
by a plane mirror. What are the properties of the image? Image formed
by a plane mirror is always virtual and erect.  The size of the image is
equal to that of the object.  The image formed is as far behind the mirror
as the object is in front of it.  Further, the image is laterally inverted.
How would the images be when the reflecting surfaces are curved? Let
us explore.
Activity 9.1 Activity 9.1 Activity 9.1 Activity 9.1 Activity 9.1
n Take a large shining spoon. Try to view your face in its curved
surface.
n Do you get the image?  Is it smaller or larger?
n Move the spoon slowly away from your face. Observe the image.
How does it change?
n Reverse the spoon and repeat the Activity.  How does the image
look like now?
n Compare the characteristics of the image on the two surfaces.
The curved surface of a shining spoon could be considered as a curved
mirror.  The most commonly used type of curved mirror is the spherical
mirror.  The reflecting surface of such mirrors can be considered to form
a part of the surface of a sphere.  Such mirrors, whose reflecting surfaces
are spherical, are called spherical mirrors.  We shall now study about
spherical mirrors in some detail.
9.2 SPHERIC 9.2 SPHERIC 9.2 SPHERIC 9.2 SPHERIC 9.2 SPHERICAL MIRRORS AL MIRRORS AL MIRRORS AL MIRRORS AL MIRRORS
The reflecting surface of a spherical mirror may be curved inwards or
outwards.  A spherical mirror, whose reflecting surface is curved inwards,
that is, faces towards the centre of the sphere, is called a concave mirror.
A spherical mirror whose reflecting surface is curved outwards, is called
a convex mirror. The schematic representation of these mirrors is shown
in Fig. 9.1. You may note in these diagrams that the back
of the mirror is shaded.
You may now understand that the surface of the spoon
curved inwards can be approximated to a concave mirror
and the surface of the spoon bulged outwards can be
approximated to a convex mirror.
Before we move further on spherical mirrors, we need to
recognise and understand the meaning of a few terms. These
terms are commonly used in discussions about spherical
mirrors. The centre of the reflecting surface of a spherical
mirror is a point called the pole.  It lies on the surface of the
mirror.  The pole is usually represented by the letter P.
Figure 9.1 Figure 9.1 Figure 9.1 Figure 9.1 Figure 9.1
Schematic representation of spherical
mirrors; the shaded side is non-reflecting.
(a) Concave mirror (b) Convex mirror
2024-25
Page 3


Science
134
Light – Reflection and
Refraction
9 CHAPTER
W
e see a variety of objects in the world around us. However, we are
unable to see anything in a dark room. On lighting up the room,
things become visible. What makes things visible? During the day, the
sunlight helps us to see objects. An object reflects light that falls on it.
This reflected light, when received by our eyes, enables us to see things.
We are able to see through a transparent medium as light is transmitted
through it. There are a number of common wonderful phenomena
associated with light such as image formation by mirrors, the twinkling
of stars, the beautiful colours of a rainbow, bending of light by a medium
and so on.  A study of the properties of light helps us to explore them.
By observing the common optical phenomena around us, we may
conclude that light seems to travel in straight lines. The fact that a small
source of light casts a sharp shadow of an opaque object points to this
straight-line path of light, usually indicated as a ray of light.
More to Know!
If an opaque object on the path of light becomes very small, light has a tendency to
bend around it and not walk in a straight line – an effect known as the diffraction of
light. Then the straight-line treatment of optics using rays fails. To explain phenomena
such as diffraction, light is thought of as a wave, the details of which you will study
in higher classes. Again, at the beginning of the 20
th
 century, it became known that
the wave theory of light often becomes inadequate for treatment of the interaction of
light with matter, and light often behaves somewhat like a stream of particles. This
confusion about the true nature of light continued for some years till a modern
quantum theory of light emerged in which light is neither a ‘wave’ nor a ‘particle’ –
the new theory reconciles the particle properties of light with the wave nature.
