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High School
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Physics Ex-54
The optical power of a lens is a measure of how much the lens
bends light. The greater the optical power, the more the lens
bends light.
Note that the optical power is the reciprocal of the focal length
of the lens. The symbol for the optical power of a lens is P and
the unit for the optical power is dioptres and is designated by
the Greek symbol “”.
More bending
High optical power
Less bending
Low optical power
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Physics Ex-54
The optical power of a lens is the reciprocal of its focal length.
Study these examples:
f
f
f
f
f
f
f
f
=
=
=
=
=
=
=
=
1 cm
2 cm
4 cm
8 cm
10 cm
25 cm
50 cm
100 cm
P
P
P
P
P
P
P
P
=
=
=
=
=
=
=
=
1/0.01 m
1/0.02 m
1/0.04 m
1/0.08 m
1/0.1 m
1/0.25 m
1/0.50 m
1/1 m
=
=
=
=
=
=
=
=
100 
50 
25 
12.5 
10 
4
2
1
Note that the optical power of a converging lens
is positive and for a diverging lens it is negative.
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Physics Ex-54
The optical power of a
convex (or converging) lens is
positive.
The optical power of a
concave (or diverging) lens
is negative.
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Physics Ex-54
Two or more lenses may be combined to form a compound lens
or an optical system.
For such a compound lens, the total optical power is given by
the following formula:
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Question-1
Physics Ex-54
Define the optical power of a lens.
The ability of a lens to bend (converge or diverge) light rays.
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Question-2
Physics Ex-54
What type of a lens has positive optical power?
Converging lens.
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Question-3
Physics Ex-54
What type of a lens has a negative optical power?
Diverging lens.
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Question-4
Physics Ex-54
Listed below are the focal lengths of five lenses.
Determine their optical powers.
a) f = 1 cm
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Question-4
Physics Ex-54
Listed below are the focal lengths of five lenses.
Determine their optical powers.
b) f = 5 cm
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Question-4
Physics Ex-54
Listed below are the focal lengths of five lenses.
Determine their optical powers.
c) f = 10 cm
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Physics Ex-54
Question-4
Listed below are the focal lengths of five lenses.
Determine their optical powers.
d) f = -20 cm
Note that the negative sign
indicates a diverging lens.
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Question-4
Physics Ex-54
Listed below are the focal lengths of five lenses.
Determine their optical powers.
e) f = 15 cm
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Question-5
Physics Ex-54
Listed below are the optical powers of four lenses.
Determine their focal lengths.
a) P = 20 
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Question-5
Physics Ex-54
Listed below are the optical powers of four lenses.
Determine their focal lengths.
b) P = 10 
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Physics Ex-54
Question-5
Listed below are the optical powers of four lenses.
Determine their focal lengths.
c) P = -25 
Note that the negative sign
indicates a diverging lens.
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Question-5
Physics Ex-54
Listed below are the optical powers of four lenses.
Determine their focal lengths.
d) P = 8 
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Question-6
Physics Ex-54
A converging lens has a focal length of 25 cm.
Determine its optical power.
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Question-7
Physics Ex-54
Note that diverging lens has a negative optical power.
The optical power of a diverging lens is – 8.33 .
Determine its focal length.
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Question-8
Physics Ex-54
Draw the rays emerging from a lens having the following optical
powers:
5 cm
a) P = 20 
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Question-8
Physics Ex-54
Draw the rays emerging from a lens having the following optical
powers:
25 cm
b) P = 4 
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Physics Ex-54
Question-8
Draw the rays emerging from a lens having the following optical
powers:
5 cm
c) P = -20 
REMINDER
By convention in using lenses,
distances are positive on the
side where light comes out.
F
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Physics Ex-54
Question-8
Draw the rays emerging from a lens having the following optical
powers:
25 cm
d) P = -4 
F
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Question-9
Physics Ex-54
Two thin lenses are placed together to form an effective lens system.
The lenses have optical powers of 20.0  and –12.0  respectively.
Find the focal length of the system.
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Physics Ex-54
Question-10
A lens system consists of a converging lens and a
diverging lens. The focal length of the converging
lens is 60 cm.
If the optical power of the system is to be 1.25  ,
what should be the focal length of the diverging lens?
The negative sign indicates
the system is acting as a
diverging (concave) lens.
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Physics Ex-54
Question-11
An optical system is made using two thin lenses placed close to
each other. The optical power of the system is 4 δ (dioptres).
Knowing that one of the lenses has a focal length of -16 cm,
determine the optical power of the second lens.
A) 13.5 δ
B) 10.3 δ
C) 9.6 δ
Convert to metres
REMINDER
The
unit
for
length
in
the
E) -2.9 δ
optical power formula must
be metres.
D) 3.4 δ
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Question-12
Physics Ex-54
Convert to metres.
Three lenses have focal lengths of 10.5 cm, -7.5 cm and 5 cm
respectively. The lenses are combined to form an optical system.
Determine the optical power of this lens system.
A) 0.08 δ
B) 0.23 δ
C) 2.70 δ
D) 16 δ
E) 43 δ
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Physics Ex-54
Question-13
Two lenses are placed together to form
an optical system. One lens has a
focal length of 20.0 cm while the other
lens has a focal length of -35.0 cm.
Object
120 cm
If an object 4.0 cm tall is placed 120 cm in front of the
system determine the characteristics of the image.
Given
Calculation of fT
Calculation of di
Calculation of hi
Negative sign indicates inversion
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Physics Ex-54
Question-14
Convert 25 cm to meters
The focal length of a lens system is 25 cm.
What is the optical power of this system?
A) 4.0 
B) -4.0 
C) 0.04 
D) -0.04 
E) 0.25 
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