ARTICLES 

 THE LAW OF REFRACTION 



By R. a. HOUSTOUN, M.A., Ph.D., D.Sc. 

 Lecturer on Physical Optics, University, Glasgow 



Every student of elementary physics knows the laws of the 

 reflection and refraction of light, how the angle of reflection is 

 equal to the angle of incidence, and the sine of the angle of 

 refraction bears a constant ratio to the sine of the angle of 

 incidence. 



The law of reflection must have been known from very early 

 times. It is proved in the first proposition of Euclid's Catoptrics 

 by means of the accompanying figure. B is the position of the 

 eye, AC the mirror, and D the object. It is assumed as an 

 axiom, the third of the three axioms placed at the beginning 



of the book, that BC is to DA as KC to KA ; the proof consists 

 in showing that the triangles are similar, and consequently 

 < DKA = < BKC. It is thus the angles which the rays make 

 with the mirror which are proved equal, not, as nowadays, the 

 angles which they make with the normal. 



It is assumed by Euclid that the rays of light go from the 

 eye to the object. This is made very clear by the first axiom 

 of the Optics, which runs : " Let it be assumed that rays are 

 emitted in straight lines from the eye, and are separated from 

 one another by intervals." A justification of this axiom is 

 given in the introduction to the Optics, which is of interest as 

 dealing with physical ideas ; all the rest of the work is 

 mathematical. This introduction first states clearly the usual 

 arguments for the rectilinear propagation of light, e.g. the 



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