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