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I am having some confusions about EM wave propagation on a stacked media, where at the interface, the magnetic field is discontinuous due to a

I am having some confusions about EM wave propagation on a stacked media, where at the interface, the magnetic field is discontinuous due to a surface charge density K=?E???, whereE??? is the tangential component of the electric field.

Attached below is the situation, where the wave is propagating along the x-direction and the electric field being polarized in the y-direction.

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