Question

A beam of light coming from a distant source is refracted by a spherical glass ball (refractive index 1.5) of radius 15 cm. Draw the ray diagram and obtain the position of the final image formed.

Hint:

For refraction at a curved surface, use the lens-maker’s equation, keeping sign conventions in mind.

Answer 1

Using the lens-maker's formula for a spherical refracting surface: \[ \frac{n_2}{v} - \frac{n_1}{u} = \frac{(n_2 - n_1)}{R} \] where:
\( n_1 = 1.0 \) (air),
\( n_2 = 1.5 \) (glass),
\( u = \infty \) (distant object),
\( R = 15 \) cm (radius of curvature), 
\( v \) is the image distance.
Since \( u = \infty \), the formula simplifies to: \[ \frac{1.5}{v} = \frac{0.5}{15} \] \[ v = \frac{1.5 \times 15}{0.5} = 45 \text{ cm} \] Thus, the final image is formed at 45 cm inside the sphere.