Abstract
The quasi-longitudinal and quasi-transverse approximations to the Appleton-Lassen refractive index formula for a homogeneous magneto-ionic medium have been known and used for over half a century. These formulae are derived by various methods, using the procedures of elementary analysis and algebra. In the present paper an investigation is made so as to discover why these formulae take the particular forms that are so well known. To this end, the basic propagation equations are generalized to n dimensions, and the corresponding refractive indices and their various approximations are examined in their generality. A ladder of such formulae is produced, with the three-dimensional case sitting at its lowest rung. The structure of all the formulae is thereby exhibited, and the reasons for their particular algebraic forms when n = 3 can be clearly demonstrated.
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