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

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

B)        \[n>\sqrt{2}\]   

C)        \[n>\frac{1}{\sqrt{2}}\]

D)        \[n<\sqrt{2}\]

Correct Answer: B

Solution :

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,          \[n=\frac{1}{\sin C}\] \[\Rightarrow \]               \[C={{\sin }^{-1}}\left( \frac{1}{n} \right)\] \[\Rightarrow \]               \[\frac{1}{n}<\sin {{45}^{o}}\] \[\Rightarrow \]               \[n>\frac{1}{\sin {{45}^{o}}}\] \[\Rightarrow \]               \[n>\frac{1}{(1/\sqrt{2})}\] \[\Rightarrow \]               \[n>\sqrt{2}\]