A transparent solid cylindrical rod has a refractive index of \[\frac{2}{\sqrt{3}}\]. It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure. |
The incident angle \[(\theta )\] for which the light ray grazes along the wall of the rod is: |
A) \[{{\sin }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\]
B) \[{{\sin }^{-1}}\left( \frac{2}{\sqrt{3}} \right)\]
C) \[{{\sin }^{-1}}\left( \frac{1}{\sqrt{3}} \right)\]
D) \[{{\sin }^{-1}}\left( \frac{1}{2} \right)\]
Correct Answer: C
Solution :
[c] \[\sin \theta =\frac{2}{\sqrt{3}}\,\,\sin r=\frac{2}{\sqrt{3}}\,\,\cos i\] ....(i) |
and \[\frac{2}{\sqrt{3}}\,\,\sin i=\sin 90{}^\circ \Rightarrow i={{60}^{o}}\] ....(ii) |
From (i) and (ii) |
\[\sin \theta =\frac{1}{\sqrt{3}}\] |
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