The particle on the lower loop and the upper loop, where the last point to enter into the second medium is the earliest and the latest respectively, are reflected at different points along the interface. The ray splits into two beams. In order to be reflected, this last point is lifted off the interface just as it enters into the second medium. The distance between the two point of reflection,
\(d=2x_vsin(\theta).\cfrac{1}{sin(90^o-\alpha)}\)
where \(x_v\) is the radius of circular motion of the particle displace from the \(\psi\) cloud center. The separation between the two rays is,
\(d_b=d.{sin(90^o-\alpha)}=2x_vsin(\theta)\)
where \(x_v\) is the radius of circular motion of the particle displace from the \(\psi\) cloud center. The separation between the two rays is,
\(d_b=d.{sin(90^o-\alpha)}=2x_vsin(\theta)\)
Since the particle are reflected off at different times, there is also a phase shift between the lower and upper loop. The \(E\) fields due to the rotating particles on the two loops are both in the same direction. These are linearly polarized light.
When \(\theta\lt90^o-\alpha\),
Both loops leave the second medium at the apex of the cone. There is no phase shift between the two loops. Both loops are reflected off at the point of reflection. The \(E\) fields due to the rotating particles on the two loops radiate from a common center; the ray remains circularly polarized.
Both instances suggest that the cause of such shifts are inherent in the nature of emitted fluorescence and not of the reflecting interface.
