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A prism of glass is shown in figure A, ray incident normally on one face is totally reflected. If θ is 45°, the index of refraction of glass is _______ . 

 (A) < √2 (B) > √2 (C) = 2 (D) None of these

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The correct option is (B) > √2.

Explanation:

 For total internal reflection i > θc ......(1)

when θc is critical angle

sin θc = (1/η) i.e. η = (1 / sin θc)

  i = 45°

 hence 45° > sin –1(1/η) From (1)

 sin 45° > (1/η)

 (1 / √2) > (1/η)     hence η > √2

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