Difference between the Brewster angle and angle of minimum reflectance for incident unpolarized or circularly...

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.