• # question_answer  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

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.