A convex mirror has its radius of curvature $20cm$. Find the position of the image of an object placed at a distance of $12cm$ from the convex side of mirror.

The correct option is A $\frac{60}{11}cm$
From mirror formula, $\frac{1}{u}+\frac{1}{v}=\frac{1}{f};u$ is $-ve$ $(\because f=\frac{R}{2}=\frac{20}{2}=10cm)$
$\frac{1}{v}=\frac{1}{f}-\frac{1}{u}$
$=\frac{-1}{10}+\frac{-1}{12}=-\left(\frac{5+6}{60}\right)=\frac{-11}{60}$ $(\because f$ is $-ve$ for a concave mirror$)$
$\therefore v=\frac{60}{11}cm$
So the distance of the image is $\frac{60}{11}cm$ and it is virtual $(-ve)$