Question

A thin lens made of glass (refractive index $=1.5$) of focal length $f=16cm$ 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 :

• A. $9$
• B. $1$
• C. $5$
• D. $17$

Answer 1

Answer: (A)

Using $\frac{1}{f}=\left(\frac{{\mu }_2}{{\mu }_1}-1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$
$\frac{1}{f}=\left(\frac{1.5}{1}-1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)....\left(1\right)$
and $\frac{1}{f}=\left(\frac{1.5}{1.42}-1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)....\left(2\right)$
equation $\left(1\right)/\left(2\right)$,
we get $\frac{f_1}{f}=\frac{0.5}{0.056}$
$=8.93\approx 9$