In this Chapter, we shall study the phenomena of reflection and
refraction of light using the straight-line propagation of light. These basic
concepts will help us in the study of some of the optical phenomena in
nature. We shall try to understand in this Chapter the reflection of light
by spherical mirrors and refraction of light and their application in real
life situations.
9.1 REFLECTION OF LIGHT 9.1 REFLECTION OF LIGHT 9.1 REFLECTION OF LIGHT 9.1 REFLECTION OF LIGHT 9.1 REFLECTION OF LIGHT
A highly polished surface, such as a mirror, reflects most of the light
falling on it. You are already familiar with the laws of reflection of light.
2024-25
Light – Reflection and Refraction 135
Let us recall these laws –
(i) The angle of incidence is equal to the angle of reflection, and
(ii) The incident ray, the normal to the mirror at the point of incidence
and the reflected ray, all lie in the same plane.
These laws of reflection are applicable to all types of reflecting surfaces
including spherical surfaces. You are familiar with the formation of image
by a plane mirror. What are the properties of the image? Image formed
by a plane mirror is always virtual and erect.  The size of the image is
equal to that of the object.  The image formed is as far behind the mirror
as the object is in front of it.  Further, the image is laterally inverted.
How would the images be when the reflecting surfaces are curved? Let
us explore.
Activity 9.1 Activity 9.1 Activity 9.1 Activity 9.1 Activity 9.1
n Take a large shining spoon. Try to view your face in its curved
surface.
n Do you get the image?  Is it smaller or larger?
n Move the spoon slowly away from your face. Observe the image.
How does it change?
n Reverse the spoon and repeat the Activity.  How does the image
look like now?
n Compare the characteristics of the image on the two surfaces.
The curved surface of a shining spoon could be considered as a curved
mirror.  The most commonly used type of curved mirror is the spherical
mirror.  The reflecting surface of such mirrors can be considered to form
a part of the surface of a sphere.  Such mirrors, whose reflecting surfaces
are spherical, are called spherical mirrors.  We shall now study about
spherical mirrors in some detail.
9.2 SPHERIC 9.2 SPHERIC 9.2 SPHERIC 9.2 SPHERIC 9.2 SPHERICAL MIRRORS AL MIRRORS AL MIRRORS AL MIRRORS AL MIRRORS
The reflecting surface of a spherical mirror may be curved inwards or
outwards.  A spherical mirror, whose reflecting surface is curved inwards,
that is, faces towards the centre of the sphere, is called a concave mirror.
A spherical mirror whose reflecting surface is curved outwards, is called
a convex mirror. The schematic representation of these mirrors is shown
in Fig. 9.1. You may note in these diagrams that the back
of the mirror is shaded.
You may now understand that the surface of the spoon
curved inwards can be approximated to a concave mirror
and the surface of the spoon bulged outwards can be
approximated to a convex mirror.
Before we move further on spherical mirrors, we need to
recognise and understand the meaning of a few terms. These
terms are commonly used in discussions about spherical
mirrors. The centre of the reflecting surface of a spherical
mirror is a point called the pole.  It lies on the surface of the
mirror.  The pole is usually represented by the letter P.
Figure 9.1 Figure 9.1 Figure 9.1 Figure 9.1 Figure 9.1
Schematic representation of spherical
mirrors; the shaded side is non-reflecting.
(a) Concave mirror (b) Convex mirror
2024-25
Science
136
The reflecting surface of a spherical mirror forms a part of a sphere.
This sphere has a centre. This point is called the centre of curvature of
the spherical mirror. It is represented by the letter C. Please note that the
centre of curvature is not a part of the mirror. It lies outside its reflecting
surface. The centre of curvature of a concave mirror lies in front of it.
However, it lies behind the mirror in case of a convex mirror. You may
note this in Fig.9.2 (a) and (b). The radius of the sphere of which the
reflecting surface of a spherical mirror forms a part, is called the radius
of curvature of the mirror. It is represented by the letter R. You may note
that the distance PC is equal to the radius of curvature. Imagine a straight
line passing through the pole and the centre of curvature of a spherical
mirror. This line is called the principal axis. Remember that principal
axis is normal to the mirror at its pole. Let us understand an important
term related to mirrors, through an Activity.
