Question

A plano-convex lens $\left(\mu \, = \frac{3}{2}\right)$ has a radius of curvature $R=15 \, cm$ and is placed at a distance $z$ from a concave lens of focal length $20 \, cm$ as shown. At what distance $x_{0}$ should a point object be placed from the plano-convex lens, so that position of the final image is independent of $z$ ?

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

Answer 1

Answer: (B)

The position of the final image will be independent of $z$ , only if the rays of light are incident on the concave lens as a beam parallel to the principal axis. This will be possible only when the object is kept at focus of the plano-convex lens.
$\therefore \frac{1}{x_{0}}=\frac{1}{f_{1}}=\left(\right.\mu -1\left.\right)\left[\frac{1}{R_{1}} - \frac{1}{R_{2}}\right]=\left(\frac{3}{2} - 1\right)\left[\frac{1}{15} - \frac{1}{\infty}\right]$
$\Rightarrow x_{0}=30 \, cm$