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. $+80cm$
• B. $-80cm$
• C. $-24cm$
• D. $-100cm$

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)
$\Rightarrow \frac{1}{F}=-\frac{3}{100}+\frac{1}{20}-\frac{3}{100}$
$\Rightarrow F=-100cm$