Question

If light travels a distance $x$ in time $t_{1}$ in air and $10x$ distance in time $t_{2}$ in a certain medium, then find the critical angle for total internal reflection, of the medium.

• A. $sin^{- 1}\left(\frac{20 t_{1}}{t_{2}}\right)$
• B. $sin^{- 1}\left(\frac{10 t_{1}}{t_{2}}\right)$
• C. $sin^{- 1}\left(\frac{t_{1}}{t_{2}}\right)$
• D. $sin^{- 1}\left(\frac{t_{2}}{10 t_{1}}\right)$

Answer 1

Answer: (B)

$\mu =\frac{\frac{x}{t_{1}}}{\frac{10 x}{t_{2}}}=\frac{t_{2}}{10 t_{1}}$
$\sin \theta_c=\frac{1}{t_2 / 10 t_1}=\frac{10 t_1}{t_2} \Rightarrow \theta_c=\sin ^{-1}\left(\frac{10 t_1}{t_2}\right)$