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An isosceles prism has apex angle A and refractive index mu. It is observed that the angle of minimum deviation equals A (i.e., deltaₘ = A). Which of the following statements are correct?

1. At minimum deviation, the refraction angle r1 at the first surface is related to the angle of incidence i1 by r1 = i1/2.
2. The refractive index and prism angle are related by A = (1/2)*cos⁻¹(mu/2), and the emergent ray becomes tangential to the second surface when i1 = sin⁻¹[sin(A)*sqrt(4*cos²(A/2) - 1) - cos(A)].
3. When the angle of incidence equals A (i.e., i1 = A), the ray inside the prism travels parallel to the base.
4. When the angle of incidence equals A (i.e., i1 = A), the ray inside the prism travels parallel to the base.

Correct answer: At minimum deviation, the refraction angle r1 at the first surface is related to the angle of incidence i1 by r1 = i1/2.

Solution

At minimum deviation with deltaₘ = A, the angle of incidence becomes i1 = A and the refraction angle r1 = A/2, so r1 = i1/2 (option A is correct). The correct relation is mu = 2*cos(A/2), which means A = 2*cos⁻¹(mu/2), not (1/2)*cos⁻¹(mu/2) as stated in option B (option B is wrong). Since i1 = A at minimum deviation, the ray inside is indeed parallel to the base (options C and D are both correct).

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