A ray of light travelling in the direction 1/2(î+√3ĵ) is incident on a plane mirror. After reflection, it travels along the direction 1/2(î-√3ĵ). The angle of incidence is:

After reflection, the only component of the direction of propagation of incident light that is perpendicular to the plane mirror changes its sign.
Here, as the y-component changes after reflection, we can assume that the direction of normal of the plane mirror is along with ĵ. Therefore angle of incidence is angle between the unit vectors 1/2(î+√3ĵ) and ĵ.
→cos(i) = 1/2(î+√3ĵ).ĵ
→i = cos⁻¹(√3/2) = 30°