The incident, reflected and transmitted rays are each characterized by a triplet of unit vectors:
* [[File:frml14_tn.png]] <math>( \mathbf{ \hat{u}_{\|}, \hat{u}_{\perp}, \hat{k} } )</math> representing the incident parallel polarization vector, incident perpendicular polarization vector and incident propagation vector, respectively.* [[File:frml15_tn.png]] <math>( \mathbf{ \hat{u}_{\|}^', \hat{u}_{\perp}^', \hat{k}^' } )</math> representing the reflected parallel polarization vector, reflected perpendicular polarization vector and reflected propagation vector, respectively.* [[File:frml16_tn.png]] <math>( \mathbf{ \hat{u}_{\|}^{''}, \hat{u}_{\perp}^{''}, \hat{k}^{''} } )</math> representing the transmitted parallel polarization vector, transmitted perpendicular polarization vector and transmitted propagation vector, respectively.
[[File:reflect.png]]
The reflected ray is assumed to originate from a virtual image source point. The three triplets constitute three orthonormal basis systems. Below, it is assumed that the two dielectric media have permittivities ε<sub>1</sub> and ε<sub>2</sub>, and permeabilities μ<sub>1</sub> and μ<sub>2</sub>, respectively. A lossy medium with a conductivity σ can be modeled by a complex permittivity ε<sub>r</sub> = ε'<sub>r</sub> âjσ/ε<sub>0</sub>. Assuming '''n''' to be the unit normal to the interface plane between the two media, and Z<sub>0</sub> = 120Ω , the incident polarization vectors as well as all the reflected and transmitted vectors are found as:
:<math> \mathbf{ \hat{u}_{\perp} = \frac{\hat{k} \times \hat{n}}{|\hat{k} \times \hat{n}|} } </math>Â :<math> \mathbf{ \hat{u}_{\|} = \hat{u}_{\perp} \times \hat{k} } </math><!--[[File:frml1.png]]-->
The reflected unit vectors are found as: