When angle of incidence on one face of the equilateral glass prism is 3 / 4^ th of the angle of prism, the ray of light undergoes minimum deviation. If the velocity of light in vacuum is ' c ' then the velocity of light in the glass is :

Step-by-step solution

For an equilateral prism, the angle of prism A = 60^ . The condition for minimum deviation is given by i = e and r₁ = r₂ = r = A/2 . Given that the angle of incidence i = 3 4 A , we have i = 3 4 60^ = 45^ . Since r = A/2 , we have r = 60^ /2 = 30^ . Using Snell's Law at the first surface, n₁ (i) = n₂ (r) , where n₁ = 1 (air) and n₂ = n (glass): (45^ ) = n (30^ ) 1 2 = n 1 2 n = 2 2 = 2 . The refractive index n is related to the velocity of light in vacuum c and the velocity of light in glass v by n = c v . Therefor