Power of a Lens
The power of a lens is the measure of its ability to produce convergence of a parallel beam of light. A convex lens of large focal length produces a small converging effect on the rays of light and a convex lens of small focal length produces a large converging effect. Due to this reason, the power of a convex lens is taken as +ve and a convex lens of large focal length has low power and a convex lens of small focal length has high power. On the other hand a concave lens produces divergence. Therefore, its power is taken as negative.
The unit in which power of a lens is measured is called diopter (D). A convex lens of focal length one metre has a power = +1 diopter and a convex lens of focal length 2 metres has a power = +1/2 diopter.
Mathematically,
If two lenses of focal length f1 and f2 are in contact
P = P1 + P2
where P1 and P2 are the powers of the two lenses and P is the equivalent power.
When two thin lenses of focal length f1 and f2 are placed coaxially and separated by a distance d, the equivalent focal length f is given by
∴ P = P1 + P2 – dP1P2
where is the equivalent power.
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