Changes

EM.Terrano

11 bytes added, 14:25, 14 June 2013
/* Ray Reflection & Transmission */
=== Ray Reflection & Transmission ===
 
[[File:reflect.png|thumb|350px|The Incident, Reflected and Transmitted Rays at the Interface Between Two Dielectric Media]]
The incident, reflected and transmitted rays are each characterized by a triplet of unit vectors:
* <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.
* <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 Incident, Reflected and Transmitted Rays at the Interface Between Two Dielectric Media
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 &epsilon;<sub>1</sub> and &epsilon;<sub>2</sub>, and permeabilities &mu;<sub>1</sub> and &mu;<sub>2</sub>, respectively. A lossy medium with a conductivity &sigma; can be modeled by a complex permittivity &epsilon;<sub>r</sub> = &epsilon;'<sub>r</sub> –j&sigma;/&epsilon;<sub>0</sub>. Assuming '''n''' to be the unit normal to the interface plane between the two media, and Z<sub>0</sub> = 120&Omega; , the incident polarization vectors as well as all the reflected and transmitted vectors are found as:
Administrator
613
edits