# Phase Shift on Reflection

Dear Experts,

When an electromagnetic wave moves from a rarer to a denser medium or gets reflected by a mirror, it encounters a phase shift of pi or (lambda/2), in that case, the reflected wave will be out of phase with the incident wave.

I have a very basic (maybe non intuitive or even stupid) doubt regarding this. Does the above mentioned statement imply that a light wave incident at 0 degrees to the normal to a surface will be completely destroyed by its reflecting counterpart?.

I am also finding it hard to understand why the phase shift occurs only in the interface between rarer to denser and not from denser to rarer. There are explanations in terms of waves on a tied string, but in case of electromagnetic waves in which fields are fluctuating, how can we relate the behavior.

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ehild
Homework Helper
The Maxwell equations predict what happens at the interface of two media: The components parallel with the interface both of the electric field E and of the magnetic field H are the same in both media and so are the normal components of D and B.

In case of an incident wave from the first medium, it follows from these boundary conditions, that there should be a reflected wave in the first medium , in addition of the refracted one, travelling in the second medium.
Also the ratio of the amplitudes r= E(reflected)/E(incident) and t= E(transmitted)/E(incident) can be derived. At normal incidence, r=(n1-n2)/(n1+n2) where n1 and n2 are the refractive indices.
You can see that the reflected amplitude is smaller than the incident one (there is never totalreflextion at normal incidence) and in case n1<n2, the reflected wave changes sign, so its phase changes by pi. In case n1>n2, the incident wave and the reflected one are in phase.
All these are true for dielectrics, having real refractive indices. The metals are different, their refractive index is complex, and the complex refractive index determines the phase change which can be anything between 0 and pi.

ehild

sophiecentaur
Gold Member
It's not only Maxwell's equations that are involved here. The same thing works for mechanical waves, too. There is something annoyingly 'mathematical' and almost arbitrary about the way waves behave - but the calculations predict what we always observe. So it's a good model.

olivermsun