Activity 9.2 Activity 9.2 Activity 9.2 Activity 9.2 Activity 9.2
CAUTION: Do not look at the Sun directly or even into a mirror
reflecting sunlight. It may damage your eyes.
n Hold a concave mirror in your hand and direct its reflecting surface
towards the Sun.
n Direct the light reflected by the mirror on to a sheet of paper held
close to the mirror.
n Move the sheet of paper back and forth gradually until you find
on the paper sheet a bright, sharp spot of light.
n Hold the mirror and the paper in the same position for a few
minutes. What do you observe? Why?
The paper at first begins to burn producing smoke. Eventually it
may even catch fire. Why does it burn? The light from the Sun is converged
at a point, as a sharp, bright spot by the mirror. In fact, this spot of light
is the image of the Sun on the sheet of paper. This point is
the focus of the concave mirror. The heat produced due to
the concentration of sunlight ignites the paper. The distance
of this image from the position of the mirror gives the
approximate value of focal length of the mirror.
Let us try to understand this observation with the help
of a ray diagram.
Observe Fig.9.2 (a) closely. A number of rays parallel
to the principal axis are falling on a concave mirror . Observe
the reflected rays. They are all meeting/intersecting at a
point on the principal axis of the mirror.  This point is called
the principal focus of the concave mirror. Similarly, observe
Fig. 9.2 (b). How are the rays parallel to the principal axis,
reflected by a convex mirror? The reflected rays appear to
come from a point on the principal axis. This point is called
the principal focus of the convex mirror. The principal focus
is represented by the letter F. The distance between the
pole and the principal focus of a spherical mirror is called
the focal length. It is represented by the letter f.
Figure 9.2 Figure 9.2 Figure 9.2 Figure 9.2 Figure 9.2
(a) Concave mirror
(b)     Convex mirror
(b)
(a)
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Science
134
Light – Reflection and
Refraction
9 CHAPTER
W
e see a variety of objects in the world around us. However, we are
unable to see anything in a dark room. On lighting up the room,
things become visible. What makes things visible? During the day, the
sunlight helps us to see objects. An object reflects light that falls on it.
This reflected light, when received by our eyes, enables us to see things.
We are able to see through a transparent medium as light is transmitted
through it. There are a number of common wonderful phenomena
associated with light such as image formation by mirrors, the twinkling
of stars, the beautiful colours of a rainbow, bending of light by a medium
and so on.  A study of the properties of light helps us to explore them.
By observing the common optical phenomena around us, we may
conclude that light seems to travel in straight lines. The fact that a small
source of light casts a sharp shadow of an opaque object points to this
straight-line path of light, usually indicated as a ray of light.
More to Know!
If an opaque object on the path of light becomes very small, light has a tendency to
bend around it and not walk in a straight line – an effect known as the diffraction of
light. Then the straight-line treatment of optics using rays fails. To explain phenomena
such as diffraction, light is thought of as a wave, the details of which you will study
in higher classes. Again, at the beginning of the 20
th
 century, it became known that
the wave theory of light often becomes inadequate for treatment of the interaction of
light with matter, and light often behaves somewhat like a stream of particles. This
confusion about the true nature of light continued for some years till a modern
quantum theory of light emerged in which light is neither a ‘wave’ nor a ‘particle’ –
the new theory reconciles the particle properties of light with the wave nature.
In this Chapter, we shall study the phenomena of reflection and
refraction of light using the straight-line propagation of light. These basic
concepts will help us in the study of some of the optical phenomena in
nature. We shall try to understand in this Chapter the reflection of light
by spherical mirrors and refraction of light and their application in real
life situations.
9.1 REFLECTION OF LIGHT 9.1 REFLECTION OF LIGHT 9.1 REFLECTION OF LIGHT 9.1 REFLECTION OF LIGHT 9.1 REFLECTION OF LIGHT
A highly polished surface, such as a mirror, reflects most of the light
falling on it. You are already familiar with the laws of reflection of light.
