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# 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.

### 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:

1. 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.

1. 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

1. The degree of convergence or divergence of light rays achieved by a lens is expressed in
terms of its power.
2. 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.
3. The power of a lens varies inversely as the focal length of the lens.
4. 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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