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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

A

20 cm from the lens, it would be a real image

B

30 cm from the lens, it would be a real image

C

30 cm from the plane mirror, it would be a virtual image

D

20 cm from the plane mirror, it would be a virtual image

Step-by-Step Solution

Using lens formula for first refraction from convex lens: 1v−1u=1f\frac{1}{v} - \frac{1}{u} = \frac{1}{f}. u=−60u = -60 cm, f=30f = 30 cm. 1v−1−60=130⇒1v=130−160=160⇒v=60\frac{1}{v} - \frac{1}{-60} = \frac{1}{30} \Rightarrow \frac{1}{v} = \frac{1}{30} - \frac{1}{60} = \frac{1}{60} \Rightarrow v = 60 cm. The image is formed 60 cm from the lens, which is 20 cm behind the mirror. The mirror reflects this to form a virtual image 20 cm in front of the mirror.

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