Textbook: Lenses

 Page 1


80
1. Indicate the following terms related to spherical mirrors in 
figure 7.1: poles, centre of curvature, radius of curvature, 
principal focus.
2. How are concave and convex mirrors constructed? 
Lenses
You must have seen lenses used in day to 
day life. Some examples are: the lenses used 
by old persons for reading, lens embedded in 
the front door of the house, the lens which the 
watch maker attaches to his eye etc.
Lenses are used in spectacles. They are 
also used in telescopes as you have learnt in 
the previous standard. 
7.1  Spherical mirror 
A lens is a transparent medium bound by two surfaces. The lens which has two 
spherical surfaces which are puffed up outwards is called a convex or double convex lens. 
This lens is thicker near the centre as compared to the edges. The lens with both surfaces 
spherical on the inside is called a concave or double concave lens. This lens is thinner at 
the centre as compared to its edges. 
Different types of lenses are 
shown in figure 7.2. A ray of light 
gets refracted twice while passing 
through a lens, once while entering 
the lens and once while emerging 
from the lens. The direction of the 
ray changes because of these 
refractions. Both the surfaces of 
most lenses are parts of a sphere. 
Ø Lenses             Ø Ray diagram for refracted light              	 	
Ø Sign convention            Ø Working of human eye and lens              
Ø Defects of vision and  their correction    
Ø Uses of lenses
7. Lenses
S
1 S
2
S
2
S
1
R
1
R
2
R
1
R
2
O
O
A
B
A B
C
1
C
2
C D
C
1
C
2
2
1
1 2
a. b.
7.3 Cross-sections of convex and concave lenses.
The cross-sections of convex and concave lenses are shown in parts a and b of figure 
7.3. The surface marked as 1 is part of sphere S
1
 while surface 2 is part of sphere S
2
. 
Can you recall?
Bi c on -
vex  
 
Plano 
Convex  
Positive
Meniscus
Plano 
Concave   
Negative 
Meniscus
7.2  Types of lenses
Bicon-
cave
Page 2


80
1. Indicate the following terms related to spherical mirrors in 
figure 7.1: poles, centre of curvature, radius of curvature, 
principal focus.
2. How are concave and convex mirrors constructed? 
Lenses
You must have seen lenses used in day to 
day life. Some examples are: the lenses used 
by old persons for reading, lens embedded in 
the front door of the house, the lens which the 
watch maker attaches to his eye etc.
Lenses are used in spectacles. They are 
also used in telescopes as you have learnt in 
the previous standard. 
7.1  Spherical mirror 
A lens is a transparent medium bound by two surfaces. The lens which has two 
spherical surfaces which are puffed up outwards is called a convex or double convex lens. 
This lens is thicker near the centre as compared to the edges. The lens with both surfaces 
spherical on the inside is called a concave or double concave lens. This lens is thinner at 
the centre as compared to its edges. 
Different types of lenses are 
shown in figure 7.2. A ray of light 
gets refracted twice while passing 
through a lens, once while entering 
the lens and once while emerging 
from the lens. The direction of the 
ray changes because of these 
refractions. Both the surfaces of 
most lenses are parts of a sphere. 
Ø Lenses             Ø Ray diagram for refracted light              	 	
Ø Sign convention            Ø Working of human eye and lens              
Ø Defects of vision and  their correction    
Ø Uses of lenses
7. Lenses
S
1 S
2
S
2
S
1
R
1
R
2
R
1
R
2
O
O
A
B
A B
C
1
C
2
C D
C
1
C
2
2
1
1 2
a. b.
7.3 Cross-sections of convex and concave lenses.
The cross-sections of convex and concave lenses are shown in parts a and b of figure 
7.3. The surface marked as 1 is part of sphere S
1
 while surface 2 is part of sphere S
2
. 
Can you recall?
Bi c on -
vex  
 
Plano 
Convex  
Positive
Meniscus
Plano 
Concave   
Negative 
Meniscus
7.2  Types of lenses
Bicon-
cave
81
Centre of curvature (C) :  The centres of spheres whose 
parts form surfaces of the lenses are called centres of 
curvatures of the lenses.  A lens with both surfaces 
spherical, has two centres of curvature C
1
 and C
2
. 
