Question

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.

Answer 1

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 $\frac{-80}{3}cmand\frac{-40}{3}cm$.