# Lambertian reflectance

When a surface is rough, the light falling on it is scattered. The amount of light an observer will see from the surface, the surface brightness, is the same no matter what angle they look. This is called Lambertian reflectance.

The Lambertian, or diffuse reflectance is, in computer graphics, calculated by taking the dot product of the surface's normalized normal vector [itex]\mathbf{N}[itex] and a normalized vector [itex]\mathbf{L}[itex] pointing from the surface to the light source. This number is then multiplied by the color of the surface and the intensity of the light hitting the surface:

[itex]I_{D}=\mathbf{L}\cdot\mathbf{N}*C*I_{L}[itex]

Where [itex]I_{D}[itex] is the intensity of the diffusely reflected light (surface brightness), [itex]C[itex] is the color and [itex]I_{L}[itex] is the intensity of the incoming light. Because

[itex]\mathbf{L}\cdot\mathbf{N}=|N||L|\cos{\alpha}[itex],

where [itex]\alpha[itex] is the angle between the direction of the two vectors, the intensity will be the highest if the normal vector points in the same direction as the light vector ([itex]\cos{(0)}=1[itex], the surface will be perpendicular to the direction of the light), and the lowest if the normal vector is perpendicular to the light vector ([itex]\cos{(\pi)}=0[itex], the surface runs parallel with the direction of the light).

Lambertian reflectance is accompanied by specular Phong reflectance, where the surface brightness is highest when the observer's angle is the same as the angle of the light source.

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