Power of a Lens – Definition and Formula
Power of a Lens
Introduction
All the lenses do not converge or diverge the light rays falling on them by the same amount. Lenses of different kinds and different focal lengths act on a light ray falling on them differently. In this section we will look at the term which measures this mathematically.
Explanation
Power of a lens:
The converging ability of the lens varies inversely as the focal length of a convex lens and the diverging ability of the lens varies inversely as the focal length of a concave lens.
The degree of convergence or divergence of light rays achieved by a lens is expressed in terms of its power.
The power of a lens is equal to the reciprocal of the focal length of the lens.
Where P is the power of a lens and f is its focal length.
This means that, a convex lens of short focal length bends the light rays through large angles by focusing them closer to the optical center.
And a concave lens of very short focal length causes a higher divergence than the one with a longer focal length.
The SI unit of the power of a lens is dioptre (D).
If the focal length of the lens ‘f’ is expressed in meters, then the power is expressed in dioptres.
Therefore, 1 D is the power of a lens with focal length 1 m.
The focal length of a convex lens is positive whereas, the focal length of a concave lens is negative.
Therefore, the power of a convex lens is positive and that of a concave lens is negative.
Questions and Solutions:
- What is the power of the lens used in your spectacles? Calculate its focal length and identify the kind of lens used in it.
Solution:
Suppose the power of the lens in the spectacles is – 2.25 D.
P = 1/f
f = 1/P
f = 1/–2.25
f = – 100/225
f = – 4/9
f = – 0.44 m
f = – 44 cm
As the focal length turned out to be negative the lens used is a concave lens.
- What is the power of the lens whose focal length is 80 cm? Identify the kind of lens used in it.
Solution:
The focal length is given to be 80 cm = 0.8 m
P = 1/f
P = 1/0.8
P = 10/8
P = 1.25 D
As the focal length and the power, both are positive the lens used is a convex lens.
Summary
- The degree of convergence or divergence of light rays achieved by a lens is expressed in
terms of its power. - The power of a lens is equal to the reciprocal of the focal length of the lens.
P= 1 / f , where P is the power of a lens and f is its focal length. - The power of a lens varies inversely as the focal length of the lens.
- The SI unit of the power of a lens is “dioptre” (D). If the focal length of the lens ‘f is
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