The differential reflection phase shift, Δ = δp - δs, associated with the external reflection of monochromatic light at the surface of an absorbing medium is a monotonically decreasing function of the angle of incidence ø which is determined by the complex dielectric function ε. A new special angle of incidence, denoted by øΔ′max, is defined at which the slope Δ′ = ∂Δ/∂ø of the Δ-ø curve is maximum negative, Δ′max, and a transcendental equation is derived that determines this angle. øΔ′max differs from the principal angle øp at which Δ = 90°. As an example, øΔ′max is calculated by numerical iteration for light reflection at the air-Si interface for photon energies hv from 1.7 to 5.6eV in steps of 0.1eV, and is plotted, along with the associ...