Question

In a long glass tube, a mixture of two liquids A and B with refractive indices 1.3 and 1.4 respectively, forms a convex refractive meniscus towards A. If an object placed at 13 cm from the vertex of the meniscus in A forms an image with a magnification of \(-2\), then the radius of curvature of the meniscus is:

• A. \( \frac{1}{3} \) cm
• B. 1 cm
• C. \( \frac{4}{3} \) cm
• D. \( \frac{2}{3} \) cm

Hint:

For refraction problems, always use sign conventions properly to avoid errors.

Answer 1

The Correct Option is D

- Using the lens-maker's formula: \[ \frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2 - n_1}{R} \] - Substituting given values: \[ \frac{1.4}{v} - \frac{1.3}{-13} = \frac{0.1}{R} \] - Simplifying the equation: \[ \frac{1.4}{v} = \frac{1 - R}{10R} \] - From magnification: \[ m = \frac{v/n_2}{u/n_1} \] \[ -2 \times (-13)/1.3 = 10R / (1 - R) \] \[ R = \frac{2}{3} { cm} \]