Question

If light travels at a distance $x$ in time $t_1$ seconds in air and $10x$ distance in time $t_2$ in a certain medium, then find the critical angle of the medium.

• A. ${\left(\sin \right)}^{-1}\left(\frac{20t_1}{t_2}\right)$
• B. ${\left(\sin \right)}^{-1}\left(\frac{10t_1}{t_2}\right)$
• C. ${\left(\sin \right)}^{-1}\left(\frac{t_1}{t_2}\right)$
• D. ${\left(\sin \right)}^{-1}\left(\frac{t_2}{10t_1}\right)$

Answer 1

Answer: (B)

$\mu =\frac{\frac{x}{t_1}}{\frac{10x}{t_2}}=\frac{t_2}{10t_1}$
$\sin {\theta }_c=\frac{1}{t_2/10t_1}=\frac{10t_1}{t_2}$
$\Rightarrow {\left(\theta \right)}_c={\left(\sin \right)}^{-1}\left(\frac{10t_1}{t_2}\right).$