Define power of a lens. What is its unit? One student uses a lens of focal length $50\, cm$ and another of $-50\, cm$. What is the nature of the lens and its power used by each of them?

(A) The power of a lens is defined as the reciprocal of its focal length in meters,given by the formula $P = \frac{1}{f(m)}$.
The $SI$ unit of power of a lens is Dioptre $(D)$.
For the first student,the focal length $f = 50\, cm = 0.5\, m$. Since the focal length is positive,the lens is a convex lens. Its power $P = \frac{1}{0.5} = +2\, D$.
For the second student,the focal length $f = -50\, cm = -0.5\, m$. Since the focal length is negative,the lens is a concave lens. Its power $P = \frac{1}{-0.5} = -2\, D$.