The conditions under which light interference in a transparent quarter-wave layer of refractive index $n_1$ on a transparent substrate of refractive index $n_2$ leads to 50% reflectance for incident unpolarized light at an angle φ are determined. Two distinct solution branches are obtained that correspond to light reflection above and below the polarizing angle, ${\phi }_p$ , of zero reflection for p polarization. The real p and s amplitude reflection coefficients have the same (negative) sign for the solution branch $\phi >{\phi }_p$ and have opposite signs for the solution branch $\phi <{\phi }_p$ . Operation at $\phi <{\phi }_p$ is the basis of a 50%–50% beam splitter that divides an incident totally polarized light beam (with p and s components of equal intensity) into reflected and refracted beams of orthogonal polarizations [ Opt. Lett. 31, 1525 (2006) ] and requires a film refractive index $n_1⩾(\sqrt{2}+1)\sqrt{n_2}$ . A monochromatic design that uses a high-index $\mathrm{Ti}{\mathrm{O}}_2$ thin film on a low-index $\mathrm{Mg}{\mathrm{F}}_2$ substrate at $488\mathrm{nm}$ wavelength is presented as an example.