Question

A plano convex glass lens $({\mu }_g=\frac{3}{2})$ of radius of curvature $R=10\text{cm}$ is placed at a distance of $b$ from a concave lens of focal length $20\text{cm}$. What should be the distance $a$ of a point object $O$ from the plano convex lens, such that the position of final image is always at same distance from concave lens?

• A. $40\text{cm}$
• B. $60\text{cm}$
• C. $30\text{cm}$
• D. $20\text{cm}$

Answer 1

The correct option is D $20\text{cm}$

Focal length of plano-convex lens is given by:

Using lens maker formula for plano convex lens,
$\frac{1}{f}=(\frac{{\mu }_l}{{\mu }_m}-1)(\frac{1}{R_1}-\frac{1}{R_2})$
$\frac{1}{f}=(\frac{3}{2}-1)(\frac{1}{10}-\frac{1}{\infty })$
$f=20\text{cm}$

If the object $O$ is placed at a distance $20\text{cm}$ from the plano-convex lens, the rays become parallel and the final image is formed at second focus or $20\text{cm}$ from the concave lens which is independent of $b$.

Why this question: This question checks the basic rules of image formation, for different positions of object.