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A prism of refractive index μ and angle of prism A is placed in the position of minimum angle of deviation. If minimum angle of deviation is also A, then in terms of refractive index

1. 2 cos⁻¹(μ/2)
2. 2 sin⁻¹(μ/2)
3. sin⁻¹(√((μ-1)/2))
4. cos⁻¹(μ/2)

Correct answer: 2 cos⁻¹(μ/2)

Solution

At minimum deviation, mu = sin((A+Dm)/2)/sin(A/2). With Dm = A this gives mu = sin(A)/sin(A/2) = 2cos(A/2), so cos(A/2) = mu/2 and A = 2 cos^-1(mu/2).

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