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Q.
A thin lens made of glass (refractive index $= 1.5$) of focal length $f= 16\, cm$ 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 :
JEE MainJEE Main 2020Ray Optics and Optical Instruments
Solution:
Using $\frac{1}{f} = \left(\frac{\mu_{2}}{\mu_{1}}-1\right)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)$
$\frac{1}{f} = \left(\frac{1.5}{1}-1\right)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right) \quad....\left(1\right)$
and $\frac{1}{f} = \left(\frac{1.5}{1.42}-1\right)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right) \quad ....\left(2\right)$
equation $\left(1\right)/\left(2\right)$,
we get $\frac{f_{1}}{f} = \frac{0.5}{0.056}$
$= 8.93 \approx 9$