Impedance boundary conditions for imperfectly conducting surfaces

TLDR: In this article, the exact electromagnetic boundary conditions at the surface of a material of large refractive index can be approximated to yield the usual impedance or Leontovich boundary conditions, which are valid for surfaces whose radii of curvature are large compared with the penetration depth.

Abstract: It is shown how the exact electromagnetic boundary conditions at the surface of a material of large refractive index can be approximated to yield the usual impedance or Leontovich boundary conditions. These conditions relate the tangential components of the electric and magnetic fields (or the normal components and their normal derivatives) via a surface impedance which is a function only of the electromagnetic properties of the material. They are valid for surfaces whose radii of curvature are large compared with the penetration depth, and also for materials which are not homogeneous but whose properties vary slowly from point to point. As the refractive index (or conductivity) increases to infinity, the conditions go over uniformly to the conditions for perfect conductivity.