# Q&A: Determining Angle of Incidence from an Incident Ray Table

Question
How can I determine the angle of an incidence for a ray relative to the surface that it intersects?

Synopsis
Determining Angle of Incidence from an Incident Ray Table

Solution
The Incident Ray Table provides the XYZ direction vectors for the ray, but these are relative to the coordinate system, not to the surface normal. The surface normal is not directly reportable by TracePro, but can be found when an Incident Ray Table is saved as a text file. The cosine of the angle of incidence is equal to the dot product of the two vectors. The direction vectors in the Incident Ray Table are all unit vectors, so the dot product to obtain the Angle of Incidence reduces to:

AOI = ARCCOS (Xvec*Xnorm + Yvec*Ynorm + Zvec*Znorm)

If you open the Incident Ray Table in Excel, the Angle of Incidence for the first ray in the table can be obtained from the equation:

=180-DEGREES(ACOS(K12*N12+L12*O12+M12*P12))

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