Question

A point source of light is kept at 50 cm from a concave mirror of focal length 30 cm. A convex lens of focal length 12 cm is placed between source and mirror as shown in figure at distance 'x' from source. Possible values of 'x' so that ray of light emerging from source after refraction from lens then reflection from mirror and then again refraction from lens can reach source is

• A. 10 cm
• B. 20 cm
• C. 30 cm
• D. 40 cm

Answer 1

Answer: (A), (B), (C)

The correct options are
A 10 cm
B 20 cm
C 30 cm


Case 1: The image of the lens fals exactly at the pole of the mirror.
For the lens, $v=50-x$ and $u=-x$
$\frac{1}{12}=\frac{1}{(50-x)}+\frac{1}{x}$

Solving we get

$x=30\text{or}20$ cm


Case 2: The image of the lens falls exactly on the centre of curvature of the mirror.
For the lens, $v=-60$ and $u=-x$
$\frac{1}{12}=\frac{1}{-60}+\frac{1}{x}$

$\frac{1}{x}=\frac{1}{12}+\frac{1}{60}\Rightarrow x=10$cm