A thin lens made of glass (refractive index $=1.5$ ) of focal length $f=16 \mathrm{~cm}$ is immersed in a liquid of refractive index 1.42. If its focal length in liquid is $f_{l}$, then the ratio $f_{l}$ /f is closest to the integer:
Correct Option: 2
(2) Using lens maker's formula
$\frac{1}{f}=\left(\frac{\mu_{g}}{\mu_{a}}-1\right)\left[\frac{1}{R_{1}}-\frac{1}{R_{2}}\right]$
Here, $\mu_{g}$ and $\mu_{a}$ are the refractive index of glass and air respectively ....(i)
$\Rightarrow \frac{1}{f}=(1.5-1)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)$
When immersed in liquid
$\frac{1}{f_{l}}=\left(\frac{\mu_{g}}{\mu_{l}}-1\right)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)$
Dividing (i) by (ii)
$\Rightarrow \quad \frac{f_{l}}{f}=\frac{(1.5-1) 1.42}{0.08}=\frac{1.42}{0.16}=\frac{142}{16} \approx 9$