2024-25
Light – Reflection and Refraction 135
Let us recall these laws –
(i) The angle of incidence is equal to the angle of reflection, and
(ii) The incident ray, the normal to the mirror at the point of incidence
and the reflected ray, all lie in the same plane.
These laws of reflection are applicable to all types of reflecting surfaces
including spherical surfaces. You are familiar with the formation of image
by a plane mirror. What are the properties of the image? Image formed
by a plane mirror is always virtual and erect.  The size of the image is
equal to that of the object.  The image formed is as far behind the mirror
as the object is in front of it.  Further, the image is laterally inverted.
How would the images be when the reflecting surfaces are curved? Let
us explore.
Activity 9.1 Activity 9.1 Activity 9.1 Activity 9.1 Activity 9.1
n Take a large shining spoon. Try to view your face in its curved
surface.
n Do you get the image?  Is it smaller or larger?
n Move the spoon slowly away from your face. Observe the image.
How does it change?
n Reverse the spoon and repeat the Activity.  How does the image
look like now?
n Compare the characteristics of the image on the two surfaces.
The curved surface of a shining spoon could be considered as a curved
mirror.  The most commonly used type of curved mirror is the spherical
mirror.  The reflecting surface of such mirrors can be considered to form
a part of the surface of a sphere.  Such mirrors, whose reflecting surfaces
are spherical, are called spherical mirrors.  We shall now study about
spherical mirrors in some detail.
9.2 SPHERIC 9.2 SPHERIC 9.2 SPHERIC 9.2 SPHERIC 9.2 SPHERICAL MIRRORS AL MIRRORS AL MIRRORS AL MIRRORS AL MIRRORS
The reflecting surface of a spherical mirror may be curved inwards or
outwards.  A spherical mirror, whose reflecting surface is curved inwards,
that is, faces towards the centre of the sphere, is called a concave mirror.
A spherical mirror whose reflecting surface is curved outwards, is called
a convex mirror. The schematic representation of these mirrors is shown
in Fig. 9.1. You may note in these diagrams that the back
of the mirror is shaded.
You may now understand that the surface of the spoon
curved inwards can be approximated to a concave mirror
and the surface of the spoon bulged outwards can be
approximated to a convex mirror.
Before we move further on spherical mirrors, we need to
recognise and understand the meaning of a few terms. These
terms are commonly used in discussions about spherical
mirrors. The centre of the reflecting surface of a spherical
mirror is a point called the pole.  It lies on the surface of the
mirror.  The pole is usually represented by the letter P.
Figure 9.1 Figure 9.1 Figure 9.1 Figure 9.1 Figure 9.1
Schematic representation of spherical
mirrors; the shaded side is non-reflecting.
(a) Concave mirror (b) Convex mirror
2024-25
Science
136
The reflecting surface of a spherical mirror forms a part of a sphere.
This sphere has a centre. This point is called the centre of curvature of
the spherical mirror. It is represented by the letter C. Please note that the
centre of curvature is not a part of the mirror. It lies outside its reflecting
surface. The centre of curvature of a concave mirror lies in front of it.
However, it lies behind the mirror in case of a convex mirror. You may
note this in Fig.9.2 (a) and (b). The radius of the sphere of which the
reflecting surface of a spherical mirror forms a part, is called the radius
of curvature of the mirror. It is represented by the letter R. You may note
that the distance PC is equal to the radius of curvature. Imagine a straight
line passing through the pole and the centre of curvature of a spherical
mirror. This line is called the principal axis. Remember that principal
axis is normal to the mirror at its pole. Let us understand an important
term related to mirrors, through an Activity.
Activity 9.2 Activity 9.2 Activity 9.2 Activity 9.2 Activity 9.2
CAUTION: Do not look at the Sun directly or even into a mirror
reflecting sunlight. It may damage your eyes.
n Hold a concave mirror in your hand and direct its reflecting surface
towards the Sun.
n Direct the light reflected by the mirror on to a sheet of paper held
close to the mirror.
n Move the sheet of paper back and forth gradually until you find
on the paper sheet a bright, sharp spot of light.
n Hold the mirror and the paper in the same position for a few
minutes. What do you observe? Why?
