Question

Two thin equi - convex lenses each of focal length f and made of glass $({\mu }_g=\frac{3}{2})$ are placed in contact. The space between them is filled with water $({\mu }_w=\frac{4}{3})$. The focal length of the combination is

• A. $\frac{f}{2}$
• B. $\frac{2f}{3}$
• C. $\frac{3f}{4}$
• D. $\frac{4f}{7}$

Answer 1

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


$\frac{1}{f_{eq}}=\frac{1}{f}+\frac{1}{f_1}+\frac{1}{f}=\frac{2}{f}+\frac{1}{f_1}Where,\frac{1}{f}=(\frac{3}{2}-1)(\frac{1}{+R}-\frac{1}{(-R)})=\frac{1}{R}\therefore \frac{1}{f_1}=\frac{-2}{3f}\Rightarrow \frac{1}{f_{eq}}=\frac{2}{f}-\frac{2}{3f}\Rightarrow f_{eq}=\frac{3f}{4}$