As shown in the figure, thin prisms P₁ and P₂ are combined to produce dispersion without deviation. For prism P₁ the angle of prism is 4° and the refractive index is 1.54. For prism P₂ the angle of prism is 3°. The refractive index of the material of P₂ is . (Hint: for a thin prism, δ = A(n-1).)

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(1) 1.72. Given: two thin prisms in contact with their refracting angles opposed; A₁ = 4° with n₁ = 1.54, and A₂ = 3°. Idea: dispersion without deviation means the mean ray carries straight on, so the two prisms must deviate it equally and in opposite senses. For a thin prism the deviation is δ = A(n-1), independent of the angle of incidence. Set the two equal: A₁(n₁-1) = A₂(n₂-1). 4°×(1.54-1) = 3°×(n₂-1), so 2.16 = 3(n₂-1) and n₂-1 = 0.72. n₂ = 1.72: the second prism is of denser glass, so its smaller angle can undo the same deviation while still contributing dispersion of its own.

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