The paper at first begins to burn producing smoke. Eventually it
may even catch fire. Why does it burn? The light from the Sun is converged
at a point, as a sharp, bright spot by the mirror. In fact, this spot of light
is the image of the Sun on the sheet of paper. This point is
the focus of the concave mirror. The heat produced due to
the concentration of sunlight ignites the paper. The distance
of this image from the position of the mirror gives the
approximate value of focal length of the mirror.
Let us try to understand this observation with the help
of a ray diagram.
Observe Fig.9.2 (a) closely. A number of rays parallel
to the principal axis are falling on a concave mirror . Observe
the reflected rays. They are all meeting/intersecting at a
point on the principal axis of the mirror.  This point is called
the principal focus of the concave mirror. Similarly, observe
Fig. 9.2 (b). How are the rays parallel to the principal axis,
reflected by a convex mirror? The reflected rays appear to
come from a point on the principal axis. This point is called
the principal focus of the convex mirror. The principal focus
is represented by the letter F. The distance between the
pole and the principal focus of a spherical mirror is called
the focal length. It is represented by the letter f.
Figure 9.2 Figure 9.2 Figure 9.2 Figure 9.2 Figure 9.2
(a) Concave mirror
(b)     Convex mirror
(b)
(a)
2024-25
Light – Reflection and Refraction 137
The reflecting surface of a spherical mirror is by-and-large spherical.
The surface, then, has a circular outline. The diameter of the reflecting
surface of spherical mirror is called its aperture. In Fig.9.2, distance MN
represents the aperture. We shall consider in our discussion only such
spherical mirrors whose aperture is much smaller than its radius of
curvature.
Is there a relationship between the radius of curvature R, and focal
length f, of a spherical mirror? For spherical mirrors of small apertures,
the radius of curvature is found to be equal to twice the focal length. We
put this as R = 2f .  This implies that the principal focus of a spherical
mirror lies midway between the pole and centre of curvature.
9.2.1  Image Formation by Spherical Mirrors
You have studied about the image formation by plane mirrors. You also
know the nature, position and relative size of the images formed by them.
How about the images formed by spherical mirrors? How can we locate
the image formed by a concave mirror for different positions of the object?
Are the images real or virtual? Are they enlarged, diminished or have
the same size? We shall explore this with an Activity.
Activity 9.3 Activity 9.3 Activity 9.3 Activity 9.3 Activity 9.3
You have already learnt a way of determining the focal length of a
concave mirror. In Activity 9.2, you have seen that the sharp bright
spot of light you got on the paper is, in fact, the image of the Sun. It
was a tiny, real, inverted image. You got the approximate focal length
of the concave mirror by measuring the distance of the image from
the mirror.
n Take a concave mirror.  Find out its approximate focal length in
the way described above. Note down the value of focal length. (You
can also find it out by obtaining image of a distant object on a
sheet of paper.)
n Mark a line on a Table with a chalk.  Place the concave mirror on
a stand.  Place the stand over the line such that its pole lies over
the line.
n Draw with a chalk two more lines parallel to the previous line
such that the distance between any two successive lines is equal
to the focal length of the mirror. These lines will now correspond
to the positions of the points P, F and C, respectively. Remember –
For a spherical mirror of small aperture, the principal focus F lies
mid-way between the pole P and the centre of curvature C.
n Keep a bright object, say a burning candle, at a position far beyond
C.  Place a paper screen and move it in front of the mirror till you
obtain a sharp bright image of the candle flame on it.
n Observe the image carefully.  Note down its nature, position and
relative size with respect to the object size.
n Repeat the activity by placing the candle – (a) just beyond C,
(b) at C, (c) between F and C, (d) at F, and (e) between P and F.
n In one of the cases, you may not get the image on the screen.
