Question

Light takes t${}_1$ sec to travel a distance x cm in vacuum and takes t${}_2$ sec to travel 10x cm in a medium. The critical angle corresponding to the media is :

• A. $si{n}^{-1}(10t_1/t_2$)
• B. $si{n}^{-1}(t_2/10$)
• C. $si{n}^{-1}(1/t_1$)
• D. $si{n}^{-1}(t_1/10t_2$)

Answer 1

The correct option is A $si{n}^{-1}(10t_1/t_2$)

${\vartheta }_{vaccum}=\frac{d_{vaccum}}{t_{vaccum}}=\frac{\chi }{t_1}$

$v_{med}=\frac{10\chi }{t_2}$

$\mu =\frac{\chi \times t_2}{t_1\times 10\chi }=\frac{t_2}{10t_1}$

${\theta }_{cric}=si{n}^{-1}\left(\frac{1}{\mu }\right)=si{n}^{-1}\left(\frac{10t_1}{t_2}\right)$