Using the theory of radiative transfer, we investigate the interaction between polarized waves and a multiple scattering medium as functions of the relative index of refraction. To study this problem, we consider circularly and linearly polarized continuous waves incident upon a medium containing spherical scatterers. With an accurate spectral method, we compute the transmitted Stokes parameters through media containing different sized scatterers and different indices of refraction. Our numerical results show that the circular depolarization length exhibits a strong dependence on the relative index of refraction, while the linear depolarization length does not.