Maximum Optical Paths

Abstract

ERRORS that have once appeared in print have a way of turning up in the most unexpected places. As Dr. Karl Darrow's interesting article on quantum mechanics in Review of Modern Physics, 6, 23, January 1934, is sure to be very widely read in Great Britain, it is not inopportune to refer to an old mistake that he repeats. He states that optical paths are routes sometimes of minimum and sometimes of maximum time, and that for this reason it is appropriate to refer to them simply as stationary paths. His foundation is wrong though his conclusion is right. The facts are that the time happens to be a minimum when the path does not include an image of an end point of the range considered, but that if the path includes such an image, the time is neither a maximum nor a minimum—it is simply stationary. Thus in Fig. 1, if A, the image of A, is an internal point of the path interval APB, so that the optical lengths APA and AQA are equal, the path APGB is obviously longer and the path AQDB obviously shorter than the stationary path APA B. It is clearly a trivial matter to demonstrate that no given optical path is ever a maximum.