Light travels a distance $x$ in time $t_1$ in air and $10x$ in time $t_2$ in another denser medium. What is th

Question

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?

Accepted Answer

Speed in air $v_1 = \frac{x}{t_1} = c$. Speed in medium $v_2 = \frac{10x}{t_2}$. Refractive index $\mu = \frac{v_1}{v_2} = \frac{x/t_1}{10x/t_2} = \frac{t_2}{10t_1}$. Critical angle $C = \sin^{-1}\left(\frac{1}{\mu}\right) = \sin^{-1}\left(\frac{10t_1}{t_2}\right)$.

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