physical optics In physics, physical optics, or wave optics, is the branch of optics that studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid. This usage tends not to include effec ...

, the Stokes relations, named after

Sir George Gabriel Stokes Sir George Gabriel Stokes, 1st Baronet, (; 13 August 1819 – 1 February 1903) was an Irish English physicist and mathematician. Born in County Sligo, Ireland, Stokes spent all of his career at the University of Cambridge, where he was the Luc ...

,Hecht, Eugene, Optics, Fourth Edition, describe the relative phase of light reflected at a boundary between materials of different refractive indices. They also relate the

transmission Transmission may refer to: Medicine, science and technology * Power transmission ** Electric power transmission ** Propulsion transmission, technology allowing controlled application of power *** Automatic transmission *** Manual transmission *** ...

and

reflection coefficient In physics and electrical engineering the reflection coefficient is a parameter that describes how much of a wave is reflected by an impedance discontinuity in the transmission medium. It is equal to the ratio of the amplitude of the reflected wa ...

s for the interaction. Their derivation relies on a time-reversal argument, so they only work when there is no absorption in the system. A reflection of the incoming field (''E'') is transmitted at the dielectric boundary to give ''rE'' and ''tE'' (where ''r'' and ''t'' are the amplitude reflection and transmission coefficients, respectively). Since there is no absorption this system is reversible, as shown in the second picture (where the direction of the beams has been reversed). If this reversed process were actually taking place, there will be parts of the incoming fields (''rE'' and ''tE'') that are themselves transmitted and reflected at the boundary. In the third picture, this is shown by the coefficients ''r'' and ''t'' (for reflection and transmission of the reversed fields). Everything must interfere so that the second and third pictures agree; beam ''x'' has amplitude ''E'' and beam ''y'' has amplitude ''0'', providing Stokes relations. The most interesting result here is that ''r=-r’''. Thus, whatever phase is associated with reflection on one side of the interface, it is 180 degrees different on the other side of the interface. For example, if ''r'' has a phase of 0, ''r’'' has a phase of 180 degrees. Explicit values for the transmission and reflection coefficients are provided by the Fresnel equations

References

Optics {{Optics-stub