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 $\left(n_2>n_1>1\right)$. 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 $L_1$

Answer 1

Answer: (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 $n_2>n_1$