A thin prism with angle 5° of refractive index 1.72 is combined with another prism of refractive index 1.9 to produce dispersion without deviation. The angle of second prism i $s ______.$
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Question

A thin prism with angle 5° of refractive index 1.72 is combined with another prism of refractive index 1.9 to produce dispersion without deviation. The angle of second prism i s ______.

G1 Physics · Accepted Answer

For zero net deviation, the deviations produced by the two thin prisms must cancel. For a thin prism, δ = (μ - 1)A. Therefore, (μ₁ - 1)A₁ + (μ₂ - 1)A₂ = 0. The prisms are oppositely oriented, so the required magnitude of the second prism angle is A₂ = [(μ₁ - 1)A₁]/(μ₂ - 1). Substitute: μ₁ = 1.72, A₁ = 5°, μ₂ = 1.9. Hence, A₂ = [(1.72 - 1)×5°]/(1.9 - 1) = (0.72×5°)/0.9 = 4°. Correct option: C.