Question

Design a shaving mirror assuming that a person keeps it 10 cm from his face and views the magnified image of the face at the closest comfortable distance of 25 cm. Find the focal length of the mirror.

Answer 1

If AB is the position of the face of the man, then A 'B' is the position of its image.
From the figure, $u=-10cm,v=+15cm$
Applying the mirror formula, $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}\Rightarrow \frac{1}{f}=\frac{1}{15}+\frac{1}{-10}=\frac{2-3}{30}=\frac{-1}{30}\Rightarrow f=-30cm$