At a boundary between two media, the tangential components of the electric field E are conserved. If there are no surface currents, the tangential components of the magnetic field
H are also conserved.
The above definition of rp is consistent with
Ref. 6 but shows the opposite sign compared to
Ref. 7. This is because
Ref. 6 defines the direction of the in-plane field component such that the s-polarized component, p-polarized component, and ray direction vector (in that order) always comprise a right-handed coordinate system; whereas in
Ref. 7 the vectors written in this order would comprise a left-handed coordinate system for the reflected ray.