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What is the relationship between the polarizing angle and the critical angle?

1. iₚ = tan⁻¹(cosec q_c)
2. iₚ = tan⁻¹(sin q_c)
3. iₚ = cot⁻¹(sin q_c)
4. iₚ = cot⁻¹(cosec q_c)

Correct answer: iₚ = tan⁻¹(cosec q_c)

Solution

Brewster's law: tan(ip) = n. Critical angle: sin(theta_c) = 1/n -> n = cosec(theta_c). Hence tan(ip) = cosec(theta_c), i.e. ip = tan^-1(cosec theta_c).

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