Question

A focal length of a concave mirror is $30cm$. Where should an object be placed so that its image is three times magnified, real and inverted ?

Answer 1

Given,

Focal length, $f=-30cm$ if $u=-x$

real $\Rightarrow$ same side $\Rightarrow v=-ve$

Magnification, $m=\frac{v}{u}\Rightarrow v=m\times u=3\times (-x)=-3x$

From mirror formula, $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

We get $\frac{1}{-30}=\frac{1}{-3x}+\frac{1}{-x}\Rightarrow \frac{1}{30}=\frac{1+3}{3x}$

$\Rightarrow \frac{3x}{4}=3\Rightarrow x=40cm$

So object should be placed at $40cm$ to the mirror.