Abstract: An annular prism capable of causing light (or other radiation) to either converge or diverge is defined by an annulus of material which is transparent to the light (or other radiation). The annulus tapers radially towards either its outer periphery or its central aperture. If the annulus tapers towards its outer periphery, light converges. If the annulus tapers towards its central aperture, light diverges. The degree of tapering determines the degree of convergence or divergence. A cross section of the annulus formed by a plane containing a principal axis of the annulus viewed on only one side of the principal axis may have a triangular shape. In some embodiments, a segment of the annulus may be missing, resulting in a penannular prism which causes light (or other radiation) to converge or diverge about the principal axis of the incomplete annulus for some angular measure less than 360 degrees.