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.

Answer 1

Using the Refraction at a Spherical Surface Formula to determine the image position for First Refraction:

`n_1/v - n_2/u = ((n_1 - n_2))/R`

Where,

Refractive index of air (n₁) = 1.0

Refractive index of glass (n₂) = 1.5

u = ∞    ...(since the light comes from a distant source)

Radius of curvature (R) = +15 cm    ...(positive as the surface is convex)

v' = Image distance inside the sphere

After putting the values,

`1.0/(v') - 1.5/15 = ((1.0 - 1.5))/(-15)`

Solving for v',

v' = 45 cm

Thus, the image of the far object resulting from the initial refraction is located 45 cm within the sphere from the first refracting surface.

The light travels the interior of the sphere and experiences refraction at the second (convex) surface upon exiting into the air.

Where,

Refractive index of glass (n₂) = 1.5,

Refractive index of air (n₁) = 1.0,

Object distance from the second surface (u) = +45-30 cm,

R = −15 cm    ...(negative because it is convex relative to exiting rays),

v' = Final image distance

After putting values,

`1.0/(v') - 1.5/15 = ((1.0 - 1.5))/(-15)`

Solving for v',

v' = 7.5 cm

Thus, the final image is formed at 7.5 cm from the second surface and 22.5 cm from the centre of the sphere.