Question

A thin bi-convex lens of focal length $20cm$ is made of glass of refractive index $1.5$. When it is dipped in a liquid of refractive index $\frac{9}{8}$, it acts as a:

• A. convex lens of focal length $150cm$
• B. concave lens of focal length $30cm$
• C. convex lens of focal length $30cm$
• D. concave lens of focal length $15cm$

Answer 1

Answer: (C)

convex lens of focal length $30cm$

The focal length of a lens is given by the formula,

$\frac{1}{f}=\frac{n_2-n_1}{n_1}(\frac{1}{R_1}-\frac{1}{R_2})$

Hence, in air, $\frac{1}{f}=\frac{1.5-1}{1}(\frac{1}{R}+\frac{1}{R})=\frac{1}{R}$. Thus $f=R=20cm$.

In the medium, $\frac{1}{f^{\prime }}=\frac{1.5-\frac{9}{8}}{\frac{9}{8}}(\frac{1}{R}+\frac{1}{R})=\frac{2}{3R}$

Hence $f=1.5R=30cm$

Since the focal length is coming out to be positive. It behaves like a convex lens of focal length $30cm$.