Radius of curvature (R) : The radii (R
1
 and R
2
) of the 
spheres whose parts form surfaces of the lenses are 
called the radii of curvature of the lens.
Principal axis : The imaginary line passing through 
both centres of curvature is called the principal axis of 
the lens. 
Optical centre (O) :  The point inside a lens on the 
principal axis, through which light rays pass without 
changing their path is called the optical centre of a lens. 
In figure 7.4, rays P
1
Q
1
, P
2
Q
2
 passing through O are 
going along a straight line. Thus O is the optical centre 
of the lens. 
Principal focus (F) : When light rays parallel to the 
principal axis are incident on a convex lens, they 
converge to a point on the principal  axis. This point is 
called the principal focus of the lens. As shown in figure 
7.5a F
1
 and F
2
 are the principal foci of the convex lens. 
Light rays parallel to the principal axis falling on a convex lens come together i.e. get 
focused at a point on the principal axis. So this type of lens is called a converging lens.
 Rays travelling parallel to the principal axis of a concave lens diverge after refraction 
in such a way that they appear to be coming out of a point on the principal axis. This point 
is called the principal focus of the concave lens. As shown in figure 7.5b F
1
 and F
2
 are the 
principal foci of the concave lens.  
 Light rays parallel to the principal axis falling on a concave lens go away from one 
another (diverge) after refraction. So this type of lens is called a divergent lens. 
Focal length (f) : The distance between the optical centre and principal focus of a lens is 
called its focal length. 
7.4  Optical centre of a lens
P
1
Q
1
P
2
Q
2
P
3
Q
3
P
1
Q
1
Q
3
Q
2
P
2
P
3
O
O
Material: Convex lens, screen, meter scale, stand for the lens etc.
7. 5  Principal focus of a lens 
F
1 F
2
F
1
F
2
f
f
Method:
  Keeping the screen fixed, obtain a clear image of a distant object like a tree or a 
building with the help of the lens on the screen.  Measure the distance between the screen 
and the lens with the help of the meter scale. Now turn the other side of the lens towards 
the screen. Again obtain a clear image of the distant object on the screen by moving the 
lens forward or backward. Measure the distance between the screen and the lens again. 
Try this.
a. b.
Page 3


80
1. Indicate the following terms related to spherical mirrors in 
figure 7.1: poles, centre of curvature, radius of curvature, 
principal focus.
2. How are concave and convex mirrors constructed? 
Lenses
You must have seen lenses used in day to 
day life. Some examples are: the lenses used 
by old persons for reading, lens embedded in 
the front door of the house, the lens which the 
watch maker attaches to his eye etc.
Lenses are used in spectacles. They are 
also used in telescopes as you have learnt in 
the previous standard. 
7.1  Spherical mirror 
A lens is a transparent medium bound by two surfaces. The lens which has two 
spherical surfaces which are puffed up outwards is called a convex or double convex lens. 
This lens is thicker near the centre as compared to the edges. The lens with both surfaces 
spherical on the inside is called a concave or double concave lens. This lens is thinner at 
the centre as compared to its edges. 
Different types of lenses are 
shown in figure 7.2. A ray of light 
gets refracted twice while passing 
through a lens, once while entering 
the lens and once while emerging 
from the lens. The direction of the 
ray changes because of these 
refractions. Both the surfaces of 
most lenses are parts of a sphere. 
Ø Lenses             Ø Ray diagram for refracted light              	 	
Ø Sign convention            Ø Working of human eye and lens              
Ø Defects of vision and  their correction    
Ø Uses of lenses
7. Lenses
S
1 S
2
S
2
S
1
R
1
R
2
R
1
R
2
O
O
A
B
A B
C
1
C
2
C D
C
1
C
2
2
1
1 2
a. b.
7.3 Cross-sections of convex and concave lenses.
The cross-sections of convex and concave lenses are shown in parts a and b of figure 
7.3. The surface marked as 1 is part of sphere S
1
 while surface 2 is part of sphere S
2
. 
Can you recall?
