Question

Two identical thin plano-convex glass lenses (refractive index $1.5$ ) each having radius of curvature of $20 \, cm$ 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. $-50 \, cm$
• D. $50 \, cm$

Answer 1

Answer: (C)

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

$\Rightarrow \frac{1}{f}=\frac{0.5}{R}$
$\Rightarrow \frac{1}{f_{c o n c a v e}}=\left(1.7 - 1\right)\left(- \frac{2}{R}\right)$
$\Rightarrow \frac{1}{f_{c o n c a v e}}=\frac{0.7 \times 2}{R}=-\frac{1.4}{R}$
$\therefore \frac{1}{f_{e q}}=\frac{0.5}{R}-\frac{1.4}{R}+\frac{0.5}{R}$
Also, $=\frac{- 0.4}{R}=\frac{- 0.4}{20}$
$\Rightarrow f_{e q}=-50 \, cm$