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Wikipedia says the Electric-field shifts by 180-degrees, but the Magnetic-field by 0-degrees.

Are there other instances where the $E$-field and $B$-field of an EM-wave are out-of-sync (out-of-phase, unsynchronized, whatever) with each other? Do they stay that way?

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The E- and B-fields do not really become out of phase, it is just that the wave changes direction upon reflection. The E-and B-fields still have a maximum modulus and zeroes at the same space/time coordinates.

Since the B-field is in the direction of $\vec{k}\times \vec{E}$, where $\vec{k}$ is the wave vector, then since both $\vec{k}$ and $\vec{E}$ are reversed, then the B-field direction is unchanged.

In general there is a phase difference between the E- and B-fields whenever a wave travels in a medium with a non-zero conductivity. For an ideal conductor, the phase difference is $\pi/4$.

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