Geometry.FresnelTerm Method

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Calculates the Fresnel term.

Definition

Visual Basic Public Shared Function FresnelTerm( _
    ByVal cosTheta As Single, _
    ByVal refractionIndex As Single _
) As Single
C# public static float FresnelTerm(
    float cosTheta,
    float refractionIndex
);
C++ public:
static float FresnelTerm(
    float cosTheta,
    float refractionIndex
);
JScript public static function FresnelTerm(
    cosTheta : float,
    refractionIndex : float
) : float;

Parameters

cosTheta System.Single
Cosine of the incident angle; must be between 0 and 1.
refractionIndex System.Single
Refraction index of a material; must be greater than 1.

Return Value

System.Single
Fresnel term for unpolarized light.

Remarks

To find the Fresnel term, use the following equation.

If F is the Fresnel term, A is the angle of incidence, and B is the angle of refraction, then 

F = 0.5 * [tan2(A - B) / tan2(A + B) + sin2(A - B) / sin2(A + B)]
  = 0.5 * sin2(A - B) / sin2(A + B) * [cos2(A + B) / cos2(A - B) + 1]

Let r   = sina(A) / sin(B)      (the relative refractive index)
Let c   = cos(A)
Let g   = (r2 + c2 - 1)1/2

Then, expand using the trigonometric identities and simplifying to produce the following result. 

F = 0.5 * (g + c)2 / (g - c)2 * ([c(g + c) - 1]2 / [c(g - c) + 1]2 + 1)

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