S Afr Optom 2011 70(1) 3-13 Graphical construction of cardinal points from the transference WF Harris Department of Optometry, University of Johannesburg, PO Box 524, Auckland Park, 2006 South Africa <
[email protected]> Received 21 December 2010; revised version accepted 24 February 2011 Abstract fected by changes in the system or when a second optical system is placed in front of the first. The Usually nodal, principal and focal points are de- paper illustrates the graphical procedure by apply- fined independently and thought of as distinct struc- ing it in several situations of interest in optometry tures with no simple relationship among them. By and ophthalmology, including the effect of a con- adopting a holistic approach, in which these three tact lens or refractive surgery on a reduced eye types of cardinal points are treated as particular and the effect of accommodation, a spectacle lens cases of a larger class of special points, this paper and an afocal telescope on the Gullstrand-Emsley develops a method of constructing the locations of schematic eye. (S Afr Optom 2011 70(1) 3-13) the cardinal points of a system graphically directly from the transference. The method provides a use- Key words: Cardinal point, nodal point, principal ful way of visualising the relationship of the loca- point, focal point, transference tions of the cardinal points and of how they are af- Introduction the system from which one can obtain the positions of the individual cardinal points by construction. The The purpose of this paper is to show how one can slopes and cutting points of the straight lines come obtain the locations of cardinal and other special directly from the entries of the system’s transference.