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)

-100 cm

Focal length of lens= $+20cm$

Refractive Index in air= $1.5$

Refractive Index in liquid= $1.6$

$F=?$

By using, $\frac{1}{f}=(u-1)(\frac{1}{R}-\frac{1}{R_2})$

$\Rightarrow \frac{1}{f_1}=(1.6-1)(\frac{1}{\infty }-\frac{1}{20})$

$=\frac{-3}{100}\to \left(1\right)$

$\Rightarrow \frac{1}{f_2}=(1.5-1)(\frac{1}{20}-\frac{1}{-20})$

$=\frac{1}{20}\to \left(2\right)$

$\Rightarrow \frac{1}{f_3}=(1.6-1)(\frac{1}{-20}-\frac{1}{\infty })=\frac{-3}{100}\to \left(3\right)$

Therefore,

$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}+\frac{1}{f_3}$

$=\frac{-3}{100}+\frac{1}{20}-\frac{3}{100}$

$=-\frac{60+100}{2000}-\frac{3}{100}$

$\Rightarrow F=-100cm$