  The interaction between a light pulse, traveling in air, and a generic
linear, non-absorbing and dispersive structure is analyzed. It is shown that
energy conservation imposes a constraint between the group velocities of the
transmitted and reflected light pulses. It follows that the two fields
propagate with group velocities depending on the dispersive properties of the
environment (air) and on the transmission properties of the optical structure,
and are one faster and the other slower than the incident field. In other
words, the group velocity of a light pulse in a dispersive medium is
reminiscent of previous interactions. One example is discussed in detail.
