A) \[{{\tan }^{-1}}\left( \frac{{{t}_{1}}}{{{t}_{2}}} \right)\]
B) \[{{\sin }^{-1}}\left( \frac{{{t}_{1}}}{{{t}_{2}}} \right)\]
C) \[{{\sin }^{-1}}\left( \frac{10{{t}_{1}}}{{{t}_{2}}} \right)\]
D) \[{{\tan }^{-1}}\left( \frac{10{{t}_{1}}}{{{t}_{2}}} \right)\]
Correct Answer: C
Solution :
From the formula of critical angle, we have \[\sin {{\theta }_{0}}=\frac{{{\upsilon }_{2}}}{{{\upsilon }_{1}}}=\frac{10x/{{t}_{2}}}{x/{{t}_{1}}}=\frac{10{{t}_{1}}}{{{t}_{2}}}\] or \[{{\theta }_{0}}={{\sin }^{-1}}\left( 10{{t}_{1}}/{{t}_{2}} \right)\]
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