A) \[30{}^\circ \]
B) \[60{}^\circ \]
C) \[45{}^\circ \]
D) \[90{}^\circ \]
Correct Answer: A
Solution :
\[\frac{{{\mu }_{2}}}{{{\mu }_{1}}}=\frac{{{\nu }_{1}}}{{{\nu }_{2}}}\,=\,\,\frac{1}{2}\,\,\,\,\Rightarrow \,\,\frac{{{\mu }_{1}}}{{{\mu }_{2}}}\,\,=\,\,2\,({{\mu }_{1}}>{{\mu }_{2}})\] For total internal reflection \[_{2}{{\mu }_{1}}\,=\,\,\frac{1}{\sin \,C}\,\,\Rightarrow \,\,\frac{{{\mu }_{1}}}{{{\mu }_{2}}}\]\[=\,\,\frac{1}{\sin \,C}\,\,\Rightarrow \,\,2=\,\,\frac{1}{\sin \,C}\,\,\Rightarrow \,\,C\,\,=\,\,30{}^\circ \] So, for total (internal reflection angle of incidence must be greater than\[30{}^\circ \].
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