Question

A shaving mirror has a radius of curvature of 30 cm. A man sees his image 2.5 times the size of his face. How far is the mirror from his face?

Answer 1

We know that a concave mirror is used as a shaving mirror.
Given, R = -30 cm
m = 2.5
$\therefore f=\frac{R}{2}=-15cm$
Now, $m=-\frac{v}{u}$
$\Rightarrow 2.5=-\frac{v}{u}$
$\Rightarrow v=-2.5u$
From the mirror formula, $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$
$\Rightarrow \frac{1}{-15}=-\frac{1}{2.5u}+\frac{1}{u}$
$\Rightarrow -\frac{1}{15}=\frac{-1}{2.5u}+\frac{2.5}{2.5u}$
$\Rightarrow u=-\frac{1.5\times 15}{2.5}=-9$
So, distance of face from the mirror = 9 cm.