Question

A plano-convex glass lens $({\mu }_g=3/2)$ of radius of curvature $R=10cm$ is placed at a distance of ${}^{\prime }{b}^{\prime }$ from a concave lens of focal length $20cm$.
What should be the distance ${}^{\prime }{a}^{\prime }$ of a point object $O$ from the plano-convex lens so that the position of final image is independent of ${}^{\prime }{b}^{\prime }$?

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

Answer 1

Answer: (B)

$60cm$

Focal length of plano convex lens is
$\frac{1}{f}=(\frac{3}{2}-1)(\frac{1}{10}-\frac{1}{\infty })$ or $f=20cm$
If point object $O$ is placed at a distance of $20cm$ from the plano-convex lens, rays becomes parallel and final image is formed at second focus or $20cm$ from concave lens which is independent of $b$.