A) \[{{\sin }^{1}}\left( \frac{1}{2} \right)\]
B) \[{{\sin }^{-1}}\left( \sqrt{\frac{8}{9}} \right)\]
C) \[{{\sin }^{-1}}\left( \frac{8}{9} \right)\]
D) \[{{\sin }^{-1}}\left( \frac{5}{7} \right)\]
Correct Answer: C
Solution :
Refractive index of glass with respect to water \[_{w}{{\mu }_{g}}=\frac{_{a}{{\mu }_{g}}}{_{a}{{\mu }_{w}}}=\frac{3/2}{4/3}=\frac{9}{8}\] \[_{w}{{\mu }_{g}}=\frac{1}{\sin C}\] \[\frac{9}{8}=\frac{1}{\sin C}\] \[\sin C=\frac{8}{9}\] \[C={{\sin }^{-1}}\left( \frac{8}{9} \right)\]
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