Bi c on -
vex  
 
Plano 
Convex  
Positive
Meniscus
Plano 
Concave   
Negative 
Meniscus
7.2  Types of lenses
Bicon-
cave
81
Centre of curvature (C) :  The centres of spheres whose 
parts form surfaces of the lenses are called centres of 
curvatures of the lenses.  A lens with both surfaces 
spherical, has two centres of curvature C
1
 and C
2
. 
Radius of curvature (R) : The radii (R
1
 and R
2
) of the 
spheres whose parts form surfaces of the lenses are 
called the radii of curvature of the lens.
Principal axis : The imaginary line passing through 
both centres of curvature is called the principal axis of 
the lens. 
Optical centre (O) :  The point inside a lens on the 
principal axis, through which light rays pass without 
changing their path is called the optical centre of a lens. 
In figure 7.4, rays P
1
Q
1
, P
2
Q
2
 passing through O are 
going along a straight line. Thus O is the optical centre 
of the lens. 
Principal focus (F) : When light rays parallel to the 
principal axis are incident on a convex lens, they 
converge to a point on the principal  axis. This point is 
called the principal focus of the lens. As shown in figure 
7.5a F
1
 and F
2
 are the principal foci of the convex lens. 
Light rays parallel to the principal axis falling on a convex lens come together i.e. get 
focused at a point on the principal axis. So this type of lens is called a converging lens.
 Rays travelling parallel to the principal axis of a concave lens diverge after refraction 
in such a way that they appear to be coming out of a point on the principal axis. This point 
is called the principal focus of the concave lens. As shown in figure 7.5b F
1
 and F
2
 are the 
principal foci of the concave lens.  
 Light rays parallel to the principal axis falling on a concave lens go away from one 
another (diverge) after refraction. So this type of lens is called a divergent lens. 
Focal length (f) : The distance between the optical centre and principal focus of a lens is 
called its focal length. 
7.4  Optical centre of a lens
P
1
Q
1
P
2
Q
2
P
3
Q
3
P
1
Q
1
Q
3
Q
2
P
2
P
3
O
O
Material: Convex lens, screen, meter scale, stand for the lens etc.
7. 5  Principal focus of a lens 
F
1 F
2
F
1
F
2
f
f
Method:
  Keeping the screen fixed, obtain a clear image of a distant object like a tree or a 
building with the help of the lens on the screen.  Measure the distance between the screen 
and the lens with the help of the meter scale. Now turn the other side of the lens towards 
the screen. Again obtain a clear image of the distant object on the screen by moving the 
lens forward or backward. Measure the distance between the screen and the lens again. 
Try this.
a. b.
82
Try This
Incident ray
Reflected ray 
F
1
O
F
2
Reflected ray 
Incident ray
F
1
O F
2
Reflected ray 
Incident ray 
F
2
F
1
O
Rule 1: When the incident ray 
is parallel to the principal axis,  
the refracted ray passes 
through the principal focus.
Rule 2: When the incident ray 
passes through the principal 
focus, the refracted ray is 
parallel to the principal axis. 
Rule 3: When the incident ray 
passes through the optical 
centre of the lens, it passes 
without changing its direction.
7. 6  Arrangement for the experiment
Can you recall?
Convex lens
Screen
Candle
F
2
2F
2
O F
1
2F
1
spherical mirrors. Similarly, one can obtain the images formed by lenses with the help of ray 
diagrams. One can obtain the position, size and nature of the images with the help of these 
diagrams. 
Images formed by convex lenses 
One can use following three rules to draw ray diagrams of images obtained by convex 
lenses.
What is this distance between the lens and the screen called? Discuss the relation 
between this distance and the radius of curvature of the lens with your teacher. The image 
of a distant object is obtained close to the focus of the lens, hence, the above distance is the 
focal length of the lens. What will happen if you use a concave lens in this experiment?
Ray diagram for refraction : You have learnt the rules for drawing ray diagrams for 
Material: A convex lens, screen, meter scale, stand for the lens, 
chalk, candle etc.
Method: 
1. Draw a straight line along the centre of a 
long table. 
2. Place the lens on the stand at the central 
point (O) of the line.
