The isoangle and isobragg are new concepts used in mapping loci of incident and reflected rays associated with a dispersive reflector. An isoangle is a line joining the points of incidence at which the angle of incidence of rays from a point source is the same. An isobragg is the line joining the points of intersection at any surface by rays of the same wavelength that have been reflected according to Bragg's law. Their patterns provide an understanding of why and where we use dispersive multilayered optics in x-ray monochromators and spectrometers with Rowland circle geometry. They have led to the design of an x-ray focusing ring for electron spectroscopy for chemical analysis (ESCA) instrumentation and the possibility of a design for a scanning x-ray microscope.