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 $n_{2} > n_{1}$