Abstract

For reflection at interfaces between transparent optically isotropic media, the difference between the Brewster angle ${\varphi }_{\mathrm{B}}$ of zero reflectance for incident $p$-polarized light and the angle ${\varphi }_{u\min }$ 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) ${\varphi }_{u\min }<{\varphi }_{\mathrm{B}}$ for all values of $n$. (ii) In external reflection $(n>1)$, the maximum difference ${({\varphi }_{\mathrm{B}}-{\varphi }_{u\min })}_{\max }=75°$ at $n=2+\sqrt{3}$. (iii) In internal reflection and $0<n\le 2-\sqrt{3}$, ${({\varphi }_{\mathrm{B}}-{\varphi }_{u\min })}_{\max }=15°$ at $n=2-\sqrt{3}$; for $2-\sqrt{3}<n<1$, ${\varphi }_{u\min }=0$, and ${({\varphi }_{\mathrm{B}}-{\varphi }_{u\min })}_{\max }=45°$ as $n\to 1$. (iv) For $2-\sqrt{3}\le n\le 2+\sqrt{3}$, the intensity reflectance $R_0$ at normal incidence is in the range $0\le R_0\le 1/3$, ${\varphi }_{u\min }=0$, and ${\varphi }_{\mathrm{B}}-{\varphi }_{u\min }={\varphi }_{\mathrm{B}}$. (v) For internal reflection and $0<n<2-\sqrt{3}$, ${\varphi }_{u\min }$ exhibits an unexpected maximum (= 12.30°) at $n=0.24265$. Finally, (vi) for $1/3\le R_0<1$, $R_{u\min }$ at ${\varphi }_{u\min }$ is limited to the range $1/3\le R_{u\min }<1/2$.

© 2015 Optical Society of America

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