A narrow parallel beam of light is incident on a transparent sphere of refractive index n . If the beam finally gets focussed at a point situated at a distance = 2 × (radius of sphere) from the centre of the sphere, then find n ?

Step-by-step solution

From first refraction μ 2 v - μ 1 u = μ 2 - μ 1 R n AI 1 - 1 ∞ = n - 1 R AI ' = n R n - 1 for 2nd refraction u = BI ′ = A I ′ - 2 R = n R n - 1 - 2 R = ( n - 2 n + 2 ) R n - 1 u = ( 2 - n ) ( n - 1 ) R apply μ 2 v - μ 1 u = μ 2 - μ 1 R 1 R - n ( n - 1 ) ( 2 - n ) R = 1 - n - R - n ( n - 1 ) ( 2 - n ) R = n - 1 R - 1 R n ( n - 1 ) ( n - 2 ) = n - 2 n n - 1 = n - 2 2 n 2 - n = n 2 + 4 - 4 n 3 n = 4 n = 4 3