Question 222 of 295

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 _____ $cm.$

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Answer: 10

For convex lenses, let radius of curvature is $R$. Then,
$\dfrac{1}{15cm}=\left(1.5-1\right)\left(\dfrac{1}{R}-\dfrac{1}{-R}\right)$
$\Rightarrow \dfrac{1}{R}=\dfrac{1}{15}\Rightarrow R=15cm$
Now for concave lens,
$\dfrac{1}{{f}_{concave}}=\left(1.25-1\right)\left(\dfrac{1}{-R}-\dfrac{1}{R}\right)$
$=\dfrac{1}{4}\times -\dfrac{2}{R}=\dfrac{-1}{30}$
$\dfrac{1}{{f}_{eff}}=\dfrac{1}{15}+\dfrac{1}{15}-\dfrac{1}{30}=-\dfrac{1}{10}$
$\Rightarrow {f}_{eff}=-10cm$