According to the law of reflection, the angle of incidence and angle of reflection are equal, when light is incident on a plane surface (such as a flat mirror). The angle of incidence is the angle made by the incident ray with a normal drawn to the reflecting surface. Similarly, angle of reflection is the angle made by the reflected ray with a normal drawn to the reflecting surface.
Thus, angle of incidence = angle of reflection.
That is, the normal line divides the angle between the incident ray and reflected ray into two equal angles.
Without a normal (drawn to the reflecting surface, in other words, a plane perpendicular to the reflecting surface), we will not be able to predict the path of the reflected light ray. To be precise, we will not be able to view an object (that is emitting the incident light ray) unless we are at the right place (along the path of reflected light), which can only be predicted by using a normal.
Hope this helps.
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