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:

In spherical lenses, the focal length is determined by the radius of curvature of the lens and the refractive index. For a spherical lens, the image is formed by the refraction at both the surfaces of the sphere.

Answer 1

When parallel rays from a distant source strike a spherical glass ball, they undergo refraction at the surface, converging to form an image. Due to the spherical shape, rays refract at both entry and exit, producing a real image on the opposite side. The image position can be determined using the formula for refraction at a spherical surface: \[ \frac{1}{f} = \left( \frac{n - 1}{R} \right) \]
Here,
\( f \) is the focal length of the spherical ball,
\( n = 1.5 \) is the refractive index of the glass,
\( R = 15 \, \text{cm} \) is the radius of the spherical ball.

Substituting the given values yields: \[ \frac{1}{f} = \frac{1.5 - 1}{15} = \frac{0.5}{15} = \frac{1}{30} \] Consequently, the focal length \( f = 30 \, \text{cm} \). A ray diagram illustrating this scenario is provided below:

The image is located 30 cm from the center of the ball, on the side opposite to the incident light. Since the source is distant, the refracted rays converge at this point after passing through the spherical ball.