Question

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

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

Answer 1

Answer: (C)

Focal length of the plano-convex lens is
$ \frac{1}{f}=({{\mu }_{0}}-1)\left( \frac{1}{20}-\frac{1}{\infty } \right) $
$ =\left( \frac{3}{2}-1 \right)\left( \frac{1}{20} \right)=\frac{1}{2}\times \frac{1}{20} $
$ \Rightarrow $ $ t=40\,cm $
If point object O is placed at a distance of 40 cm from the plano-convex lens, rays become parallel and final image is formed at second focus or 40 cm from concave lens which is independent of a.