Question

A diverging lens of focal length $20cm$ having refractive index $1.5$ is immersed in a liquid of refractive index $3$. The focal length and nature of the lens in liquid is

• A. $20cm$ divergent
• B. $20cm$ convergent
• C. $10cm$ divergent
• D. $10cm$ convergent

Answer 1

The correct option is B $20cm$ convergent

For a lens of refractive index $n$ immessed in a liquid of refractive index $n_r$ the focal length is
$\frac{1}{f}=(\frac{n}{n_r}-1)(\frac{1}{R_1}-\frac{1}{R_2})...\left(1\right)$
Given,
Focal length in air $=-20cm$ (divergent)
$\frac{1}{-20}=(\frac{1.5}{1}-1)(\frac{1}{R_1}-\frac{1}{R_2})$
$\Rightarrow (\frac{1}{R_1}-\frac{1}{R_2})=-\frac{1}{10}...\left(2\right)$
Substituting $\left(2\right)$ in $\left(1\right)$ gives

$\frac{1}{f}=(\frac{1.5}{n_r}-1)\left(\frac{-1}{10}\right)$
$\frac{1}{f}=(\frac{1.5}{3}-1)\left(\frac{-1}{10}\right)$
$=\frac{1}{20}$
$f=+20cm$
i.e., $20cm$ convergent.