Q. A hollow double concave lens is made of very thin transparent material. It can be filled with air or either of two liquids $L_{1}$ and $L_{2}$ having refractive indices $n_{1}$ and $n_{2}$ respectively $(n_{2} > n_{1} > 1)$. The lens will diverge a parallel beam of light if it is filled with
A) Air and placed in air
B) Air and immersed in $L_{1}$
C) $L_{1}$ and immersed in $L_{2}$
D) $L_{2}$ and immersed in $L_{1}$
Explanation
(d) $\frac{1}{f} = \left( \frac{n_{2}}{n_{1}} - 1 \right)\left( \frac{1}{R_{1}} - \frac{1}{R_{2}} \right)$ where $n_{2}$ and $n_{1}$ are the refractive indices of the material of the lens and of the surroundings respectively. For a double concave lens, $\left( \frac{1}{R_{1}} - \frac{1}{R_{2}} \right)$ is always negative
Hence $f$ is negative only when $n_{2} > n_{1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.