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Question

The critical angle for refraction from medium 1 to air is θ1 and that from medium 2 to air is θ2. The critical angle for refraction from medium 2 to medium 1 will be

A
sin1(sinθ2sinθ1)
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B
sin1(sinθ1sinθ2)
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C
sin1(sinθ2)
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D
sin1(sinθ1)
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Solution

The correct option is A sin−1(sinθ2sinθ1)For medium 1 and air, μ1sinic=μasin90∘ ⇒μ1sinθ1=1 ⇒μ1=1sinθ1 ...........(i) For medium 2 and air, μ2sinic=μasin90∘ ⇒μ2sinθ2=1 ⇒μ2=1sinθ2 ...........(ii) Now for medium 2 and medium 1, μ2sinic=μ1sin90∘ ⇒μ2sinic=μ1 ⇒sinicsinθ2=1sinθ1 [from (i) and (ii)] ⇒sinic=sinθ2sinθ1 ⇒ic=sin−1(sinθ2sinθ1) Why this question? Tips: Instead of going for formula based approach, it is recommended to apply Snell's law for each pair of media and then couple it with condition of critical incidence.

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