The interference of the incident light reflected from the surface of a medium and from a picosecond strain pulse propagating through it results in temporal oscillations of the reflected intensity. This phenomenon, called time-domain Brillouin scattering, enables us to gain information about the optical field inside the medium. The oscillation amplitude decreases with increase of the distance from the strain pulse to the surface if the incident light is strongly absorbed, while it remains constant if the medium is transparent. Here we exploit time domain Brillouin scattering to probe the optical field inside a multiple quantum well layer for light strongly coupling to excitons and forming polaritons. At low excitation density, we observe conventional Brillouin oscillations whose amplitude is small when the strain pulse is positioned far from the surface due to the strong absorption of polaritons in the vicinity of the exciton resonance. At elevated optical density, the absorption disappears, the medium becomes transparent, and the amplitude of the oscillations does not depend on the distance of the strain pulse from the surface. We explain this effect of polariton-induced transparency by the increase of the incoherent exciton density generated as result of polariton scattering. Finally, the increase of the exciton density leads to transition of the exciton gas to a collective state, resulting in collapse of the polariton state and propagation of the incident light in the medium without absorption.