Question

The power of a lens is $5D$. Find its focal length.

Answer 1

First we will define the power of a lens and how it differs in different lenses, its Si unit and finally the relation between power and focal length of a lens. There is an inverse relation between the power and the focal length of a lens. And using that relation we can find the focal length where power is known to us. The power of the lens is positive for convex lenses and negative for concave lenses.

Complete step by step answer:
Power of a lens is the ability of a lens to bend the light rays. In a convex lens it converges the light ray towards the principal axis whereas in a concave lens it diverges the light rays away from the principal axis. And in this way lenses bends the light rays that are incident on it.
A lens that has shorter focal length bends the light ray more, hence it has greater power or we can say focal length decreases with increase in power and vice versa. Hence power of a lens is defined as the reciprocal of its focal length which is in meters.
So mathematically we can write,
$P = \dfrac{1}{f}$
Where,
P is the power of a lens.
And f is the focal length of the lens.
We know,
$P = + 5D$
Unit of power of the lens is meter inverse and SI unit is diopter denoted as D.
Now putting this vale we can say focal length as,
$5D = \dfrac{1}{f}$
$f = 0.2m = 20cm$

Note: Remember that greater the power of a lens the greater is the ability to refract light or in other word we can say power of a lens has a direct relation with refraction of light. Another important point to note about power of a lens is that for a convex lens a converging ability is defined by power while in a concave lens the diverging ability defines.