I have seen a lot about when light undergoes a phase change when it is reflected. But does it undergo a phase change when refracted and if so why and if not why not?
Answer
The key word here is continuity.
The continuity boundary conditions for the electromagnetic field vectors sets these phenomenons. The tangential components of $\vec{E}$ and $\vec{H}$ must be continuous across an interface - the only way that they can not be is if there is a surface current flowing (which cannot happen in dielectrics). Likewise, the normal components of the displacement and induction must be continuous across the boundary (the only way that they cannot is if nett charge gathers on the surface - again - not possible in a dielectric.
On the incidence side there are two fields - the incident and reflected one. The sum of these two must have the same phase as the transmitted wave, by the continuity conditions. If you write down boundary conditions for tangential and normal components, then you find that the only way that continuity can be upheld is if the incident and transmitted waves are in phase, whilst the reflected wave may be either exactly in or out of phase, depending on whether the waves are crossing an increase or decrease in refractive index.
Continuity of boundary conditions holds for different physical reasons for different waves, but the conditions are often similar. We don't often find fields in nature with a sudden, discontinuous change in them.
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