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XXXIII. Notes on Geometrical Optics. — Part I. 

 By Professor Silvanus P. Thompson, D.Sc* 



1. The Deduction of the Elementary Theory of Tenses and 

 Mirrors from Wave Principles. 



JNTRODUCTOR K— The division of Optics into a " geo- 

 metrical " part, founded upon the treatment of the 

 subject from the ray point of view, and a " physical " part, 

 founded upon the treatment of the subject from the wave 

 point of view, has long seemed illogical. Experience in 

 the teaching of the science suggests that it would be pre- 

 ferable to adopt the wave theory as a common basis, provided 

 the formulae of lenses and mirrors which form the staple 

 of geometrical optics are as readily established on wave prin- 

 ciples as on ray principles. Five years ago the author of 

 these notes made an attempt to rewrite the elementary part 

 of geometrical optics on wave principles ; and though hitherto 

 he has published nothing on the subject, he has subjected the 

 method to the test of experience, and has made it the basis of 

 his optical lectures year by year. The form finally adopted, 

 and now for the first time set forth, has been modified from 

 time to time and simplified. As a result, whilst the formulae 

 for second approximations, aberration and the like, can be 

 deduced with no greater difficulty than in the orthodox 

 way, the elementary formulae for first approximations are 

 much more simply deduced, and do not even require the use of 

 trigonometrical functions. This is the more striking because, 

 as all teachers of the subject know, the very first assumptions 

 made in establishing the elementary formulae of spherical 

 mirrors and lenses are that angles may be written instead 

 of their sines or tangents. The assumptions made in the 

 method now published are, it is true, different, but involve no 

 greater sacrifice of accuracy, the formulae being true to the 

 same degree of approximation, and, indeed, though written in 

 a different notation, are in substance identical with those in 

 common acceptance. 



It will be convenient, first, to set forth the general bases of 

 the method ; next to define the method of reckoning cur- 

 vatures ; then to explain the notation employed ; lastly, 

 to develop the elementary formulae. 



2. General Bases. 



In treating optics from the new standpoint, we have to 

 think about surfaces instead of thinking about mere lines. 

 * Communicated by the Physical Society; read June 8, 1889. 



