A ray of light suffers minimum deviation in a prism of angle 60°. The refractive index of the prism material is √2. Find the angle of incidence in degrees.
Physics · Geometrical optics · Prisms & Thin Prisms
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Question

A ray of light suffers minimum deviation in a prism of angle 60°. The refractive index of the prism material is √2. Find the angle of incidence in degrees.

G1 Physics · Accepted Answer

At minimum deviation, the path through the prism is symmetric, so r₁ = r₂ = A/2. Given A = 60°, therefore r = 30°. Using Snell's law at the first surface: μ = sin i / sin r. Thus √2 = sin i / sin30° = sin i /(1/2). Therefore sin i = √2/2, so i = 45°. Answer: 45.