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# A hollow double concave lens is made of very thin transparent material It can be filled with air or either of two liquids $L_1$ or $L_2$ having refracting 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) $L_2$ and immersed in $L_1$ (b)air and immersed in $L_1$ (c) $L_1$ and immersed in $L_2$ (d)air and placed on air

The makers formula is
$\large\frac{1}{f} =\bigg( \large\frac{n_L}{n_m}-1 \bigg) \bigg( \frac{1}{R_1}-\frac{1}{R_2}\bigg)$
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.
$\therefore \bigg( \large \frac{1}{R_1}-\large\frac{1}{R_2} \bigg)$ will be negative.
For the lens to be diverging in nature, focal length 'f' should be negative or $\bigg( \large\frac{n_L}{n_m}-1 \bigg)$ should be +ve or $n_L > n_m$ but since $n_2 > n_1 (given)$
$\therefore$ the lens should be filled with $L_2$ and immersed in $L_1$
Hence a is the correct answer.

edited Jul 24, 2014