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For a dioptric system with elements which may be heterocentric and astigmatic an optical axis has been defined to be a straight line along which a ray both enters and emerges from the system. Previous work shows that the dioptric system may or may not have an optical axis and that, if it does have one, then that optical axis may or may not be unique. Formulae were derived for the locations of any optical axes. The purpose of this paper is to extend those results to allow for reflecting surfacesdoi:10.4102/aveh.v69i3.133 fatcat:sih4xqomdndd3gucq4tho4x7mm