A) \[{{\sin }^{-1}}\left( \frac{10{{t}_{1}}}{{{t}_{2}}} \right)\]
B) \[{{\sin }^{-1}}\left( \frac{{{t}_{1}}}{10\,{{t}_{2}}} \right)\]
C) \[{{\sin }^{-1}}\left( \frac{{{t}_{2}}}{10\,{{t}_{1}}} \right)\]
D) \[{{\sin }^{-1}}\left( \frac{10\,{{t}_{2}}}{{{t}_{1}}} \right)\]
Correct Answer: A
Solution :
\[{{v}_{0}}=\frac{x}{{{t}_{1}}}\] \[v=\frac{10x}{{{t}_{2}}}\] \[\sin C=\frac{1}{\mu }\] \[C={{\sin }^{-1}}\left( \frac{1}{\mu } \right)\] Refractive index\[\mu \]is given by \[=\frac{{{v}_{0}}}{v}=\frac{x}{{{t}_{1}}}\times \frac{{{t}_{2}}}{10x}=\frac{{{t}_{2}}}{10\,{{t}_{1}}}\] \[C={{\sin }^{-1}}\left( \frac{1}{\mu } \right)={{\sin }^{-1}}\left( \frac{10\,{{t}_{1}}}{{{t}_{2}}} \right)\]
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