A hollow sphere of glass of inner and outer radii R and 2R respectively has a small mark on its inner surface. This mark is observed from a point outside the sphere such that the centre of the sphere lies in between. Prove that the mark will appear nearer than it really it, by a distance `(mu-1)(R)//(3mu-1)`

Answer

`(n-1) R//(3n-1)`

Explanation

For lst refraction
`(n)/(v_(1))-(1)/(-2R)=(n-1)/(-R) ………….(i)`
For llnd refraction
`(1)/(v_(2))-(n)/(v_(1)-R)=(1-n)/(-2R)……….(ii)`
From `(i)` and `(ii)`
`v_(2)=(2R(4n-1))/(1-3n)`
so shift `=|v_(2)-(-3R)|`
`=3R+2((4n-1)R)/(1-3n)=((n-1)R)/((3n-1))`