Question

An object is placed at a distance of 100 cm in air from a convex spherical surface of glass of refractive index 1.5. The radius of curvature is 20 cm. What is the image distance?

Options

• 200 cm from the spherical surface inside the glass medium

• 100 cm from the spherical surface inside the glass medium

• 50 cm from the spherical surface inside the glass medium

• 40 cm from the spherical surface in air

Answer 1

Using \[ \frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2 - n_1}{R} \] with n₁ = 1, n₂ = 1.5, u = −100 cm, R = +20 cm: \[ \frac{1.5}{v} + \frac{1}{100} = \frac{0.5}{20} = \frac{1}{40} \], so \[ \frac{1.5}{v} = \frac{1}{40} - \frac{1}{100} = \frac{3}{200} \], giving v = 100 cm. The image is formed 100 cm from the spherical surface inside the glass medium.