Question

Two identical thin biconvex lenses of focal length $15cm$ and refractive index $1.5$ are in contact with each other. The space between the lenses is filled with a liquid of refractive index $1.25$. The focal length of the combination is ____$cm$.

Answer 1

Answer: 10

$\frac{1}{f_1}=\frac{1}{15}=\left(\frac{3}{2}-1\right)\left[\frac{2}{R}\right]$
$\frac{1}{R}=\frac{1}{15}$
$\frac{1}{f_{eq}}=\frac{1}{f_1}+\frac{1}{f_2}+\frac{1}{f_3}$
$=\frac{1}{15}+\left(\frac{5}{4}-1\right)\left[\frac{-2}{R}\right]+\frac{1}{15}$
$=\frac{1}{15}-\frac{1}{30}+\frac{1}{15}$
$=\frac{2-1+2}{30}$
$=\frac{3}{30}=\frac{1}{10}$
$=10$