Special Relativity in Refracting Media

A reformulation of the Lorentz transformations for an observer in a refracting but non-dispersive medium is suggested. In this statement of the transformations, the speed ($\mathbf{c}=\frac{c}{n}$) of light signals in the medium replaces the free space speed ($c$) which appears in the usual form. It is shown that the Fresnel drag coefficient takes the same form in the new formulation that it did in the old. Other consequences of this assumption are discussed and, in particular, the mechanics of the photon are shown to lead to correct expressions for Snell's law and for the pressure of radiation at the boundary of the medium.