Question

Light takes $t_1$ sec to travel a distance x cm in vacuum and the same light takes $t_2$ sec to travel 10 x cm in the medium, critical angle for the corresponding medium is

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

Answer 1

Answer: (A)

$v_0=\frac{x}{t_1}$ $v=\frac{10x}{t_2}$ $\sin C=\frac{1}{\mu }$ $C={\sin }^{-1}\left(\frac{1}{\mu }\right)$ Refractive index $\mu$ is given by $=\frac{v_0}{v}=\frac{x}{t_1}\times \frac{t_2}{10x}=\frac{t_2}{10t_1}$ $C={\sin }^{-1}\left(\frac{1}{\mu }\right)={\sin }^{-1}\left(\frac{10t_1}{t_2}\right)$