The equations of propagation of electromagnetic waves, simple harmonic in time, in an optically anisotropic stratified medium are obtained from the treatment of the refracted wave as the resultant of the incident wave and wavelets scattered by the elements of volume of the medium, and are reduced to a simple form.
The primitive property of the medium, from which the other optical properties are derived, is the scattering tensor, relating the induced dipole moment per unit volume to the applied electric field.
The relation between the dielectric tensor (corresponding to the dielectric constant of an isotropic medium) and the scattering tensor is obtained.
A medium consisting of classical oscillators in an external magnetic field is then considered, the scattering tensor and dielectric tensor are evaluated for such a medium, and finally a formula for the refractive index is obtained.
For an ionised medium the formula differs from that obtained by Goldstein; the difference is due to the inclusion in the present treatment of a term omitted by Goldstein; the significance of this term is discussed, and its inclusion justified.
Taking this term into account makes an important difference to the properties of the medium for long waves; an example is given.