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

A

Explanation

We have to see the image of `O` from the other side.
Applying, `(mu_(2))/(v- (mu_(1))/(u) = (mu_(2) - mu_(1))/(R)` twice, we have
`(mu)/(AI_(1)) - (1)/(-2R) = (mu - 1)/(-R)`
`:. AI_(1) = (2muR)/(1 - 2mu)`
Further, `(1)/(BI_(2)) - (mu)/((AI_(1) - R)) = (1-mu)/(-R)`
Solving this equation, we get
`BI_(2) = (2R(4mu - 1))/(3mu - 1)`

`:.` Distance between the final image and object
`d = 3R - (2R(4mu - 1))/(3mu - 1)`
`= ((mu - 1)R)/((3mu - 1))`