The Fresnel Laws describe the behaviour of light at the interface between two different media. A part of the incoming light is reflected, while another part  is trasmitted (i.e. refracted or absorbed).  The proportion of reflected light only depends on on the (complex) refractive index and on the angle of incidence.

For more details concerning the Fresnel equations, please refer to
http://www.odforce.net/wiki/index.php/ReflectanceFunctions#The_Fresnel_Effect 

In the T2S_Illumination shader the Fresnel Mask can be evaluated by one of the following Modes :

• Physical
• Custom
• Preset
• T2S File
  

                - Physical Mode will evaluate the Fresnel equations to determine the Reflection coefficient  R  and the Transimission coefficient  T  = 1 - R..

and

where n1 and n2 are the "In" and "Out" complex refractive index, (IOR and MediaIn in the shader)
qi is the incident angle and qt the transmitted angle deduced by the Snell Law  ( n1 sin(qi)  = n2 sin(qt) )
Rs and Rp correspond therefore to the fraction of s-polarized and p-polarized light which is reflected (here an average of these two waves is used)

If the refractive index are complex, an absorbtion coefficient k , which determines how fast the light is absorbed, needs to be determined.

The Schlick approximation can also be chosen for fast calculations.

• Custom mode allows to set manually the Base Weight for facing angles and Edge Weight for grazing angles. An Edge Falloff parameter is used to control the Fresnel Falloff ( this mode is similar to what is included in mib_glossy_reflections)
  
  
• Preset Mode will allow to choose among a list of predetermined Materials, which contain the Refractive Index for Red, Green and Blue light. A Physical "Complex Fresnel" Calculation is then performed. This procedure tints the reflections depending on the Fresnel Reflectivity.
  
  
• T2S Files  can be used to input user-defined complex Fresnel parameters (IOR and Absorbtion Coef) for R, G and B. For more details concerning the T2S File Format, please click here.

The first image has been rendered with a simple Lambert with a Reflectivity of 0.5.

- The second image has been rendered with the T2S_FresnelMask plugged into the reflectivity port of the Lambert node, using a refractive index of 5 with Schlick's approximation. It can be seen how the grazing angles become much more reflective, adding realism to the scene.