3. Place the screen on one side, of the lens. 
Move it along the line so as to get a clear 
image of a distant object. Mark its 
position as F
1
. 
4. Measure the distance between O and F
1
. 
Mark a point at distance 2F
1
 from O on 
the same side of F
1
 and mark it as 2F
1
.
5. Repeat actions 3 and 4 on the other side of the lens and mark F
2 
and 2F
2
 on the straight 
line. 
6. Now place the burning candle on  the other side of lens far beyond 2F
1
. Place the screen 
on the opposite side of the lens and obtain a clear image of the candle by moving it 
forward or backward along the line. Note the position, size and nature of the image.
7. Repeat action 6 by placing the candle beyond 2F
1
, at 2F
1
, between 2F
1
 and F
1
, at F
1
 and 
between F
1
 and O. Note your observations.
What are real and virtual images? How will you find 
out whether  an image is real or virtual? Can a virtual 
image be obtained on a screen?
Page 4


80
1. Indicate the following terms related to spherical mirrors in 
figure 7.1: poles, centre of curvature, radius of curvature, 
principal focus.
2. How are concave and convex mirrors constructed? 
Lenses
You must have seen lenses used in day to 
day life. Some examples are: the lenses used 
by old persons for reading, lens embedded in 
the front door of the house, the lens which the 
watch maker attaches to his eye etc.
Lenses are used in spectacles. They are 
also used in telescopes as you have learnt in 
the previous standard. 
7.1  Spherical mirror 
A lens is a transparent medium bound by two surfaces. The lens which has two 
spherical surfaces which are puffed up outwards is called a convex or double convex lens. 
This lens is thicker near the centre as compared to the edges. The lens with both surfaces 
spherical on the inside is called a concave or double concave lens. This lens is thinner at 
the centre as compared to its edges. 
Different types of lenses are 
shown in figure 7.2. A ray of light 
gets refracted twice while passing 
through a lens, once while entering 
the lens and once while emerging 
from the lens. The direction of the 
ray changes because of these 
refractions. Both the surfaces of 
most lenses are parts of a sphere. 
Ø Lenses             Ø Ray diagram for refracted light              	 	
Ø Sign convention            Ø Working of human eye and lens              
Ø Defects of vision and  their correction    
Ø Uses of lenses
7. Lenses
S
1 S
2
S
2
S
1
R
1
R
2
R
1
R
2
O
O
A
B
A B
C
1
C
2
C D
C
1
C
2
2
1
1 2
a. b.
7.3 Cross-sections of convex and concave lenses.
The cross-sections of convex and concave lenses are shown in parts a and b of figure 
7.3. The surface marked as 1 is part of sphere S
1
 while surface 2 is part of sphere S
2
. 
Can you recall?
Bi c on -
vex  
 
Plano 
Convex  
Positive
Meniscus
Plano 
Concave   
Negative 
Meniscus
7.2  Types of lenses
Bicon-
cave
81
Centre of curvature (C) :  The centres of spheres whose 
parts form surfaces of the lenses are called centres of 
curvatures of the lenses.  A lens with both surfaces 
spherical, has two centres of curvature C
1
 and C
2
. 
Radius of curvature (R) : The radii (R
1
 and R
2
) of the 
spheres whose parts form surfaces of the lenses are 
called the radii of curvature of the lens.
Principal axis : The imaginary line passing through 
both centres of curvature is called the principal axis of 
the lens. 
Optical centre (O) :  The point inside a lens on the 
principal axis, through which light rays pass without 
changing their path is called the optical centre of a lens. 
In figure 7.4, rays P
1
Q
1
, P
2
Q
2
 passing through O are 
going along a straight line. Thus O is the optical centre 
of the lens. 
Principal focus (F) : When light rays parallel to the 
principal axis are incident on a convex lens, they 
converge to a point on the principal  axis. This point is 
called the principal focus of the lens. As shown in figure 
7.5a F
1
 and F
2
 are the principal foci of the convex lens. 
Light rays parallel to the principal axis falling on a convex lens come together i.e. get 
focused at a point on the principal axis. So this type of lens is called a converging lens.
