A sunshine recorder globe of `30 cm` diameter is made of glass of `mu = 1.5`. A ray enters the globe parallel to its axis. Find the position from the centre of the sphere, where the ray crosses the axis.

Explanation

For first refraction at surface `AP_1`
`u = oo, v = P_1 I_1 = ?`
`R = + 15 cm, mu_2 = 1.5, mu_1 = 1`
`-(mu_1)/(u)+(mu_2)/(v)=(mu_2 - mu_1)/( R)`
`-(1)/(oo)+(1.5)/(v) = (1.5 - 1)/(15) = (1)/(30), v = 45 cm`.
The image would have been formed at `I_1` if glass medium were continuous.
For second refraction at source `BP_2`
`I_2` acts as virtual object.
`u = P_2 I_1 = P_1 I_1 - P_1 P_2 = 45 - 30 = 15 cm`
`R = -15 cm, v = P_2 I = ?`
`-(mu_2)/(u)+(mu_1)/(v)=(mu_1 - mu_2)/( R)`
`-(1.5)/(15)+(1)/(v)=(1 - 1.5)/(-15)=(1)/(30)`
`(1)/(v)=(1)/(30)+(1)/(10)=(4)/(30)`
`v = (30)/(4)= 7.5 cm`
Distance of image `I` from the centre of sphere
`CI = CP_2 + P_2 I = 15 + 7.5 = 22.5 cm`.
.