Question

The image of a square hole in a screen illuminated by light is obtained on another screen with the help of a converging lens. The distance of the hole from the lens is $40cm$. If the area of the image is nine times that of the hole, the focal length of the lens is :

• A. $30cm$
• B. $50cm$
• C. $60cm$
• D. $75cm$

Answer 1

The correct option is A $30cm$

Given, $\frac{A^{\prime }}{A}=m^2$

$9=m^2$

Magnification, $m=3=\frac{v}{u}$

We have $u=40cm$

$\therefore v=120cm$

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\frac{1}{120}-\frac{1}{-40}=\frac{1}{f}$

$f=30cm$