Question: 34. A point object is placed at a distance of 60 cm from a convex lens of focal length 30 cm . If a plane mirror were put perpendicular to the principal axis of the lens and at a distance of 40 cm from it, the final image would be formed at a distance of:
(1) 20 cm from the lens, it would be a real image.
(2) 30 cm from the lens, it would be a real image.
(3) 30 cm from the plane mirror, it would be a virtual image.
(4) 20 cm from the plane mirror, it would be a virtual image.
Answer: Option (4)
Explanation:
For the convex lens, focal length is f=+30\ \mathrm{cm}
and object distance is u=-60\ \mathrm{cm}.
Using the lens formula \frac{1}{f}=\frac{1}{v}+\frac{1}{u}.
Substituting values, \frac{1}{30}=\frac{1}{v}-\frac{1}{60}.
Solving, \frac{1}{v}=\frac{1}{30}+\frac{1}{60}=\frac{1}{20},
hence v=+20\ \mathrm{cm}.
Thus, the lens alone forms a real image at 20 cm to the right of the lens.
The plane mirror is placed 40 cm to the right of the lens, so this image lies 20 cm in front of the mirror.
A plane mirror forms a virtual image at the same distance behind the mirror.
Hence, the mirror forms a virtual image 20 cm behind it.
This virtual image now acts as an object for the lens during the return path of light.
Since the rays retrace their path through the lens, the final image is formed at the same position where the mirror image is located.
Therefore, the final image is formed 20 cm from the plane mirror and is virtual in nature.
Hence, the correct answer is Option (4).