A) \[{{\sin }^{-1}}\left( \frac{2}{\sqrt{13}} \right)\]
B) \[{{\tan }^{-1}}\left( \frac{3}{2} \right)\]
C) \[{{\cos }^{-1}}\left( \frac{1}{7} \right)\]
D) \[{{\sin }^{-1}}\left( \frac{2}{3} \right)\]
Correct Answer: D
Solution :
Using the relation \[\frac{\sin i}{\sin r}=\frac{{{\mu }_{2}}}{{{\mu }_{1}}}=\frac{{{\lambda }_{1}}}{{{\lambda }_{2}}}=\frac{4000\overset{\text{o}}{\mathop{\text{A}}}\,}{6000\overset{\text{o}}{\mathop{\text{A}}}\,}=\frac{2}{3}\] So, \[Sin\,\,C=\frac{{{\mu }_{rarer}}}{{{\mu }_{denser}}}=\frac{{{\mu }_{2}}}{{{\mu }_{1}}}=\frac{2}{3}\] So, \[C={{\sin }^{-1}}\left( \frac{2}{3} \right)\]
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