Question

A man uses a concave mirror for shaving. He keeps his face at a distance of 25 cm from the mirror and gets an image which is 1.4 times enlarged. Find the focal length of the mirror.

Answer 1

u = -25 cm

$m=\frac{A_1{B}_1}{AB}=\frac{u}{v}$

$\Rightarrow 1.4=-\frac{\left(v\right)}{-25}$

$\Rightarrow \frac{14}{10}=\frac{v}{25}$

$\Rightarrow v=\frac{25\times 14}{10}=35\text{cm}$

Now, $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

$\Rightarrow \frac{1}{f}=\frac{1}{35}-\frac{1}{25}$

$=\frac{5-7}{175}=-\frac{2}{175}$

$\Rightarrow f=-87.5$

So, focal length of the concave mirror is 87.5 cm.