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 ϕ which is determined by the complex dielectric function ∊. A new special angle of incidence, denoted by ϕΔ′max, is defined at which the slope Δ′ = ∂Δ/∂ϕ of the Δ–ϕ curve is maximum negative, and a transcendental equation is derived that determines this angle. ϕΔ′max differs from the principal angle ϕp at which Δ = 90°. As an example, ϕΔ′ max is calculated by numerical iteration for light reflection at the air–Si interface for photon energies hν from 1.7 to 5.6 eV in steps of 0.1 eV, and is plotted, along with the associated maximum slope vs wavelength λ. It is noted that ϕΔ′ max > ϕp at every λ, a result that may hold in general. Also, for 4.5 ≤ hν ≤ 5.6 eV, ϕΔ′ max = 90°, so that a maximum negative slope occurs at grazing incidence in this spectral range. Another interesting observation is that, when |∊| ≫ 1 (e.g., for metals in the IR), Δ′(90°) is a direct measure of the extinction coefficient k = Im∊1/2.
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