Question

The diagram shows a mirror system. If after two reflections the image and the object $O$ coincide with each other, then the value of radius of curvature (in metre) of the concave mirror is (Take $a=3\, m$ )

Answer 1

For the image to coincide with object, image formed by concave mirror must be at $a$ in front of plane mirror.
$\therefore \frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$ \Rightarrow \frac{1}{-2 a}+\frac{1}{-4 a}=\frac{1}{f} $
$\Rightarrow f=-4 \,m$
$\therefore R=8 \,m$