Question

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

• A. $si{n}^{-1}\left[\frac{10t_2}{t_1}\right]$
• B. $si{n}^{-1}\left[\frac{t_2}{10t_1}\right]$
• C. $si{n}^{-1}\left[\frac{10t_1}{t_2}\right]$
• D. $si{n}^{-1}\left[\frac{t_1}{10t_2}\right]$

Answer 1

The correct option is C $si{n}^{-1}\left[\frac{10t_1}{t_2}\right]$

Speed of light in vacuum = $\frac{x}{t_1}⟶\left(1\right)$

Speed of light in medium = $\frac{10x}{t_2}⟶\left(II\right)$

$\mu =\frac{\left(I\right)}{\left(II\right)}\left(fromdefinition\right)$

$\mu =\frac{\frac{x}{t_1}}{\frac{10x}{t_2}}=\frac{t_2}{10t_1}$

& Since critical angle

$C={sin}^{-1}\left(\frac{1}{\mu }\right)$

$C={sin}^{-1}\left(\frac{10t_1}{t_2}\right)$