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Light travels a distance $x$ in time $t_1$ in air and $10x$ in time $t_2$ in another denser medium. What is the critical angle for this medium?
A
$\sin^{-1}\left(\frac{10t_1}{t_2}\right)$
B
$\sin^{-1}\left(\frac{t_2}{t_1}\right)$
C
$\sin^{-1}\left(\frac{10t_2}{t_1}\right)$
D
$\sin^{-1}\left(\frac{t_1}{10t_2}\right)$
Explanation
$\mu=\frac{t_2}{10t_1}$ and $\sin C=\frac{1}{\mu}=\frac{10t_1}{t_2}$.
Detailed Solution
Speed of light in air: $C=\frac{x}{t_1}$
Speed of light in the denser medium: $C_2=\frac{10x}{t_2}$
$\Rightarrow\mu=\frac{C}{C_2}=\frac{x}{t_1}\times\frac{t_2}{10x}=\frac{t_2}{10t_1}$
For total internal reflection $\sin C=\frac{1}{\mu}\Rightarrow\sin C=\frac{10t_1}{t_2}$
$C=\sin^{-1}\left(\frac{10t_1}{t_2}\right)$