The reflection and refraction of light of wavelength lambda at an angle of incidence Phi by the interface between two dielectric media of refractive indices N(0) and N(2) can be made completely independent of polarization by introducing a thin layer of refractive index N(1) = (N(0) N(2))(1/2) and thickness d = (lambda/4) (N(1)(2) - N(0)(2) sin(2)Phi)(-1/2). This is the basis of an ideal beam splitter, whose general characteristics are presented here. A particularly simple result is that the device reflectance has an upper limit of tan(4)(Phi/2), so that a 50-50% beam splitter must operate at Phi > 80.121 degrees . Lower reflectances, attainable at lower angles, are suited for applications such as optical feedback and monitoring the output power and state of polarization of high-power lasers.