Question

What is meant by the power of a lens? Write its SI unit. A student uses a lens of the focal length of $40\mathrm{cm}$ and another of $20\mathrm{cm}$. Write the nature and power of the lens.

Answer 1

Definition

The power of a lens is defined as the inverse of its focal length measured in $\mathrm{meters}\left(\mathrm{m}\right)$.

1. The S.I unit of power is $\mathrm{Dioptre}\left(\mathrm{D}\right)$.
2. Formula: $\mathrm{Power}\mathrm{of}\mathrm{lens}=\frac{1}{\mathrm{Focal}\mathrm{length}}$

Nature and power of the lens

Step 1: Given:

The focal length of 1^st lense,

$$\begin{gathered} {\mathrm{f}}_1=40\mathrm{cm} \\ =0.4\mathrm{cm} \end{gathered}$$

The focal length of the 2^nd lense,

$$\begin{gathered} {\mathrm{f}}_2=20\mathrm{cm} \\ =0.2\mathrm{m} \end{gathered}$$

Step 2: Power of Lenses:

The power of the first lens will be:

$$\begin{gathered} {\mathrm{P}}_1=\frac{1}{{\mathrm{f}}_1} \\ =\frac{1}{0.4} \\ =2.5\mathrm{D} \end{gathered}$$

It is convex in nature.

The power of the second lens will be:

$$\begin{gathered} {\mathrm{P}}_2=\frac{1}{{\mathrm{f}}_2} \\ =\frac{1}{0.2} \\ =5\mathrm{D} \end{gathered}$$

It is convex in nature.

Therefore, the power of the lens is $2.5\mathrm{D}$ and $5\mathrm{D}$.