Question

A virtual image three time's the size of the object with a concave mirror of radius of curvature 36cm. Find the distance of the object from the mirror.

Answer 1

Given that,

Magnification $m=3$

We know that,

The magnification is

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

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

$v=-3u$

Now, by using mirror formula

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

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

$\frac{1}{f}=\frac{2}{3u}....\left(I\right)$

We know that,

$f=\frac{R}{2}$

$f=\frac{36}{2}$

$f=-18cm$

Now, put the value of f in equation (I)

$\frac{1}{f}=\frac{2}{3u}$

$\frac{-1}{18}=\frac{2}{3u}$

$-3u=36$

$u=-\frac{36}{3}$

$u=-12cm$

Hence, the distance of the object from the mirror is -$12cm$