Explanation

(c) According to lens maker’s formula
The focal length of plano convex lens is
[image:9_image87.emf]
$\frac{1}{f} = (n - 1)\left( \frac{1}{\infty} - \frac{1}{- R} \right)$
$\frac{1}{f} = \left( \frac{3}{2} - 1 \right)\left( \frac{1}{R} \right) = \frac{1}{2R}$
or $R = \frac{f}{2}$ …(i)
The focal length of liquid lens is
$\frac{1}{f_{1}} = \left( n_{l} - 1 \right)\left( \frac{1}{- R} - \frac{1}{\infty} \right)$
$\frac{1}{f_{1}} = \frac{(n_{l} - 1)}{R}$
$\frac{1}{f_{1}} = \frac{2(n_{l} - 1)}{f}$ [Using (i)]
Effective focal length of the combination is
$\frac{1}{2f} = \frac{1}{f} + \frac{1}{f_{1}}$
$\frac{1}{2f} = \frac{1}{f} - \frac{2\left( n_{l} - 1 \right)}{f} \Rightarrow 2\left( n_{l} - 1 \right) = 1 - \frac{1}{2} = \frac{1}{2}$
$\Rightarrow n_{l} - 1 = \frac{1}{4} \Rightarrow n_{l} = \frac{5}{4} = 1.25$