Question

A hollow double concave lens is made of very thin transparent material. It can be filled with air or either of two liquids $L_1\space and\space L_2$ having refracting indices $n_1\space and\space n_2$ 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 $L_1$

Answer 1

Answer: (D)

$L_2$ and immersed in $L_1$

Answer 2

The correct answer is D:$L_2$ and immersed in $L_1$
The lens makers' formula is
$\frac{1}{f}=\Bigg(\frac{n_L}{n_m}-1\Bigg)\Bigg(\frac{1}{R_1}-\frac{1}{R_2}\Bigg)$
where, $n_L$ = Refractive index of lens and
$n_m$ = Refractive index of medium.
In case of double concave lens, $R_1$ is negative and $R_2$ is
positive.
Therefore $\Bigg(\frac{1}{R_1}-\frac{1}{R_2}\Bigg)$ I will be negative.
For the lens to be diverging in nature, focal length f should
be negative or $\Bigg(\frac{n_L}{n_m}-1\Bigg)$ should be positive or $n_L > n_m$ but
since, $n_2 > n_1$ x (given), therefore the lens should be filled with
$L_2$ and immersed $L_1$.