 Rays travelling parallel to the principal axis of a concave lens diverge after refraction 
in such a way that they appear to be coming out of a point on the principal axis. This point 
is called the principal focus of the concave lens. As shown in figure 7.5b F
1
 and F
2
 are the 
principal foci of the concave lens.  
 Light rays parallel to the principal axis falling on a concave lens go away from one 
another (diverge) after refraction. So this type of lens is called a divergent lens. 
Focal length (f) : The distance between the optical centre and principal focus of a lens is 
called its focal length. 
7.4  Optical centre of a lens
P
1
Q
1
P
2
Q
2
P
3
Q
3
P
1
Q
1
Q
3
Q
2
P
2
P
3
O
O
Material: Convex lens, screen, meter scale, stand for the lens etc.
7. 5  Principal focus of a lens 
F
1 F
2
F
1
F
2
f
f
Method:
  Keeping the screen fixed, obtain a clear image of a distant object like a tree or a 
building with the help of the lens on the screen.  Measure the distance between the screen 
and the lens with the help of the meter scale. Now turn the other side of the lens towards 
the screen. Again obtain a clear image of the distant object on the screen by moving the 
lens forward or backward. Measure the distance between the screen and the lens again. 
Try this.
a. b.
82
Try This
Incident ray
Reflected ray 
F
1
O
F
2
Reflected ray 
Incident ray
F
1
O F
2
Reflected ray 
Incident ray 
F
2
F
1
O
Rule 1: When the incident ray 
is parallel to the principal axis,  
the refracted ray passes 
through the principal focus.
Rule 2: When the incident ray 
passes through the principal 
focus, the refracted ray is 
parallel to the principal axis. 
Rule 3: When the incident ray 
passes through the optical 
centre of the lens, it passes 
without changing its direction.
7. 6  Arrangement for the experiment
Can you recall?
Convex lens
Screen
Candle
F
2
2F
2
O F
1
2F
1
spherical mirrors. Similarly, one can obtain the images formed by lenses with the help of ray 
diagrams. One can obtain the position, size and nature of the images with the help of these 
diagrams. 
Images formed by convex lenses 
One can use following three rules to draw ray diagrams of images obtained by convex 
lenses.
What is this distance between the lens and the screen called? Discuss the relation 
between this distance and the radius of curvature of the lens with your teacher. The image 
of a distant object is obtained close to the focus of the lens, hence, the above distance is the 
focal length of the lens. What will happen if you use a concave lens in this experiment?
Ray diagram for refraction : You have learnt the rules for drawing ray diagrams for 
Material: A convex lens, screen, meter scale, stand for the lens, 
chalk, candle etc.
Method: 
1. Draw a straight line along the centre of a 
long table. 
2. Place the lens on the stand at the central 
point (O) of the line.
3. Place the screen on one side, of the lens. 
Move it along the line so as to get a clear 
image of a distant object. Mark its 
position as F
1
. 
4. Measure the distance between O and F
1
. 
Mark a point at distance 2F
1
 from O on 
the same side of F
1
 and mark it as 2F
1
.
5. Repeat actions 3 and 4 on the other side of the lens and mark F
2 
and 2F
2
 on the straight 
line. 
6. Now place the burning candle on  the other side of lens far beyond 2F
1
. Place the screen 
on the opposite side of the lens and obtain a clear image of the candle by moving it 
forward or backward along the line. Note the position, size and nature of the image.
7. Repeat action 6 by placing the candle beyond 2F
1
, at 2F
1
, between 2F
1
 and F
1
, at F
1
 and 
between F
1
 and O. Note your observations.
What are real and virtual images? How will you find 
out whether  an image is real or virtual? Can a virtual 
image be obtained on a screen?
83
As shown in the figure 7.7, an object 
AB is placed beyond the point 2F
1
. The 
incident ray BC, starting from B and going 
parallel to the principal axis, goes through 
the principal focus F
2
 after refraction along 
CT. The ray BO, starting from B and 
passing through the optical centre O of the 
lens goes along OS without changing its 
direction. It intersects CT in B
¢
. This means 
that the image of B is formed at B
¢
.  
