Why does light experience a phase shift when reflected and not experience one when passing from a higher to lower refractive index?

Question

Why does light experience a phase shift when reflected, but not when passing from a higher to a lower refractive index?

If anyone could explain this conceptually it would be greatly appreciated!

Answer 1

Phase shift occurs only when reflecting back to medium of lower index of refraction (e.g. reflection off an air-glass boundary back to the air). When we have a wave reflecting back to a medium of higher index of refraction (e.g a wave coming from glass, back to the glass), there is no phase shift. And finally, the transmitted wave passing through a boundary does not get a phase shift either.

This behaviour of waves on a boundary having a jump in the speed of propagation is quite universal, it holds also for e.g. sound waves. But in EM theory, we can explain more about the mechanism behind the phase shift, as follows.

Let there be the primary wave coming from vacuum towards a material body, head on towards the planar boundary (perpendicularly). This wave acts (its electric field) on charged particles in the body near the boundary, and accelerates them. From Maxwell's equations and the usual boundary conditions (retarded fields), it follows that the accelerated charged particles generate their own secondary EM fields, with a wave component, with the same frequency, but, on a line towards the primary source, with opposite direction of electric field compared to the electric field of the primary wave there.

When these elementary secondary waves due to all particles in the body (close and far from the boundary) are superposed, in the vacuum half-space, it turns out they form a wave of same frequency and opposite direction of propagation; and, at the boundary, with opposite direction of electric field compared to the primary wave. Again, this fact that the secondary electric field has the opposite direction follows from Maxwell's equations and the usual boundary conditions on the EM field. On the line towards the source, the charged particle acceleration field (a part of its electric field proportional to its acceleration) is in direction opposite to the product of acceleration and charge $q\mathbf a$, and thus always points against the primary field.

So, the 180 degree phase shift of the light wave reflecting back to vacuum is a natural consequence of interaction of EM field with a body full of charged particles. What really needs explaining then, is why there is no phase shift for the wave that reflects back into medium of higher index of refraction, and also for the wave that continues in the original direction. But this post is quite long already, so I'll let someone else explain that part...