Identify the position of the object in such a case. Then, look for its
virtual image in the mirror itself.
n Note down and tabulate your observations.
2024-25
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Science
134
Light – Reflection and
Refraction
9 CHAPTER
W
e see a variety of objects in the world around us. However, we are
unable to see anything in a dark room. On lighting up the room,
things become visible. What makes things visible? During the day, the
sunlight helps us to see objects. An object reflects light that falls on it.
This reflected light, when received by our eyes, enables us to see things.
We are able to see through a transparent medium as light is transmitted
through it. There are a number of common wonderful phenomena
associated with light such as image formation by mirrors, the twinkling
of stars, the beautiful colours of a rainbow, bending of light by a medium
and so on.  A study of the properties of light helps us to explore them.
By observing the common optical phenomena around us, we may
conclude that light seems to travel in straight lines. The fact that a small
source of light casts a sharp shadow of an opaque object points to this
straight-line path of light, usually indicated as a ray of light.
More to Know!
If an opaque object on the path of light becomes very small, light has a tendency to
bend around it and not walk in a straight line – an effect known as the diffraction of
light. Then the straight-line treatment of optics using rays fails. To explain phenomena
such as diffraction, light is thought of as a wave, the details of which you will study
in higher classes. Again, at the beginning of the 20
th
 century, it became known that
the wave theory of light often becomes inadequate for treatment of the interaction of
light with matter, and light often behaves somewhat like a stream of particles. This
confusion about the true nature of light continued for some years till a modern
quantum theory of light emerged in which light is neither a ‘wave’ nor a ‘particle’ –
the new theory reconciles the particle properties of light with the wave nature.
In this Chapter, we shall study the phenomena of reflection and
refraction of light using the straight-line propagation of light. These basic
concepts will help us in the study of some of the optical phenomena in
nature. We shall try to understand in this Chapter the reflection of light
by spherical mirrors and refraction of light and their application in real
life situations.
9.1 REFLECTION OF LIGHT 9.1 REFLECTION OF LIGHT 9.1 REFLECTION OF LIGHT 9.1 REFLECTION OF LIGHT 9.1 REFLECTION OF LIGHT
A highly polished surface, such as a mirror, reflects most of the light
falling on it. You are already familiar with the laws of reflection of light.
2024-25
Light – Reflection and Refraction 135
Let us recall these laws –
(i) The angle of incidence is equal to the angle of reflection, and
(ii) The incident ray, the normal to the mirror at the point of incidence
and the reflected ray, all lie in the same plane.
These laws of reflection are applicable to all types of reflecting surfaces
including spherical surfaces. You are familiar with the formation of image
by a plane mirror. What are the properties of the image? Image formed
by a plane mirror is always virtual and erect.  The size of the image is
equal to that of the object.  The image formed is as far behind the mirror
as the object is in front of it.  Further, the image is laterally inverted.
How would the images be when the reflecting surfaces are curved? Let
us explore.
Activity 9.1 Activity 9.1 Activity 9.1 Activity 9.1 Activity 9.1
n Take a large shining spoon. Try to view your face in its curved
surface.
n Do you get the image?  Is it smaller or larger?
n Move the spoon slowly away from your face. Observe the image.
How does it change?
n Reverse the spoon and repeat the Activity.  How does the image
look like now?
n Compare the characteristics of the image on the two surfaces.
The curved surface of a shining spoon could be considered as a curved
mirror.  The most commonly used type of curved mirror is the spherical
mirror.  The reflecting surface of such mirrors can be considered to form
a part of the surface of a sphere.  Such mirrors, whose reflecting surfaces
are spherical, are called spherical mirrors.  We shall now study about
spherical mirrors in some detail.
9.2 SPHERIC 9.2 SPHERIC 9.2 SPHERIC 9.2 SPHERIC 9.2 SPHERICAL MIRRORS AL MIRRORS AL MIRRORS AL MIRRORS AL MIRRORS
The reflecting surface of a spherical mirror may be curved inwards or
outwards.  A spherical mirror, whose reflecting surface is curved inwards,
that is, faces towards the centre of the sphere, is called a concave mirror.
