Question

A bright source S is kept on the principal axis of a concave mirror of focal length f = 20 cm at a distance d = 30 cm from its pole. Find the distance D in cm in front of the concave mirror where a plane mirror should be placed so that the ray, after being reflected first at the concave mirror and then by the plane mirror, returns to point S.

Answer 1

u = –30
f = –20
$v\Rightarrow \frac{uf}{u-f}\Rightarrow \frac{600}{-10}=-60$
For plane mirror, for the ray to return to S, the mirror must lie midway between S and $I_1$.
$\Rightarrow$ Distance of plane mirror from concave
mirror $=\frac{60+30}{2}=45\text{cm}$