Question

How far should an object be kept from the concave mirror of focal length 20 cm to form a real image one-fifth of its size?

Answer 1

$m=\left(-\frac{1}{5}\right)=-\frac{V}{U}$

$\Rightarrow \frac{V}{U}=\frac{1}{5}$

$\Rightarrow V=\frac{U}{5}$

Now by applyng the mirror formula
$\frac{1}{U}+\frac{1}{V}=\frac{1}{f}$

$\frac{1}{U}+\frac{5}{U}=\frac{-1}{20}$

$\frac{6}{U}=\frac{-1}{20}$
$U=-120cm$