Question

A point source of light ${}^{\prime }{S}^{\prime }$ is placed on the principal axis of the concave mirror at a distance of $60\text{cm}$. At what distance from the concave mirror should a flat mirror be placed, for the rays to converge at the source after two successive reflections $($first one from the concave mirror$)$?
$[$Radius of curvature of concave mirror is $80\text{cm}]$

Answer 1

For first reflection at concave mirror,
$u=-60\text{cm},f=\frac{-80}{2}=-40\text{cm}$
Using mirror formula,
$\frac{1}{v}-\frac{1}{60}=\frac{-1}{40}$
$\Rightarrow \frac{1}{v}=\frac{-1}{120}$
$\Rightarrow v=-120\text{cm}$
The first image will be formed at $120\text{cm}$ from the concave mirror in front of it.

From the ray diagram, we can see that,
$60+x+x=120$
$\Rightarrow x=30\text{cm}$
So, the flat mirror should be placed at the distance of $60+30=90\text{cm}$ from the concave mirror.

Why this question? It requires your understanding of the virtual object and phenomenon of successive reflections from the mirrors.