Question

A converging beam of light traveling in air converges at a point P as shown in the figure. When a glass sphere of refractive index 1⋅5 is introduced in between the path of the beam, calculate the new position of, the image. Also, draw the ray diagram for the image formed.

Answer 1

For refraction at curved surfaces, using the relation, `mu_2/"v" - mu_1/"u" = (mu_2 - mu_1)/"R"` .......(1)

For the given conditions:

The first refraction takes place at the left side of the sphere. As the incident rays are going to converge at a point 20 cm away from the pole of the curved surface so,
`mu = +20 "cm", "R" =+5 "cm", mu_1 = 1, mu_2 = 1.5`

Using equation 1,

`1.5/"v" - 1/20 = (1.5 - 1)/5`

⇒ `1.5/"v" = 0.5/5 + 1/20 = 1/10 + 1/20 = 3/20`

⇒ v = 10 cm

As the image distance equal to the diameter of the glass sphere, hence the final image will form at point Q, on the circumference of the sphere, as shown in the figure.