Media interface can be used for changing the state of polarization of an Electromagnetic Wave
The electric field for any state of polarization can be resolved into two orthogonal components one parallel to the
plane of incidence and other perpendicular to it. Therefore the incident electric field can be written as
The reflected and transmitted fields can be written as
where the reflection coefficients and are real for ordinary reflection and complex for Total Internal Reflection.
Linearly Polarized Incident Wave
For a linearly polarized wave then
(a)
For ordinary reflection since and are real the reflected and transmitted fields also remain linearly polarized.
However, since in general and the plane of polarization changes.
(b)
If the reflection is total internal then and are complex and therefore the reflected and transmitted
field components are not in phase. Consequently the transmitted and reflected waves are elliptically polarized.
Circularly Polarized Incident Wave
In this case
and
In general since and the reflected and transmitted both waves will become elliptically polarized.
Conclusion
A linearly polarizeed wave remains linearly polarized at orid reflection. But becomes elliptically polarized
at Total Internal Reflection.
An elliptical or circularly polarized wave become elliptically polarized wave become elliptically polarized wave
with change in actual ratio and the tilt angle.
Click here to see an interactive visualization:Applet 5.1
and 
are real for ordinary reflection and complex for Total Internal Reflection. 
then 
and 
are real the reflected and transmitted fields also remain linearly polarized.
However, since in general 
and 
the plane of polarization changes. 
and 
