At 2 K, at low intensity, and in good-quality samples, the source of the exciton-polariton dipole dephasing time (or phase-coherence time) is found to be extrinsic in nature and due to dephasing elastic collisions for excitation below the transverse-^-exciton frequency, and purely intrinsic and due to quasielastic collisions with acoustical phonons for excitation above the longitudinal-^4-exciton frequency. The damping increases linearly with detuning for excitation above the longitudinal-^-exciton frequency.PACS numbers: 72.10.Di, 78.50.Ge In this Letter, we report detailed measurements and a comprehensive study of the damping dispersion of both the A and B exciton polaritons in CdS over a wide frequency range. We identify the source of the damping and we demonstrate for the first time that, at low temperatures and in high-quality samples, the source of the damping is completely different for excitation above and below the lowest transverse-exciton frequency (w^). It is found that the damping below the co TA frequency is extrinsic in nature and is governed by the impurity (and point defects) content of the sample. Above the coj A resonance, the dephasing is intrinsic and the results can be well explained by an exciton-acoustic-phonon interaction through the deformation-potential mechanism. This leads to a damping coefficient above the CO T A frequency proportional to the detuning from the COTA resonance. These results challenge the common use of a constant, detuning-independent, phenomenological damping coefficient in the expression of the exciton contribution to the complex dielectric function. Our approach for extracting the exciton-polariton damping is based on the precise measurement of the optical transmission of high-quality CdS platelets. By working in a spectral region away from the longitudinal (&>/,) and transverse (COT) excitons, the present study deliberately avoids the need of determining the correct additional boundary condition and the appropriate dead-layer thickness. 1,2 Given the sample thickness and purity used in the experiment, the additional wave is of too small amplitude to perturb significantly the observed Fabry-Perot fringes. Future work in and around the CO L T region should provide a means of testing different additional boundary conditions, as was already suggested by Broser, Pantke, and Rosenzweig, 3 but this is not the present intent.We have restricted our present studies in CdS to light polarized perpendicular to the c axis and to frequencies around the A and B excitons. The dispersion relation, expressed by the dielectric function e(k,co), is given by the following expression 4 " 6 :