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

Answer 1

Answer: (B)

$\mu =\frac{\frac{x}{t_{1}}}{\frac{10 x}{t_{2}}}=\frac{t_{2}}{10 t_{1}}$
$\sin\theta _{c}=\frac{1}{t_{2} / 10 t_{1}}=\frac{10 t_{1}}{t_{2}}$
$\Rightarrow \left(\theta \right)_{c}=\left(\sin\right)^{- 1}\left(\frac{10 t_{1}}{t_{2}}\right).$