As A is situated on the principal axis, its image will also be located along the principal 
axis at A
¢
, vertically above B
¢
.  Thus, A
¢
B
¢
 will be the image of AB formed by the lens. So 
we learn that if an object is placed beyond 2F
1
, the image is formed between F
2
 and 2F
2
. 
It is real and inverted and its size is smaller than that of the object. 
S.
No.
Position of the 
object
Position of the 
image
Size of the 
image
Nature of the 
image
1 At infinity At focus F
2
Point image Real and inverted
2 Beyond 2F
1
Between F
2
 and 2F
2
Smaller Real and inverted
3 At 2F
1
At 2F
2
Same size Real and inverted
4 Between F
1
 and 2F
1
Beyond 2F
2
Larger Real and inverted
5 At  focus F
1
At infinity Very large Real and inverted
6 Between F
1
 and O On the same side of 
the lens as the object
Very large Virtual and erect
2F
1
F
1
O
C
2F
2
F
2
T
S 
B
A
B
l
A
l
7.7 Real image formed by a convex lens  
Images formed by convex lenses for different positions of the object.
7.8 Images formed by position of an object
Observe
Images formed by concave lenses
 We can obtain the images obtained by concave lenses using the following rules.
1. When the incident ray is parallel to the principal axis, the refracted ray when extended 
backwards, passes through the focus.
2. When the incident ray passes through the focus, the refracted ray is parallel to the 
principal axis. 
Study figure 7.8. Determine the 
position, size and nature of images 
formed for different positions of an 
object  with the help of ray diagrams. 
Check your  conclusions and 
observations in the previous activity 
with those given in the table.
Page 5


80
1. Indicate the following terms related to spherical mirrors in 
figure 7.1: poles, centre of curvature, radius of curvature, 
principal focus.
2. How are concave and convex mirrors constructed? 
Lenses
You must have seen lenses used in day to 
day life. Some examples are: the lenses used 
by old persons for reading, lens embedded in 
the front door of the house, the lens which the 
watch maker attaches to his eye etc.
Lenses are used in spectacles. They are 
also used in telescopes as you have learnt in 
the previous standard. 
7.1  Spherical mirror 
A lens is a transparent medium bound by two surfaces. The lens which has two 
spherical surfaces which are puffed up outwards is called a convex or double convex lens. 
This lens is thicker near the centre as compared to the edges. The lens with both surfaces 
spherical on the inside is called a concave or double concave lens. This lens is thinner at 
the centre as compared to its edges. 
Different types of lenses are 
shown in figure 7.2. A ray of light 
gets refracted twice while passing 
through a lens, once while entering 
the lens and once while emerging 
from the lens. The direction of the 
ray changes because of these 
refractions. Both the surfaces of 
most lenses are parts of a sphere. 
Ø Lenses             Ø Ray diagram for refracted light              	 	
Ø Sign convention            Ø Working of human eye and lens              
Ø Defects of vision and  their correction    
Ø Uses of lenses
7. Lenses
S
1 S
2
S
2
S
1
R
1
R
2
R
1
R
2
O
O
A
B
A B
C
1
C
2
C D
C
1
C
2
2
1
1 2
a. b.
7.3 Cross-sections of convex and concave lenses.
The cross-sections of convex and concave lenses are shown in parts a and b of figure 
7.3. The surface marked as 1 is part of sphere S
1
 while surface 2 is part of sphere S
2
. 
Can you recall?
Bi c on -
vex  
 
Plano 
Convex  
Positive
Meniscus
Plano 
Concave   
Negative 
Meniscus
7.2  Types of lenses
Bicon-
cave
81
Centre of curvature (C) :  The centres of spheres whose 
parts form surfaces of the lenses are called centres of 
curvatures of the lenses.  A lens with both surfaces 
spherical, has two centres of curvature C
1
 and C
2
. 
Radius of curvature (R) : The radii (R
1
 and R
2
) of the 
spheres whose parts form surfaces of the lenses are 
called the radii of curvature of the lens.
Principal axis : The imaginary line passing through 
both centres of curvature is called the principal axis of 
the lens. 
