Question

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

Answer 1

$u=-25cm$
$m=\frac{A^{\prime }{B}^{\prime }}{AB}=-\frac{v}{u}\Rightarrow 1.4=-\left(\frac{v}{-25}\right)\Rightarrow \frac{14}{10}=\frac{v}{25}$'
$\Rightarrow v=\frac{25\times 14}{10}=35cm$
Now, $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{f}=\frac{1}{35}-\left(\frac{1}{-25}\right)=\frac{5-7}{175}=-\frac{2}{175}\Rightarrow f=-87.5cm$
So, focal length of the concave mirror is $87.5cm$.