Abstract
We report two experiments. The first is an accurate measurement of the phase of the light reflected by a CdSe crystal in the excitonic region. The second is a direct measurement of the time delay experienced by a reflected wave packet in the same frequency range. We show that it is necessary to take into account the existence of an exciton-free surface layer to satisfactorily fit the experimental results. The very fast variation of phase near the longitudinal exciton frequency, larger than \ensuremath{\pi} over 0.3 meV, and the very large delay of 12 ps observed under the same conditions are attributed to multiple reflections inside the exciton-free layer in a frequency range where the layer acts as an antireflecting Fabry-P\'erot plate.