Question

The focal length of a concave mirror is $50cm$. Where should an object be placed, so that its image is two times and is inverted

• A. $75cm$
• B. $60cm$
• C. $125cm$
• D. $50cm$

Answer 1

The correct option is A $75cm$

Magnification formula for a mirror is given as $m=-\frac{v}{u}$

Given, that the image formed should be two times and inverted

Hence, $m=-2$

$\Rightarrow -2=-\frac{v}{u}$

$\Rightarrow v=2u$

Using the mirror's formula , $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

Since, mirror is concave. We have $f=-50cm$

$\Rightarrow \frac{1}{2u}+\frac{1}{u}=-\frac{1}{50}$

$\Rightarrow \frac{3}{2u}=-\frac{1}{50}$

$\Rightarrow u=-75cm$

Hence, object should be placed $75cm$ in front of the mirror.