Question

A pair of mirror and lens are placed or shown in figure. A beam of light coming from $\infty$, after refraction falls on mirror, if light ray retraces its path after reflection, find "d".

• A. d = 18 cm
• B. d = 6 cm
• C. d = 12 cm
• D. d = 4 cm

Answer 1

The correct option is B d = 6 cm

For the light to retrace its path, the focus of the lens and the centre of curvature of the mirror should coincide as to make the angle of incidence at mirror to the angle of reflection from mirror.
So given that
Focal length of lens $f=30\text{cm}$
Focal length of mirror $f^{\prime }=12\text{cm}$
So Radius of curvature of mirror $=2f^{\prime }=2\times 12=24\text{cm}$
Now distance between lens and mirror $d$ is given by
$d+24=30$
$d=6\text{cm}$