A light ray falls on a glass surface of refractive index $\sqrt{3}$, at an angle $60^{\circ }$. The angle between the refracted and reflected rays would be:

Angle of incidence $i=60^{\circ }$. By law of reflection, angle of reflection $r_{ref}=60^{\circ }$.Using Snell's Law for refraction:
$$\mu =\frac{\sin i}{\sin r}$$
$$\sqrt{3}=\frac{\sin 60^{\circ }}{\sin r}=\frac{\sqrt{3}/2}{\sin r}$$
$$\sin r=\frac{1}{2}⟹r=30^{\circ }$$
The angle between reflected and refracted ray is $180^{\circ }-(r_{ref}+r)$:
$$\text{Angle}=180^{\circ }-(60^{\circ }+30^{\circ })=90^{\circ }$$
(Note: This occurs at Brewster's angle, where $\tan i_B=\mu ⟹\tan 60^{\circ }=\sqrt{3}$).