Why does light undergo a phase change when reflecting from a denser medium?

[metalrose]

What is the explanation for the phase change of pie that occurs when a light ray gets reflected from an optically denser medium?

This fact was demonstrated by the Llyod's mirror experiment, but what is the theoretical explanation for it?

Thanks

 

[Petr Mugver]

When encountering a discontinuity in the propagation medium, the electromagnetic field must satisfy certain boundary conditions. Let n be the vector normal to the surface of discontinuity, Ei, Er, Ed the incident, reflected and refracted electric fields, and similarly for the magnetic field B and for the fields D=eE and H=B/m, wher e is the dielectric constant and m the magnetic constant of the medium of propagation. Then the Maxwell equations say that, at the discontinuity, it must be

(Ei + Er) x n = Ed x n
(Di + Dr) . n = Dd . n
(Hi + Hr) x n = Hd x n
(Bi + Br) . n = Bd . n

Assuming a exp[i(k.r-wt)] dependence of the fields (Fourier transform), the above equations relate the amplitudes and phases of the incident, reflected and refracted fields. Depending on the problem under examination, you can then calculate all the phase shifts and amplitude variations.