question_answer

A light ray is incident perpendicular to one face of a\[90{}^\circ \]prism and is totally internally reflected at the glass-air interface. If the angle of reflection is\[45{}^\circ ,\] we conclude that the refractive index\[n\]is                   [AIEEE 2004]

A) \[n<\frac{1}{\sqrt{2}}\]

B) \[n<\sqrt{2}\]

C) \[n>\frac{1}{\sqrt{2}}\]

D) \[n<\sqrt{2}\]

Correct Answer: B

Solution :

[b] For total internal reflection from glass-air interface, critical angle C must be less than angle of incidence.

i.e.,           \[C<i\]

or              \[C<45{}^\circ \]             \[(\because \angle i=45{}^\circ )\]

But,          \[n=\frac{1}{\sin C}\]

\[\Rightarrow \]            \[C={{\sin }^{-1}}\left( \frac{1}{n} \right)\]

\[\Rightarrow \]            \[\frac{1}{n}<\sin {{45}^{o}}\]

\[\Rightarrow \]            \[n>\frac{1}{\sin {{45}^{o}}}\]

\[\Rightarrow \]            \[n>\frac{1}{(1/\sqrt{2})}\]

\[\Rightarrow \]            \[n>\sqrt{2}\]