Power of a Lens
You have already learnt that the ability of a lens to converge or diverge light rays depends on its focal length. For example, a convex lens of short focal length bends the light rays through large angles, by focusing them closer to the optical centre. Similarly, the concave lens of a very short focal length causes higher divergence than the one with a longer focal length. 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 defined as the reciprocal of its focal length. It is represented by the letter P. The power P of a lens of focal length f is given by
\(m\,=\,\frac{1}{f}\)
The SI unit of power of a lens is ‘dioptre’. It is denoted by the letter D. If f is expressed in metres, then, power is expressed in dioptres. Thus, 1 dioptre is the power of a lens whose focal length is 1 metre. 1D = 1m–1. You may note that the power of a convex lens is positive and that of a concave lens is negative.
Opticians prescribe corrective lenses indicating their powers. Let us say the lens prescribed has power equal to + 2.0 D. This means the lens prescribed is convex. The focal length of the lens is + 0.50 m. Similarly, a lens of power – 2.5 D has a focal length of – 0.40 m. The lens is concave.
More to know!
Many optical instruments consist of a number of lenses. They are combined to increase the magnification and sharpness of the image. The net power (P ) of the lenses placed in contact is given by the algebraic sum of the individual powers P1, P2, P3, … as
P = P1 + P2 + P3 + …
The use of powers, instead of focal lengths, for lenses is quite convenient for opticians.
During eye-testing, an optician puts several different combinations of corrective lenses of known power, in contact, inside the testing spectacles’ frame. The optician calculates the power of the lens required by simple algebraic addition. For example, a combination of two lenses of power + 2.0 D and + 0.25 D is equivalent to a single lens of power + 2.25 D. The simple additive property of the powers of lenses can be used to design lens systems to minimise certain defects in images produced by a single lens. Such a lens system, consisting of several lenses, in contact, is commonly used in the design of lenses of camera, microscopes and telescopes.