convex from the discussion relating to fig7 it can next be shown that when an arbitrary number of n 1 reflections by a sequence of n 1 confocal reflectors u03c3 1 to u03c3 n 1 have distorted the initial symmetry of a spherical wave originating from for example focal point f 0 beam symmetry can easily be restored by the introduction of an additional reflector u03c3 n to place the feedhorn coincident with the equivalent axis to illustrate this technique in fig8 a principal ray 12 through focal point f 0 is reflected n 1 times where n 3 by reflectors u03c3 1 and u03c3 2 and is assumed to have its initial symmetry distorted the reflector u03c3 n to be added must be chosen so that the principal ray 12 also becomes one of the two central rays in the sequence of reflections by reflectors u03c3 1 to u03c3 n this requires that the path of ray 12 must close after 2 n successive reflections as has been explained previously in the discussions of fig3 and 4 since reflectors u03c3 1 and u03c3 2 are fixed the path of principal ray 12 from focal point f 0 and the reflections from reflectors u03c3 1 and u03c3 2 are also fixed in advance since ray 12 must also be one of the two central rays after 2 n reflections ray 12.