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 $30cm$ ?

• A. 10 cm
• B. 30 cm
• C. 90 cm
• D. 20 cm

Answer 1

Answer: (D)

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