The aim of the work is to confirm and to clarify a result in an earlier paper which showed that the refractive index of an ionized medium is given by µ2-1=-4πNe2/mv2 and not by the corresponding formula in 3(µ2-1)/(µ2+2). This is done by a direct analysis of the effects of collisions between free electrons and positive ions. It is shown that the perturbation of the electron’s path by the light has a secondary effect during a collision, so that if before entry into collision its position was displaced sideways, it will emerge from the collision with a changed velocity. The average effect of such changed velocities is equivalent to an acceleration, which reduces the effective force on the electron from E + 4π/3 P to E. This result is proved first for a positive ion composed of a uniform spherical charge, then for a proton and finally for any centrally symmetrical distribution of charge. Though it has not been proved for a system of unsymmetrical charges arbitrarily orientated, such as ionized molecules, there can be little doubt that the result is general.
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A 1943 study studied this question.