An illumination system using, in place of a more typical beam splitter, two right angle triangular prisms that are aligned to each other along their respective hypotenuses to form a cube, but without any reflective materials being used at their interface, and with the two halves separated by some distance so as to create an open/air gap between the two halves. When the upper/lower cube faces are normal to an optical axis of the illumination system, the cube structure reflects virtually all of the illumination from a transverse illumination source using total internal reflection so that said illumination is reflected out of the cube along the system's optical axis. However, rotating the cube structure past the critical angle eliminates total internal reflection and allows the cube to transmit almost all illumination entering the cube out of the cube parallel to the system's optical axis.