We consider the plane-wave spectrum generated by two arbitrary current distributions, J 1( r) and J 2( r), in free space below, or above, a plane stratified ionosphere. We apply the 2×2 ionospheric reflection or transmission matrices R( k) or T ±( k) defined in terms of the TE or TM modal amplitudes, and perform an inverse Fourier transform on the reflected or transmitted spectral components, to obtain the resultant fields, E 1( r) and E 2( r), reflected from, or transmitted through the ionosphere. A scattering theorem is then applied which connects the scattering matrices in a given problem with those in a ‘conjugate’ problem, namely, R ±(k) = R ̃ ±(k c) , T ±(k) = T ̃ ∓(k c) , where the propagation vector k c is the mirror image of k with respect to the vertical, magnetic east-west plane. It is shown that ∝ E 1( r) · J 2( r) d 3 r = ∝ E 2 c ( r) · J 1 c ( r) d 3 r where E i c ( r), i = 1, 2, represents the respective fields generated by the image or mirrored, current systems J i c ( r), i.e. mirrored with respect to the vertical magnetic meridian plane. It is noted that whereas the Lorentz reciprocity theorem relates currents and fields in the presence of (or inside) a given medium with those in the presence of a transposed medium (i.e. in the presence of a hypothetical ionosphere in which the geomagnetic field has been reversed), the result here derived relates instead a given and a mirrored pair of current systems, and their associated wave fields, in the same physical system.