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: 

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. 

2. 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