Question

Shown in figure here is a convergent lens placed inside a cell filled with a liquid. The lens has focal length +20 cm when in air and its material has refractive index 1.50. If the liquid has refractive index 1.60, the focal length of the system is

• A. + 80 cm
• B. – 80 cm
• C. – 24 cm
• D. – 100 cm

Answer 1

The correct option is D – 100 cm

Here $\frac{1}{f_1}=(1.6-1)(\frac{1}{\infty }-\frac{1}{20})=\frac{-3}{100}......\left(i\right)$
$\frac{1}{f_2}=(1.5-1)(\frac{1}{20}-\frac{1}{-20})=\frac{1}{20}.......\left(ii\right)\frac{1}{f_3}=(1.6-1)(\frac{1}{-20}-\frac{1}{\infty })=\frac{-3}{100}.......\left(iii\right)$
By using $\frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}+\frac{1}{f_3}\Rightarrow \frac{1}{F}=\frac{-3}{100}+\frac{1}{20}-\frac{3}{100}\Rightarrow F=-100cm$