Question

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 $L_i$
• C. $L_1$ and immersed in $L_2$
• D. $L_2$ and immersed in $L_1$

Answer 1

The correct option is D $L_2$ and immersed in $L_1$

$\frac{1}{f}=(\frac{n_2}{n_1}-1)(\frac{1}{R_1}-\frac{1}{R_2})$ 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,$(\frac{1}{R_1}-\frac{1}{R_2})$ is always negative.

Hence f is negative only when $n_2>n_1$