Question

Light takes $ {{t}_{1}} $ sec to travel a distance x cm in vacuum and the same light takes $ {{t}_{2}} $ sec to travel 10 x cm in the medium, critical angle for the corresponding medium is

• 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) $

Answer 1

Answer: (A)

$ {{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) $