Question

A thin hollow equi-convex lens, silvered at the back, converges a parallel beam of light at a distance of $0.2$m in front of it. Where will it converge the same light if filled with water having $\mu =4/3$?

Answer 1

When lens is hollew , it will act as a concave mirror

$\because$ Parallel beam is focused at focus at mirror

$f=-0.2m(\therefore R=2f=-0.4m)$

When filled with water

Pnet $=2P_L+P_M=2(\frac{4}{3}-1)(\frac{1}{R}-\frac{1}{(-R)})+\frac{1}{-(-0.2)}$

$=\frac{2}{3}\times \frac{2}{2}+\frac{1}{0.2}=\frac{50}{6}(R=0.4m)$

fnet $=\frac{-1}{Pnet}=\frac{-6}{50}=-0.12m$

$\therefore$ parallel beam will now be focused at a distance of $12m$ from the lens (on the order of object.)