Physics Question on Ray optics and optical instruments

Question

A person wants a real image of his own, $3$ times enlarged. Where should he stand infront of a concave mirror of radius of curvature $30\, cm$ ?

Answer 1

Solution

Given, $m = - 3, R = 30 \,cm$ ,
$f=-\frac{R}{2}=-15\, cm$
We know that, $m=-\frac{v}{u}$
$\Rightarrow \,-3=\frac{-v}{u}$
$v = 3 \,u$
We know that, $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$
$\frac{1}{-15}=\frac{1}{3u}+\frac{1}{u}$
$\frac{-1}{15}=\frac{1+3}{3u}$
$-3u=4\times15$
$u=\frac{-4\times15}{3}$
Initial position of a person,
$u = - 20\, cm$