The problem treated here is that of reflection of plane waves from the free plane boundary of a half-space made of a medium with microstructure. It is shown that an incident ray of either dilatational or distortional type, in general, gives rise to four reflected rays, two of each type. Two of these reflected waves are evanescent and the other two propagate into the medium. Each of these reflected waves have their own phase shifts relative to the incident wave.

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