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Reflection and transmission of electromagnetic waves at an interface between two homogeneous materials is modified when a transition zone of linearly increasing permittivity is inserted between the half spaces. Mathematical expressions for reflection and transmission coefficients are derived for waves at arbitrary incidence angles and polarized either in or perpendicular to the plane of incidence. Discontinuities in permittivity at the transition zone boundaries are allowed. There is efficient transmission between the two half-spaces for transition zone thicknesses of a wavelength or greater. For sharper changes the matching layer has diminishing effect and the wave-interface interaction is characterized by the difference in properties between the two half-spaces. Examples applicable to lunar radar astronomy and airborne terrestrial remote sensing are used to illustrate the relationship between wavelength and thickness of the transition layer. A lossy transition layer also masks the electrical properties of the far half-space. Using only reflected power it is generally difficult to distinguish between dielectric models which are lossy and those which are gradational. For the lunar case, however, experimental values of attenuation indicate that gradations in soil permittivity should be observable.