Optics Question 987
Question: If light travels a distance x in $ t _{1} $ sec in air and 10 x distance in $ t _{2} $ sec in a medium, the critical angle of the medium will be
[MH CET 2003]
Options:
A) $ {{\tan }^{-1}}( \frac{t _{1}}{t _{2}} ) $
B) $ {{\sin }^{-1}}( \frac{t _{1}}{t _{2}} ) $
C) $ {{\sin }^{-1}}( \frac{10t _{1}}{t _{2}} ) $
D) $ {{\tan }^{-1}}( \frac{10t _{1}}{t _{2}} ) $
Show Answer
Answer:
Correct Answer: C
Solution:
From the formula $ \sin C=\frac{1}{ _{1}{\mu _{2}}} $
$ \Rightarrow \sin C{= _{2}}{\mu _{1}} $
$ =\frac{u _{1}}{u _{2}}=\frac{v _{2}}{v _{1}} $
$ \Rightarrow \sin C=\frac{10x/t _{2}}{x/t _{1}} $
$ \Rightarrow \sin C=\frac{10t _{1}}{t _{2}} $
$ \Rightarrow C={{\sin }^{-1}}( \frac{10t _{1}}{t _{2}} ) $
