An object is kept in front of a concave mirror of focal length 20 cm. The image is three times the size of the object.Calculate two possible distance of the object from the mirror.

It is given that,

Focal length

$f=-20cm$

$h_i=3h_o$

The image is three times the size of the object. So there are two cases.

Case 1. For real image

$m=-\frac{v}{u}=-3$

$v=3u$

Using mirror’s formula

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

$\frac{1}{-20}=\frac{1}{3u}+\frac{1}{u}$

$u=\frac{-80}{3}cm$

Case 2. For virtual image

$m=\frac{-v}{u}=+3$

$v=-3u$

Again using mirror’s formula

$\frac{1}{-20}=\frac{1}{-3u}+\frac{1}{u}$

$u=\frac{-40}{3}cm$

The possible values of u are $\frac{-80}{3}cmand\frac{-40}{3}cm$.