H. S. Uhler — Deviation of Pays by Prisms. 223 



Art. XIV. — On the Deviation of Rays by Prisms; by 



H. S. Uhler. 



While making certain deductions from the formulae for the 

 directions of rays passing obliquely through prisms, as given 

 in standard text-books,* the writer found that conclusions 

 which are at variance with physical facts were unavoidable. 

 An investigation of the source of this difficulty showed that 

 the primary error consisted in tacitly changing the definition 

 of deviation in passing from considerations which refer to 

 principal sections of prisms to cases where the rays traverse 

 the prisms outside of these sections. If it were never neces- 

 sary to combine the formulae for rays in principal sections 

 with formulae for rays not in such planes, the error would 

 only amount to inconsistency of notation and hence it would 

 hardly deserve formal notice. As a matter of fact, how- 

 ever, it is sometimes necessary to combine formulae for the 

 two cases and; when this is done, false results follow. There- 

 fore, it may not be superfluous to give a brief discussion of 

 the fundamental formula for ra}^s not in principal sections in 

 such a manner as to retain the definition of deviation in the 

 form which is usually, if not universally, given to it when 

 principal sections alone are concerned. 



This definition may be concisely stated as follows : The 

 deviation of a ray is the angle through which the unlocalized 

 vector representing the initial direction of the ray must be 

 turned in order to make it coincide in sense and direction 

 with the like vector ivhich symbolizes the filial direction of the 

 ray. This sentence expresses precisely what is meant by the 

 deviation of light when making observations with an ordinary 

 spectrometer or even when considering the passage of plane 

 waves through a plane-parallel layer of some transparent me- 

 dium. On the other hand, the above definition makes the angle 

 of deviation supplementary to the deviation involved in the 

 current formula for obliquely transmitted rays. 



If D and D' denote respectively the deviations, produced by 

 a single prism of greater index of refraction than the surround- 

 ing medium, of a ray not in a principal section- and of the 

 projection of the same ray on a principal section, and if \ 

 symbolizes the angle which the incident (or emergent) ray 

 makes with the plane of such a section, then the mutual 

 dependence of these quantities upon one another is given by 



siniD=sin JD' eos^ (1) 



* Czapski, Heath, Kayser, Winkelmann, etc. 



