The graph of angle of deviation versus angle of incidence i for a transparent prism shows that the minimum deviation occurs when the angle of incidence is exactly equal to the angle of the prism. If the speed of light in the material of the prism is 3 2 10^8 m/s , the angle of the prism (in degrees) is _______. (Take the speed of light in vacuum as 3 10^8 m/s )

Step-by-step solution

The refractive index of the prism is given by: = c v = 3 10^8 3 2 10^8 = 2 At minimum deviation, the angle of incidence i is equal to the angle of emergence e . The deviation is given by: _ = 2i - A We are given that minimum deviation occurs when i = A . Substituting this: _ = 2A - A = A Using the prism formula: = ( A + _ 2 ) ( A 2 ) 2 = ( A + A 2 ) ( A 2 ) = (A) ( A 2 ) Using the double angle identity (A) = 2 ( A 2 ) ( A 2 ) : 2 = 2 ( A 2 ) ( A 2 ) = 1 2 A 2 = 45^ A = 90^ Answer: 90