A light ray strikes a horizontal plane mirror and gets deviated by $\frac{\mathrm{\pi }}{3}$. The reflected ray becomes verticals, when the mirror is rotated by an angle of $\frac{\mathrm{\pi }}{\mathrm{X}}$radians. The value of X is

$\mathrm{d}={60}^{\circ }\Rightarrow 180-2\mathrm{i}={60}^{\circ }\Rightarrow \mathrm{i}={60}^{\circ }$ 

For the reflected ray to become vertical, it should be rotated through 60° for the same incident ray. Hence the mirror has to be rotated through $\frac{{60}^{\mathrm{o}}}{2}={30}^0=\frac{\mathrm{\pi }}{6}$radians.