  Transfer matrix method is a well-known and extensively used tool to compute
the reflection and transmission coefficients of electromagnetic waves when
interacting with a system of layers parallel to each other. We present here a
modified form of transfer matrix method including the effects of any possible
kinetic movements of layers with respect to each other with a constant
velocity. We present a comprehensive analysis of the effect of velocity on the
phase and amplitude of the reflection coefficient as a function of velocity.
Additionally, to mimic the flow of liquids on top of layers we also present the
effect of velocity gradients in the direction normal to the planar layers.
