General Formulas of Effective Earth Radius and Modified Refractive Index

The effective earth radius can transform the curved ray path into a straight line, and modified refractive index spherical ground plane. Using them simplify propagation modeling of electromagnetic waves in atmosphere, so they are widely used calculation long-range wave, adopted by ITU Recommendations IEEE Standards. In this paper, upon employing simple geometric methods, we provide general formulas for index, pointing out that both originate from use conformal transformations. turn, prove quantities contained Standards special cases given paper. Our results solid mathematical background to concepts pave way their beyond e.g. other types generic media.