Question

Two identical thin plano-convex glass lenses (refractive index $1.5$ ) each having radius of curvature of $20cm$ are placed with their convex surfaces in contact at the centre. The intervening space is filled with the oil of refractive index $1.7$ . The focal length of the combination is:

• A. $-20cm$
• B. $-25cm$
• C. $-50cm$
• D. $50cm$

Answer 1

Answer: (C)

Consider the situation shown in figure.
As $\frac{1}{f}=\left(1.5-1\right)\left(\frac{1}{R}-\frac{1}{\in fty}\right)$

$\Rightarrow \frac{1}{f}=\frac{0.5}{R}$
$\Rightarrow \frac{1}{f_{concave}}=\left(1.7-1\right)\left(-\frac{2}{R}\right)$
$\Rightarrow \frac{1}{f_{concave}}=\frac{0.7\times 2}{R}=-\frac{1.4}{R}$
$\therefore \frac{1}{f_{eq}}=\frac{0.5}{R}-\frac{1.4}{R}+\frac{0.5}{R}$
Also, $=\frac{-0.4}{R}=\frac{-0.4}{20}$
$\Rightarrow f_{eq}=-50cm$