A spherical mirror whose reflecting surface is curved outwards, is called
a convex mirror. The schematic representation of these mirrors is shown
in Fig. 9.1. You may note in these diagrams that the back
of the mirror is shaded.
You may now understand that the surface of the spoon
curved inwards can be approximated to a concave mirror
and the surface of the spoon bulged outwards can be
approximated to a convex mirror.
Before we move further on spherical mirrors, we need to
recognise and understand the meaning of a few terms. These
terms are commonly used in discussions about spherical
mirrors. The centre of the reflecting surface of a spherical
mirror is a point called the pole.  It lies on the surface of the
mirror.  The pole is usually represented by the letter P.
Figure 9.1 Figure 9.1 Figure 9.1 Figure 9.1 Figure 9.1
Schematic representation of spherical
mirrors; the shaded side is non-reflecting.
(a) Concave mirror (b) Convex mirror
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The reflecting surface of a spherical mirror forms a part of a sphere.
This sphere has a centre. This point is called the centre of curvature of
the spherical mirror. It is represented by the letter C. Please note that the
centre of curvature is not a part of the mirror. It lies outside its reflecting
surface. The centre of curvature of a concave mirror lies in front of it.
However, it lies behind the mirror in case of a convex mirror. You may
note this in Fig.9.2 (a) and (b). The radius of the sphere of which the
reflecting surface of a spherical mirror forms a part, is called the radius
of curvature of the mirror. It is represented by the letter R. You may note
that the distance PC is equal to the radius of curvature. Imagine a straight
line passing through the pole and the centre of curvature of a spherical
mirror. This line is called the principal axis. Remember that principal
axis is normal to the mirror at its pole. Let us understand an important
term related to mirrors, through an Activity.
Activity 9.2 Activity 9.2 Activity 9.2 Activity 9.2 Activity 9.2
CAUTION: Do not look at the Sun directly or even into a mirror
reflecting sunlight. It may damage your eyes.
n Hold a concave mirror in your hand and direct its reflecting surface
towards the Sun.
n Direct the light reflected by the mirror on to a sheet of paper held
close to the mirror.
n Move the sheet of paper back and forth gradually until you find
on the paper sheet a bright, sharp spot of light.
n Hold the mirror and the paper in the same position for a few
minutes. What do you observe? Why?
The paper at first begins to burn producing smoke. Eventually it
may even catch fire. Why does it burn? The light from the Sun is converged
at a point, as a sharp, bright spot by the mirror. In fact, this spot of light
is the image of the Sun on the sheet of paper. This point is
the focus of the concave mirror. The heat produced due to
the concentration of sunlight ignites the paper. The distance
of this image from the position of the mirror gives the
approximate value of focal length of the mirror.
Let us try to understand this observation with the help
of a ray diagram.
Observe Fig.9.2 (a) closely. A number of rays parallel
to the principal axis are falling on a concave mirror . Observe
the reflected rays. They are all meeting/intersecting at a
point on the principal axis of the mirror.  This point is called
the principal focus of the concave mirror. Similarly, observe
Fig. 9.2 (b). How are the rays parallel to the principal axis,
reflected by a convex mirror? The reflected rays appear to
come from a point on the principal axis. This point is called
the principal focus of the convex mirror. The principal focus
is represented by the letter F. The distance between the
pole and the principal focus of a spherical mirror is called
the focal length. It is represented by the letter f.
Figure 9.2 Figure 9.2 Figure 9.2 Figure 9.2 Figure 9.2
(a) Concave mirror
(b)     Convex mirror
(b)
(a)
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The reflecting surface of a spherical mirror is by-and-large spherical.
The surface, then, has a circular outline. The diameter of the reflecting
surface of spherical mirror is called its aperture. In Fig.9.2, distance MN
represents the aperture. We shall consider in our discussion only such
spherical mirrors whose aperture is much smaller than its radius of
curvature.
