Question

Two identical equal convex lesses of focal length f are kept in contact. The space between them is filled with water $({\mu }_w=\frac{4}{3})$. The focal length of the combination is $({\mu }_g=\frac{3}{2})$

• A. f
• B. $\frac{f}{2}$
• C. $\frac{4f}{3}$
• D. $\frac{3f}{4}$

Answer 1

The correct option is D $\frac{3f}{4}$

$\frac{1}{F}=\frac{1}{f}+\frac{1}{f}+\frac{1}{f_w}\frac{1}{f_w}=-({\mu }_w-1)\left[\frac{2}{R}\right]\frac{1}{f}=({\mu }_s-1)\frac{2}{R}\frac{1}{f}=(\frac{3}{2}-1)\frac{2}{R};R=f\frac{1}{f_w}=-(\frac{4}{3}-1)\frac{2}{f}=-\frac{2}{3f}\frac{1}{F}=\frac{2}{f}-\frac{2}{3f=\frac{6-2}{3f}}=\frac{4}{3f}F=\frac{3f}{4}$