Question

A sphere 5 cm in diameter has a small scratch on its surface. When the scratch is viewed through the glass from a position directly opposite, where does the scratch appear and what is its magnification? Assume n = 1.5 for the glass.

Answer 1

given,

diameter of sphere = 5 cm

radius of sphere = -2.5 cm

refractive index for glass n₁ = 1.5

refractive index for air n₂ = 1

magnification of the glass = ?

now,

`(n_1)/(S) +(n_2)/(S')= (n_2-n_1)/(R)`

`(1.5)/(5) +(1)/(S')= (1-1.5)/(-2.5)`

`(1.5)/(5) +(1)/(S')= (0.5)/(-2.5)`

S' = - 10 cm

magnification

`m = (-n_1S')/(n_2S)`

`m = (-1.5* -10)/(1* 5)`

m = + 3