Question

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

Answer 1

Hint : The focal length of a lens is the distance from the lens at which parallel rays will converge after getting refracted from a lens. The focal length is also the inverse of the power of a lens.

Formula Used: In this solution we will be using the following formula,
$f = \dfrac{1}{D}$ where $f$ is the focal length and $D$ is the power of the lens

Complete step by step answer
We’ve been given that the power of a lens is -5 dioptres or -5D. The focal length of any lens is the inverse of the power of the lens. So, we can find the focal length of the lens usually represented by the variable $f$ as
$f = \dfrac{1}{D}$
$\Rightarrow f = \dfrac{1}{{ - 5}}$
Multiplying the numerator and the denominator with 2 on the right side of the above equation, we get
$f = \dfrac{2}{{ - 10}}$
$\therefore f = - 0.2\,m$.

Additional Information
The dioptre is the unit of measure for the refractive power of a lens. The diameter of a lens has the units of inverse length. The power of a reading glass has a power usually from $+ 0.75\,D$ to $+ 3.00\,D$ . The longer the viewing distance, the less reading power is needed for the lens, and the smaller the viewing distance, the higher the power of lenses needed. Dioptres are usually preferred to focal length since the lens formula uses the inverse of image distance, object distance, and focal length so our calculations are simplified.

Note
We should be aware of the simple relation of the focal length as the inverse of the power of the lens. Since the focal length of the lens is negative, the lens will be concave in nature as concave lenses have a negative focal length while convex lenses have a positive focal length.