Optical centre (O) :  The point inside a lens on the 
principal axis, through which light rays pass without 
changing their path is called the optical centre of a lens. 
In figure 7.4, rays P
1
Q
1
, P
2
Q
2
 passing through O are 
going along a straight line. Thus O is the optical centre 
of the lens. 
Principal focus (F) : When light rays parallel to the 
principal axis are incident on a convex lens, they 
converge to a point on the principal  axis. This point is 
called the principal focus of the lens. As shown in figure 
7.5a F
1
 and F
2
 are the principal foci of the convex lens. 
Light rays parallel to the principal axis falling on a convex lens come together i.e. get 
focused at a point on the principal axis. So this type of lens is called a converging lens.
 Rays travelling parallel to the principal axis of a concave lens diverge after refraction 
in such a way that they appear to be coming out of a point on the principal axis. This point 
is called the principal focus of the concave lens. As shown in figure 7.5b F
1
 and F
2
 are the 
principal foci of the concave lens.  
 Light rays parallel to the principal axis falling on a concave lens go away from one 
another (diverge) after refraction. So this type of lens is called a divergent lens. 
Focal length (f) : The distance between the optical centre and principal focus of a lens is 
called its focal length. 
7.4  Optical centre of a lens
P
1
Q
1
P
2
Q
2
P
3
Q
3
P
1
Q
1
Q
3
Q
2
P
2
P
3
O
O
Material: Convex lens, screen, meter scale, stand for the lens etc.
7. 5  Principal focus of a lens 
F
1 F
2
F
1
F
2
f
f
Method:
  Keeping the screen fixed, obtain a clear image of a distant object like a tree or a 
building with the help of the lens on the screen.  Measure the distance between the screen 
and the lens with the help of the meter scale. Now turn the other side of the lens towards 
the screen. Again obtain a clear image of the distant object on the screen by moving the 
lens forward or backward. Measure the distance between the screen and the lens again. 
Try this.
a. b.
82
Try This
Incident ray
Reflected ray 
F
1
O
F
2
Reflected ray 
Incident ray
F
1
O F
2
Reflected ray 
Incident ray 
F
2
F
1
O
Rule 1: When the incident ray 
is parallel to the principal axis,  
the refracted ray passes 
through the principal focus.
Rule 2: When the incident ray 
passes through the principal 
focus, the refracted ray is 
parallel to the principal axis. 
Rule 3: When the incident ray 
passes through the optical 
centre of the lens, it passes 
without changing its direction.
7. 6  Arrangement for the experiment
Can you recall?
Convex lens
Screen
Candle
F
2
2F
2
O F
1
2F
1
spherical mirrors. Similarly, one can obtain the images formed by lenses with the help of ray 
diagrams. One can obtain the position, size and nature of the images with the help of these 
diagrams. 
Images formed by convex lenses 
One can use following three rules to draw ray diagrams of images obtained by convex 
lenses.
What is this distance between the lens and the screen called? Discuss the relation 
between this distance and the radius of curvature of the lens with your teacher. The image 
of a distant object is obtained close to the focus of the lens, hence, the above distance is the 
focal length of the lens. What will happen if you use a concave lens in this experiment?
Ray diagram for refraction : You have learnt the rules for drawing ray diagrams for 
Material: A convex lens, screen, meter scale, stand for the lens, 
chalk, candle etc.
Method: 
1. Draw a straight line along the centre of a 
long table. 
2. Place the lens on the stand at the central 
point (O) of the line.
3. Place the screen on one side, of the lens. 
Move it along the line so as to get a clear 
image of a distant object. Mark its 
position as F
1
. 
4. Measure the distance between O and F
1
. 
Mark a point at distance 2F
1
 from O on 
the same side of F
1
 and mark it as 2F
1
.
5. Repeat actions 3 and 4 on the other side of the lens and mark F
2 
and 2F
2
 on the straight 
line. 
6. Now place the burning candle on  the other side of lens far beyond 2F
1
. Place the screen 
on the opposite side of the lens and obtain a clear image of the candle by moving it 
forward or backward along the line. Note the position, size and nature of the image.
7. Repeat action 6 by placing the candle beyond 2F
1
, at 2F
1
, between 2F
1
 and F
1
, at F
1
 and 
between F
1
 and O. Note your observations.
