An ultra-broadband beam splitter arrangement, with a spectral amplitude response that is over seven orders-of-magnitude more uniform than broadband, multi-layer dielectric beam splitters, can be created by the combination of multiple Fresnel events on an uncoated, optical flat when used at a specific angle-of-incidence. This beam splitter arrangement produces three, spectral copies of the original, two of which have identical spectral phase. In this manuscript we derive the precise angle at which this maximally flat spectral amplitude response occurs for any material and present this angle's material and polarization dependence.