Question

In vacuum, to travel distance $d$, light takes time $t$ and in medium to travel $5d$, it takes time $T$. The critical angle of the medium is :

• A. ${\sin }^{-1}\left(\frac{5T}{t}\right)$
• B. ${\sin }^{-1}\left(\frac{5t}{3T}\right)$
• C. ${\sin }^{-1}\left(\frac{5t}{T}\right)$
• D. ${\sin }^{-1}\left(\frac{3t}{5T}\right)$

Answer 1

The correct option is C ${\sin }^{-1}\left(\frac{5t}{T}\right)$

In vacuum, $c=d/t$

In medium, $v=\frac{5d}{T}$

As refractive index, $\mu =\frac{c}{v}=\frac{d/t}{5dT}=\frac{T}{5t}$

Also, $\sin C=\frac{1}{\mu }\therefore C={\sin }^{-1}\left[\frac{5t}{T}\right]$