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

Answer 1

The correct option is A $10cm$

Focal length of concave mirror $f=\frac{-R}{2}=\frac{-30}{2}=-15$ cm

Let the person stands at a distance $x$ infront of mirror i.e. $u=-x$

Magnification of image $m=3$

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

Or $3=\frac{-v}{-x}$ $⟹v=3x$

Using mirror formula : $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\therefore$ $\frac{1}{3x}+\frac{1}{-x}=\frac{1}{-15}$ $⟹x=10$ cm

Thus the person should stand at a distance of $10$ cm infront of the mirror.