Is there a relationship between the radius of curvature R, and focal
length f, of a spherical mirror? For spherical mirrors of small apertures,
the radius of curvature is found to be equal to twice the focal length. We
put this as R = 2f .  This implies that the principal focus of a spherical
mirror lies midway between the pole and centre of curvature.
9.2.1  Image Formation by Spherical Mirrors
You have studied about the image formation by plane mirrors. You also
know the nature, position and relative size of the images formed by them.
How about the images formed by spherical mirrors? How can we locate
the image formed by a concave mirror for different positions of the object?
Are the images real or virtual? Are they enlarged, diminished or have
the same size? We shall explore this with an Activity.
Activity 9.3 Activity 9.3 Activity 9.3 Activity 9.3 Activity 9.3
You have already learnt a way of determining the focal length of a
concave mirror. In Activity 9.2, you have seen that the sharp bright
spot of light you got on the paper is, in fact, the image of the Sun. It
was a tiny, real, inverted image. You got the approximate focal length
of the concave mirror by measuring the distance of the image from
the mirror.
n Take a concave mirror.  Find out its approximate focal length in
the way described above. Note down the value of focal length. (You
can also find it out by obtaining image of a distant object on a
sheet of paper.)
n Mark a line on a Table with a chalk.  Place the concave mirror on
a stand.  Place the stand over the line such that its pole lies over
the line.
n Draw with a chalk two more lines parallel to the previous line
such that the distance between any two successive lines is equal
to the focal length of the mirror. These lines will now correspond
to the positions of the points P, F and C, respectively. Remember –
For a spherical mirror of small aperture, the principal focus F lies
mid-way between the pole P and the centre of curvature C.
n Keep a bright object, say a burning candle, at a position far beyond
C.  Place a paper screen and move it in front of the mirror till you
obtain a sharp bright image of the candle flame on it.
n Observe the image carefully.  Note down its nature, position and
relative size with respect to the object size.
n Repeat the activity by placing the candle – (a) just beyond C,
(b) at C, (c) between F and C, (d) at F, and (e) between P and F.
n In one of the cases, you may not get the image on the screen.
Identify the position of the object in such a case. Then, look for its
virtual image in the mirror itself.
n Note down and tabulate your observations.
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You will see in the above Activity that the nature, position and size of
the image formed by a concave mirror depends on the position of the
object in relation to points P, F and C. The image formed is real for some
positions of the object. It is found to be a virtual image for a certain other
position. The image is either magnified, reduced or has the same size,
depending on the position of the object. A summary of these observations
is given for your reference in Table 9.1.
Table 9.1 Image formation by a concave mirror for different positions of the object
Position of the Position of the Size of the Nature of the
object image image image
At infinity At the focus F Highly diminished, Real and inverted
point-sized
Beyond C Between F and C Diminished Real and inverted
At C At C Same size Real and inverted
Between C and F Beyond C Enlarged Real and inverted
At F At infinity Highly enlarged Real and inverted
Between P and F Behind the mirror Enlarged Virtual and erect
9.2.2 Representation of Images Formed by Spherical
Mirrors Using Ray Diagrams
We can also study the formation of images by spherical mirrors by
drawing ray diagrams. Consider an extended object, of finite size, placed
in front of a spherical mirror. Each small portion of the extended object
acts like a point source. An infinite number of rays originate from each
of these points. To construct the ray diagrams, in order to locate the
image of an object, an arbitrarily large number of rays emanating from a
point could be considered.  However, it is more convenient to consider
only two rays, for the sake of clarity of the ray diagram. These rays are
so chosen that it is easy to know their directions after reflection from the
mirror.
The intersection of at least two reflected rays give the position of image
of the point object.  Any two of the following rays can be considered for
locating the image.
(i) A ray parallel to the principal
axis, after reflection, will pass
through the principal focus
in case of a concave mirror
or appear to diverge from
the principal focus in
case of a convex mirror.
This is illustrated in Fig.9.3
(a) and (b).
(a) (b)
Figure Figure Figure Figure Figure 9.3 9.3 9.3 9.3 9.3
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