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The refractive index of an ionized medium in a magnetic field is complex. The formula for the refractive index is the cornerstone of the theory useful to establish the background study for radio wave propagation in uniform magneto-plasma. In the present paper, the expression for refractive index have been derived by considering Ionosphere as an anisotropic media with a constant drift so that it could be applied to any type of irregularities observed in the ionosphere. The formula has been derived taking variation in electron collision frequency with electron speed in drifting plasma. This expression is useful and helps to study the propagation characteristics of drifting plasma. The relativistic drift velocities of the plasma, generally reached by astrophysical plasma, will change the refractive index of the plasma considerably for example during re-entry of space vehicle in earth's atmosphere, the creation of high density plasma medium affects the radiated signal from the space craft. The medium of upper atmosphere gets affected under this condition.