Which group velocity of light in a dispersive medium?

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 that of 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.