Question

Light from a point source in air falls on a convex curved surface of radius 20 cm and refractive index 1.5. If the source is located at 100 cm from the convex surface, the image will be formed at____ cm from the object.

Answer 1

Given: - Radius of curvature $R = 20 \, \text{cm}$, - Refractive indices: $\mu_1 = 1$ (air) and $\mu_2 = 1.5$ (medium).

Using the lens maker’s formula:

$\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}.$

Substitute $u = -100 \, \text{cm}$:

$\frac{1.5}{v} - \frac{1}{-100} = \frac{1.5 - 1}{20}.$

Solving for $v$:

$\frac{1.5}{v} + \frac{1}{100} = \frac{0.5}{20},$ $\frac{1.5}{v} = \frac{0.5}{20} - \frac{1}{100},$ $v = 100 \, \text{cm}.$

Thus, the image is formed at a distance:

$100 + 100 = 200 \, \text{cm from the object}.$