Question

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.

Answer 1

Answer: (D)

Position of the image formed by lens.
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\frac{1}{v}+\frac{1}{60}=\frac{1}{30}$
$\frac{1}{v}=\frac{1}{30}-\frac{1}{60}=\frac{1}{60}$
$v=60 \,cm$
So, position of the image is $(60-40)=20\, cm$ behind the plane mirror, it acts as a virtual object. So final image is a real image $20\, cm$ from the plane mirror.
This real image will act as an object for the lens and final image is
$\frac{1}{v}+\frac{1}{20}=\frac{1}{30}$
$\frac{1}{v}=\frac{-1}{60}$
$v=-60\, cm$ from lens
i.e., $20\, cm$ behind the plane mirror.