The specular reflection of plane waves is treated by the wave theory method. For the case in which the velocity of wave propagation and the radiation impedance vary sufficiently slowly that multiple reflection may be neglected the reflection coefficient is first obtained for monochromatic waves incident on a set of $n$ plane parallel plates with otherwise arbitrary properties. The method may also be used to obtain the reflection coefficient in the case of large reflectivity but the results are exceedingly cumbersome for a large number of plates. The result for monochromatic waves is used to obtain the reflection coefficient for a plane wave pulse of arbitrary shape and duration. It is shown that the reflected wave train consists of a series of pulses of exactly the same form as the incident pulse with the amplitude of each reduced by the value of the appropriate Fresnel reflection coefficient. The interference effects are also represented. The sufficient condition for reproduction of the form of the incident pulse in the reflected wave is that the reflection coefficient for monochromatic waves be expressible as a sum of terms each of which is periodic in the frequency. In contrast to previous statements in the literature, periodicity of the coefficient itself is unnecessary. The results for the $n$ plate problem are generalized for both monochromatic waves and pulses for the case of stratified media having reflective properties which vary continuously in any manner. The special case of rectangularly shaped pulses is analyzed and application is made to the reflection in sea water and in the atmosphere.

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