From wikipedia:
Phong reflection is an empirical model of local illumination. It describes the way a surface reflects light as a combination of the diffuse reflection of rough surfaces with the specular reflection of shiny surfaces. It is based on Bui Tuong Phong's informal observation that shiny surfaces have small intense specular highlights, while dull surfaces have large highlights that fall off more gradually. The reflection model also includes an ambient term to account for the small amount of light that is scattered about the entire scene.
For each light source in the scene, we define the components is and id as the intensities (often as RGB values) of the specular and diffuse components of the light sources respectively. A single term ia controls the ambient lighting; it is sometimes computed as a sum of contributions from all light sources.
For each material in the scene, we define:
ks: specular reflection constant, the ratio of reflection of the specular term of incoming light
kd: diffuse reflection constant, the ratio of reflection of the diffuse term of incoming light (Lambertian reflectance)
ka: ambient reflection constant, the ratio of reflection of the ambient term present in all points in the scene rendered
α: is a shininess constant for this material, which is larger for surfaces that are smoother and more mirror-like. When this constant is large the specular highlight is small.
We further define lights as the set of all light sources, L as the direction vector from the point on the surface toward each light source, N as the normal at this point on the surface, R as the direction that a perfectly reflected ray of light would take from this point on the surface, and V as the direction pointing towards the viewer (such as a virtual camera).
Note L, N, R, V are all unit vecters.
Then the Phong reflection model provides an equation for computing the shading value of each surface point Ip:
The diffuse term is not affected by the viewer direction (V). The specular term is large only when the viewer direction (V) is aligned with the reflection direction R. Their alignment is measured by the α power of the cosine of the angle between them. The cosine of the angle between the normalized vectors R and V is equal to their dot product. When α is large, in the case of a nearly mirror-like reflection, the specular highlight will be small, because any viewpoint not aligned with the reflection will have a cosine less than one which rapidly approaches zero when raised to a high power.
When we have color representations as RGB values, this equation will typically be calculated separately for R, G and B intensities.
Although the above formulation is the common way of presenting the Phong model, a particular term in the sum should only be included if it is positive, i.e. the equation is formally incorrect.
Therefore, in the above fomulation, (Lm·N) should be exactly max(Lm·N, 0) and similarly (Rm·V) should be max(Rm·V, 0).
