I've seen in several places (such as here) that when studying normal incidence of a plane EM wave on a dielectric the boundary condition


is applied. In words, the tangential component of $\mathbf{H}$ has to be conserved.

However, as far as I know, that is not true, as that boundary condition for the magnetic field depends on whether there is a surface density current in the boundary:


If the surface current $\mathbf{K}$ is $0$, then the first equality is true. But why is the surface current assumed to be $0$?


1 Answer 1


$\mathbf{K}$ here is the free surface current that is already there on the surface as opposed to bound current induced by the incident field. Since there is no reason to expect a source for such a free current especially at optical frequencies we neglect it. This would not be the case if we were considering EM waves at the AC frequency reflecting from a current carrying conductor for example.


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