Define power of a lens,obtain its equation and write its $SI$ unit.

(N/A) Power of a lens is a measure of the convergence or divergence,which a lens introduces in the light falling on it.
Clearly,a lens of shorter focal length bends the incident light more,converging it in the case of a convex lens and diverging it in the case of a concave lens.
The power $P$ of a lens is defined as the tangent of the angle by which it converges or diverges a beam of light falling at unit distance from the optical centre.
From the figure,
$\tan \delta = \frac{h}{f}$. If $h = 1$,then $\tan \delta = \frac{1}{f}$.
For small values of $\delta$,$\tan \delta \approx \delta$.
Therefore,$\delta = \frac{1}{f}$. Thus,Power $P = \frac{1}{f}$.
The $SI$ unit for the power of a lens is dioptre $(D)$.
$1 \ D = 1 \ m^{-1}$.
The power of a lens of focal length $1 \ m$ is one dioptre.
Power of a lens is positive for a converging lens and negative for a diverging lens.