The light from a point source placed in air is incident on a convex spherical glass surface of radius of curvature 30 cm. The refractive index of the glass is 1.5. The distance of light source from the glass surface is 120 cm. The distance of the image formed from the glass surface is

180 cm

The correct answer is Option (3) → 180 cm

Given:

Radius of curvature: $R = 30\ \text{cm}$

Refractive index of glass: $\mu_2 = 1.5$, refractive index of air: $\mu_1 = 1$

Object distance: $u = -120\ \text{cm}$ (negative as per sign convention)

Formula for refraction at spherical surface:

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

Substitute values:

$\frac{1.5}{v} - \frac{1}{-120} = \frac{1.5 - 1}{30}$

$\frac{1.5}{v} + \frac{1}{120} = \frac{0.5}{30}$

$\frac{1.5}{v} + \frac{1}{120} = \frac{1}{60}$

$\frac{1.5}{v} = \frac{1}{60} - \frac{1}{120}$

$\frac{1.5}{v} = \frac{2 - 1}{120} = \frac{1}{120}$

$v = \frac{1.5 \times 120}{1} = 180\ \text{cm}$

Answer: Image is formed at $180\ \text{cm}$ inside the glass from the surface