Velocity of Light in Dark Matter with Charge

We propose an interesting mechanism to reconcile the recent experiments of the Michelson-Morley type and slowdown of the velocity of light in dark matter with a fractional electric charge when the index of refraction of dark matter depends on the frequency of a photon. After deriving the formula for the velocity of light in a medium with the index of refraction $n(\omega)$ in a relativistic regime, it is shown that the local anisotropy of the light speed is proportional to the second order in $n(\omega) - 1$. This result implies that the experiments of the Michelson-Morley type do not give rise to a stringent constraint on the slowdown of the velocity of light in dark matter with electric charge.