Question

Shown in the 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

Answer: (D)

$\frac{1}{F}=\frac{1}{f_{1}}+\frac{1}{f_{2}}+\frac{1}{f_{3}}$

$ \frac{1}{f_{1}} =(1.6-1)\left(\frac{1}{\infty}-\frac{1}{20}\right)=-\frac{0.6}{20}=-\frac{3}{100} $ ....(i)
$ \frac{1}{f_{2}} =(1.5-1)\left(\frac{1}{20}-\frac{1}{-20}\right)=\frac{1}{20}$ .....(ii)
$ \frac{1}{f_{3}} =(1.6-1)\left(\frac{1}{-20}-\frac{1}{\infty}\right)=-\frac{3}{100} $ .....(iii)
$\Rightarrow \frac{1}{F} =-\frac{3}{100}+\frac{1}{20}-\frac{3}{100}$
$ \Rightarrow F=-100 \,cm$