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Light is incident normally on the face AB of a prism as shown in the figure. A layer of liquid of refractive index μ is applied on the face AC of the prism. If the prism is made of glass of refractive index 3 2 , then the limit of μ for which total internal reflection takes place on face AC is

Options

  1. Aμ < 3 3 4
  2. Bμ > 5 2
  3. Cμ > 2
  4. Dμ < 3

Correct answer

A. μ < 3 3 4

Step-by-step solution

For critical angle at the glass-liquid interface we have μ 1 s i n C = μ 2 s i n 90 ° ⇒ 3 2 s i n C = μ ⇒ s i n C = 2 μ 3 For total internal reflection 60 ° > C ⇒ s i n 60 ° > s i n C ⇒ 3 2 > 2 μ 3 μ < 3 3 4

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