Question

Two identical thin biconvex lenses of focal length $15\, cm$ 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

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