Determine the angle of minimum deviation for an equilateral prism constructed from a material with a refractive index of 1.732 . What is the corresponding angle of incidence for this deviation?

Step-by-step solution

For an equilateral prism, the angle of the prism is A = 60^ . The refractive index of the material is given as = 1.732 = 3 . The relation between the refractive index, angle of prism, and angle of minimum deviation _m is: = ( A + _m 2 ) ( A 2 ) Substituting the given values: 3 = ( 60^ + _m 2 ) ( 60^ 2 ) 3 = (30^ + _m 2 ) (30^ ) 3 = (30^ + _m 2 ) 1 2 (30^ + _m 2 ) = 3 2 Since (60^ ) = 3 2 , we get: 30^ + _m 2 = 60^ _m 2 = 30^ _m = 60^ The corresponding angle of incidence i at minimum deviation is given by: i = A + _