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Question:

The angle of incidence for a ray of light at a refracting surface of a prism is 45°. The angle of prism is 60°. If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are?

30°;1√2

30°;√2

45°;√2

45°;1√2

Solution:

Angle of incidence, i = 45°
Angle of prism, A = 60°
Angle of minimum deviation, δm = 2i - A = 2(45°) - 60° = 30°
∴ μ = sin((A + δm)/2) / sin(A/2) = sin(45°)/sin(30°) = (1/√2)/(1/2) = √2