A person looks into a spherical mirror. The size of the image of his face is twice the actual size of his face. If the face is at a distance of $20\text{cm}$ from the mirror, then the nature and radius of curvature of the mirror is

The correct option is D Concave, $80\text{cm}$
Given:
$m=+2$
$[$ as a person is able to see image of his face, so the image is virtual$]$
$u=-20\text{cm}$
So, $m=\frac{f}{f-u}$
$\Rightarrow +2=\frac{f}{f-(-20)}$
On solving this, we get,
$f=-40\text{cm}$
As focal length is negative, the mirror is concave.
Now, radius of curvature of the mirror,
$|R|=2|f|=80\text{cm}$