Abstract
For fifty years the quasi-longitudinal and quasi-transverse approximations to the refractive index formula for an ionised plasma have been used. Recent investigations have sought to generalise the traditional treatment in various ways. In the author's opinion, something further remains to be explained, and in the present paper various algebraic identities are examined between distinct forms of the refractive index, whereby a radical can sometimes be switched between numerator and denominator. Approximations to this radical are kept distinct algebraically from any subsequent expansions that may be made in the refractive index formula. The properties of this radical and its various approximations are examined in detail, both algebraically and numerically.
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