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Reflection

The law stating that when light strikes a surface, it bounces back according to the angle of incidence, as described by the law of reflection: \angle of incidence = \angle of reflection.
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The statement of the theorem

Let I∈R3\mathbf{I} \in \mathbb{R}^3 be the unit vector representing the incident ray, and let N∈R3\mathbf{N} \in \mathbb{R}^3 be the unit normal vector to the reflecting surface at the point of incidence. The reflected ray vector R\mathbf{R} is defined by the vector reflection formula:\n\nR=I−2(I⋅N)N\mathbf{R} = \mathbf{I} - 2 \left( \mathbf{I} \cdot \mathbf{N} \right) \mathbf{N}\n\nFurthermore, the condition for specular reflection requires that the angle θi\theta_i between I\mathbf{I} and −N-\mathbf{N} (the direction into the surface) equals the angle θr\theta_r between R\mathbf{R} and N\mathbf{N} (the direction away from the surface). This is equivalent to the requirement that the component of I\mathbf{I} parallel to the surface is preserved, leading to the geometric constraint: R⋅N=−I⋅N\mathbf{R} \cdot \mathbf{N} = -\mathbf{I} \cdot \mathbf{N}.
Source: Wikipedia