Question

A plano-convex glass lens $({\mu }_g=3/2)$ of radius of curvature $R=20cm$ is placed at a distance ${}^{\prime }{a}^{\prime }$ from a concave lens of focal length $40cm$. What should be the distance ${}^{\prime }{b}^{\prime }$ of a point object $O$ from plano-convex lens so that the position of final image is independent of $a$?

• A. $20cm$
• B. $60cm$
• C. $40cm$
• D. $30cm$

Answer 1

The correct option is C $40cm$

Focal length of the plano-convex lens is,

$\frac{1}{f}=({\mu }_0-1)(\frac{1}{20}-\frac{1}{\infty })$

$\therefore f=40cm$

If point object O is placed at a distance 40 cm from plano-convex lens, rays becomes parallel and final image is formed at second focus or 40 cm from concave lens which is independent of a.