Question

A person looks into a spherical mirror. The size of image of his face is twice the actual size of his face. If the face is at a distance 20 cm then find the nature of radius of curvature of the mirror.

Answer 1

The only mirror that forms the magnified virtual image is the $concave$ mirror.

$m=\frac{-v}{u}=2⟹v=-2u$

And, $u=-20cm$

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

$⟹\frac{1}{40}+\frac{-1}{20}=\frac{1}{f}$

$⟹f=-40cm$

Hence, radius of curvature is $R=2f=80cm$ and the mirror is concave.