Question

The focal length of a thin converging lens in air is 20 cm. When the lens is immersed in a liquid, it behaves like a concave lens of power 1 D. If the refractive index of the material of the lens is 1.5, the refractive index of the liquid is

• A. \( \frac{5}{3} \)
• B. \( \frac{4}{3} \)
• C. \( \frac{5}{4} \)
• D. \( \frac{7}{4} \)

Hint:

For lenses in different media, the sign of the focal length indicates whether the lens acts as converging or diverging.

Answer 1

The Correct Option is A

Using the lens maker's formula: \[ \frac{1}{f} = (n_{\text{lens}} - n_{\text{medium}}) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \] For air: \[ \frac{1}{20} = (1.5 - 1) K \] \[ K = \frac{1}{10} \] For the liquid: \[ \frac{1}{-100} = (1.5 - n) K \] Solving for \( n \): \[ n = \frac{5}{3} \] Thus, the correct answer is \( \frac{5}{3} \).