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 oil of refractive index $\mathrm{1.7.}$ The focal length of the combination is :

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

Answer 1

The correct option is C $-50cm$

Given, ${\mu }_g=1.5,{\mu }_{oil}=1.7,R=20cm$

From lens maker's formula for plano convex lens,

$\frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})$

Here $R_1=R$ and for plane surface $R=\infty$

$\frac{1}{f_{lens}}=(15-1)(\frac{1}{R}-0)$

$\frac{1}{f_{lens}}=\frac{0.5}{R}$

When intervening medium is filled with oil,

$\frac{1}{f_{concave}}=(1.7-1)(-\frac{1}{R}-\frac{1}{R})$

$=-0.7\times \frac{2}{R}=\frac{-14}{R}$

Here we have 2 concave surfaces,

So, $\frac{1}{f_{eq}}=2\times \frac{1}{f}+\frac{1}{f}$

$=2\times \frac{0.5}{R}+\frac{-14}{R}=\frac{1}{R}-\frac{14}{R}=\frac{-0.4}{R}$

So $f_{eq}=\frac{-R}{0.4}=\frac{-20}{0.4}=-50cm$