What are real and virtual images? How will you find 
out whether  an image is real or virtual? Can a virtual 
image be obtained on a screen?
83
As shown in the figure 7.7, an object 
AB is placed beyond the point 2F
1
. The 
incident ray BC, starting from B and going 
parallel to the principal axis, goes through 
the principal focus F
2
 after refraction along 
CT. The ray BO, starting from B and 
passing through the optical centre O of the 
lens goes along OS without changing its 
direction. It intersects CT in B
¢
. This means 
that the image of B is formed at B
¢
.  
As A is situated on the principal axis, its image will also be located along the principal 
axis at A
¢
, vertically above B
¢
.  Thus, A
¢
B
¢
 will be the image of AB formed by the lens. So 
we learn that if an object is placed beyond 2F
1
, the image is formed between F
2
 and 2F
2
. 
It is real and inverted and its size is smaller than that of the object. 
S.
No.
Position of the 
object
Position of the 
image
Size of the 
image
Nature of the 
image
1 At infinity At focus F
2
Point image Real and inverted
2 Beyond 2F
1
Between F
2
 and 2F
2
Smaller Real and inverted
3 At 2F
1
At 2F
2
Same size Real and inverted
4 Between F
1
 and 2F
1
Beyond 2F
2
Larger Real and inverted
5 At  focus F
1
At infinity Very large Real and inverted
6 Between F
1
 and O On the same side of 
the lens as the object
Very large Virtual and erect
2F
1
F
1
O
C
2F
2
F
2
T
S 
B
A
B
l
A
l
7.7 Real image formed by a convex lens  
Images formed by convex lenses for different positions of the object.
7.8 Images formed by position of an object
Observe
Images formed by concave lenses
 We can obtain the images obtained by concave lenses using the following rules.
1. When the incident ray is parallel to the principal axis, the refracted ray when extended 
backwards, passes through the focus.
2. When the incident ray passes through the focus, the refracted ray is parallel to the 
principal axis. 
Study figure 7.8. Determine the 
position, size and nature of images 
formed for different positions of an 
object  with the help of ray diagrams. 
Check your  conclusions and 
observations in the previous activity 
with those given in the table.
84
As shown in figure 7.9, object PQ is placed between F
1
 and 2F
1
 in front of a concave 
lens. The incident ray PA, starting from P and going parallel to the principal axis goes 
along AD after refraction. If AD is extended backwards, it appears to come from F
1
. 
The incident ray PO, starting from P and passing through O, goes along the same direction 
after refraction. PO intersects the extended ray AF
1
 at P
1
, i.e. P
1
 is the image of P. 
P
Q 
P
1
Q
1
F
1
2F
1
D
A
7.9 Image formed by a concave lens
Sr.
No.
Position of the object
Position of the 
image
Size of the 
image
Nature of the 
image
1 At infinity On the first focus F
1
Point image Virtual and erect
2
Anywhere between optical 
centre O and infinity
Between optical 
centre and focus F
1
Small Virtual and erect
 As the point Q is on the principal 
axis, its image is formed along the 
axis at the point Q
1
 directly below 
P
1
. Thus, P
1
Q
1
 is the image of PQ. 
The image formed by a concave 
lens is always virtual, erect and 
smaller than the object.
7.10  Cartesian sign convention
1      1        1 
v     u      f
 -  -  -  =  -
 The lens formula is same for any spherical lens and any distance 
of the object from the lens. It is however necessary to use the sign 
convention properly.
Sign convention
What is the Cartesian sign convention used for spherical 
mirrors?
Direction of incident ray
Distance on the left 
of the origin (-ve)
Distance on the right 
of the origin (+ve)
Direction of incident ray
Distance on the left 
of the origin (-ve)
Distance on the right 
of the origin (+ve)
x
Lens formula 
The formula showing the relation between distance of the object (u), the distance 
of the image (v) and the focal length (f) is called the lens formula. It is given below.
Height above
- ve
Height below
Height above
Principal axis
+ ve
- ve
Height below
Principal axis
+ ve
x
Can you recall?