title: Difference between the Brewster angle and angle of minimum reflectance for incident unpolarized or circularly polarized light at interfaces between transparent media.
abstract: For reflection at interfaces between transparent optically isotropic media, the difference between the Brewster angle ϕB of zero reflectance for incident p-polarized light and the angle ϕu min of minimum reflectance for incident unpolarized or circularly polarized light is considered as function of the relative refractive n in external and internal reflection. We determine the following. (i) ϕu min < ϕB for all values of n. (ii) In external reflection (n > 1), the maximum difference (ϕB - ϕu min)max = 75° at n = 2 + √3. (iii) In internal reflection and 0 < n ≤ 2 - √3, (ϕB - ϕu min)max = 15° at n = 2 - √3; for 2 - √3 < n < 1, ϕu min = 0, and (ϕB - ϕu min)max = 45° as n → 1. (iv) For 2 - √3 ≤ n ≤ 2 + √3, the intensity reflectance R0 at normal incidence is in the range 0 ≤ R0 ≤ 1/3, ϕu min = 0, and ϕB - ϕu min = ϕB. (v) For internal reflection and 0 < n < 2 - √3, ϕu min exhibits an unexpected maximum (= 12.30°) at n = 0.24265. Finally, (vi) for 1/3 ≤ R0 < 1, Ru min at ϕu min is limited to the range 1/3 ≤ Ru min < 1/2.
authors.forename: R M A
authors.initials: RM
authors.lastname: Azzam
mesh_terms: D008027:Light; D055620:Optical Phenomena