First, we will consider a particular type of surface called an ideal diffuse reflector. An ideal diffuse surface is, at the microscopic level a very rough surface. Chalk is a good approximation to an ideal diffuse surface. Because of the microscopic variations in the surface, an incoming ray of light is equally likely to be reflected in any direction over the hemisphere.
Ideal diffuse reflectors reflect light according to Lambert's cosine law, (there are sometimes called Lambertian reflectors). Lambert's law states that the reflected energy from a small surface area in a particular direction is proportional to cosine of the angle between that direction and the surface normal. Lambert's law determines how much of the incoming light energy is reflected. Remember that the amount energy that is reflected in any one direction is constant in this model. In other words the reflected intensity is independent of the viewing direction. The intensity does however depend on the light source's orientation relative to the surface, and it is this property that is governed by Lambert's law.
The Ilight term represents the intensity of the incoming light at the particular wavelength (the wavelength determines the light's color). The kd term represents the diffuse reflectivity of the surface at that wavwlength.
When computing this equation we can take use vector analysis to compute this cosine term indirectly. If both the normal vector and the incoming light vector are normalized (unit length) then the diffuse shading component can be computed by:
In this equation we need only consider angles from 0 to 90 degrees. Greater angles are blocked by the surface, and the reflected energy is 0. Below are several examples of a spherical diffuse reflector with a varying lighting angles. Why do you think we use spheres as examples when shading?
