Abstract
We give an exact solution of the electromagnetic s and p wave equations for a medium where the reciprocal of the refractive index varies linearly with distance. This solution leads to analytical expressions for the reflection amplitudes r s and r p, which reduce at normal incidence to the result obtained by Lord Rayleigh. These results are compared at long wavelength with those obtained recently to second-order in the (interfacial thickness/wavelength) expansion.
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