In multiple quantum well (MQW) structures with equidistant, identical QW's and large period P (comparable to the wavelength lambda of light in the barrier material at the exciton energy), coupled exciton photon (polariton) states are formed. When the Bragg condition P = lambda/2, is satisfied, a large increase of the exciton reflectivity is observed. The shape of the reflectivity spectrum depends also on the distance C of the last QW to the sample surface, i.e., the cladding layer thickness. When C = lambda/4 and the Bragg reflection condition P = lambda/2 is exactly fulfilled, the exciton signal appears as a symmetrical, deep dip in the reflectivity background, associated to the reflection from the sample surface. We present here a study of the effect of detuning the exciton wavelength slightly off the Bragg condition lambda = 2 P. The investigated structure contains 10 Cd0.96Mn0.04Te QW's (100 Angstrom thick) occurring between Cd a barriers (1100 Angstrom thick), MBE grown on Cd0.95Zn0.05Te substrates. The growth conditions were carefully controlled in order to obtain a perfectly periodic structure with constant barrier's and QW's widths. The RHEED intensity oscillations were observed during growth of the whole structure. The period of the MQW structure and the cladding layer thickness were very close to lambda/2 and lambda/4, respectively. We use the giant Zeeman effect in the CdMnTe QW's to continuously tune the exciton energy across the Bragg condition. The reflectivity spectrum is shown to vary dramatically for a relative detuning as small as 10(-3).