Given, refractive index of glass plate, \(\mu=\sqrt{3}\)
Polarising angle \(\theta\) of incident light is given as,
\(\mu=\tan \theta\)
or \(\sqrt{3}=\tan \theta \text { or } \theta=\tan ^{-1}(\sqrt{3})\)
\(\therefore\) angle of incident, \(\theta=60^{\circ}\) \([\because \tan 60=\sqrt{3}]\)
refractive index is given as,
\(\mu=\frac{\sin i}{\sin r}\)
or \(\sqrt{3} \sin r=\sin 60^{\circ} \quad \left[\because i=\theta=60^{\circ}\right]\)
or \(\sqrt{3} \sin r=\frac{\sqrt{3}}{2} \text { or } \sin r=\frac{1}{2}\)
or \(r=\sin ^{-1}\left(\frac{1}{2}\right) \Rightarrow r=30^{\circ}\)
Thus, the angle of refraction of the ray is \(30^{\circ}\).