Angularly symmetric splitting of a light beam upon reflection and refraction at an air-dielectric plane boundary

Conditions for achieving equal and opposite angular deflections of a light beam by reflection and refraction at an air-dielectric boundary are determined. Such angularly symmetric beam splitting (ASBS) is possible only if the angle of incidence is >60° by exactly one third of the angle of refraction. This simple law, plus Snell's law, leads to several analytical results that clarify all aspects of this phenomenon. In particular, it is shown that the intensities of the two symmetrically deflected beams can be equalized by proper choice of the prism refractive index and the azimuth of incident linearly polarized light. ASBS enables a geometrically attractive layout of optical systems that employ multiple prism beam splitters.