How will you design a shaving mirror assuming that a person keeps it $10cm$ from his face and view the magnified image of the face at the closest comfortable distance of $25cm$. The radius of curvature of the mirror would then be:

The correct option is B $-33.3cm$
Given:

A person keeps a mirror at a distance of $10cm$ from his face and view the magnified image of the face at the closest comfortable distance of$25cm.$

Since magnified image on other side of mirror is produced it is clearly a concave mirror with case of object between POLE and FOCUS of mirror.

To find the radius of curvature of the mirror

Solution:

From given criteria,

Object distance, $u=-10cm$

Image distance, $v=25cm$ refer above fig.

Applying the mirror formula, we get

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}⟹\frac{1}{f}=\frac{1}{25}+\frac{1}{(-10)}⟹\frac{1}{f}=\frac{-3}{50}⟹f=\frac{-50}{3}cm$

And Radius of curvature, $R=2f=2\times \frac{-50}{3}=-33.3cm$

Hence the radius of curvature of the mirror will be $-33.3cm.$