For light reflection at a planar interface between two homogeneous isotropic media with complex relative dielectric function epsilon , it is shown that the constant-principal-angle contours are a family of semicircles, whereas the constant-principal-azimuth contours are a family of (segments of) hyperbolas in the complex epsilon plane. Also found are the exact envelope curve of both families and hence determine the domain of the epsilon plane of multiple (three) principal angles that is bounded by the envelope curve and the real axis. A unique and peculiar interface is shown to have three coincident principal angles of 30 degree and an associated curve of relative phase shift versus angle of incidence that exhibits a distinct shoulder at the principal angle.
