Question

In vacuum, to travel distance 'd', light takes time 't' and in medium to travel distance ${}^{\prime }5d^{\prime }$, 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 ${\sin }^{-1}\left(\frac{5t}{T}\right)$

speed of light in medium of refractive index $\mu$ is given by

$v=\frac{c}{\mu }$

In vacuum, speed=$c=\frac{d}{t}$

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

$⟹\mu =\frac{c}{v}$

$⟹\mu =\frac{T}{5t}$

Critical angle, $C={\sin }^{-1}\frac{1}{\mu }$

$⟹C={\sin }^{-1}\frac{5t}{T}$

Answer-(C)