Question

A long-sighted person has a distance of distinct vision of $40cm$. Find the nature and the focal length of the lens used by him to read a book $20cm$ from the eye, using spectacles.

Answer 1

Step 1: Given data

The distance at which the user wants to reads the book is $u=-20cm$

The distance of the actual near point is $v=-40cm$

Step 2: Finding the focal length

Using lens formula, $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\Rightarrow \frac{1}{f}=\frac{1}{-40cm}-\frac{1}{-20cm}$

$\Rightarrow \frac{1}{f}=\frac{1}{40cm}$

By taking reciprocal on each side, we get,

$f=40cm$

Here, the positive sign is indicating the converging nature of the lens.

Hence, a convex lens of the focal lens $f=40cm$ is to be used.