Question

A person with myopic eyes is not able to see objects beyond $3m$. Determine the nature, focal length, and power of the correcting lens.

Answer 1

Step 1: Find the focal length of the lens.

Image distance, $v=-3m$

Object distance, $u=-\infty$

Use the lens formula, $\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$

Substitute the known parameters in the lens formula as-

$$\begin{gathered} \frac{1}{u}+\frac{1}{v}=\frac{1}{f} \\ \Rightarrow \frac{1}{\infty }+\left(\frac{1}{-3}\right)=\frac{1}{f} \\ \Rightarrow \frac{1}{f}=\frac{-1}{3} \\ \Rightarrow f=-3m \end{gathered}$$

So, the focal length is $3m$.

Step 2: Find the power of the correcting lens

The power of the correcting lens is given as - $P=\frac{1}{f}$

Substitute the known parameters in the power formula as-

$$\begin{gathered} P=\frac{1}{f} \\ =\frac{-1}{3} \\ =-0.33dioptre \end{gathered}$$

The nature of the lens for the myopic eyes is concave lens.

So, the nature, focal length, and power of the correcting lens for the myopic eyes are concave lens , $3m$ and $-0.33dioptre$ respectively.