Consequences of FresneVs Reflexion of Light Theory. 305 



and absorbing media, such interaction must be recognized as 

 fundamental — just as the principle of: the resonance of the 

 simple system under isjchronous force is fundamental in 

 dealing with the more obvious phenomena. 



Note. — In the paper on displacements in the spectrum due 

 to pressure the suggestion as 10 the influence of radiation of 

 frequency n\2ir is over definite in giving the direction of the 

 displacement. The effect of a slow oscillation, symmetrical 

 or asymmetrical, may be in either direction in so far as 

 general considerations of normal motions are concerned. The 

 displacement must evidently be in the same direction as that 

 under pressure. 



March, 1911. 



___ 



XXXI. Some Consequences of Fresnefs Reflexion of Light 

 1 theory, ivith Formulae for Determining the Angle of Inci- 

 dence in order to reflect 1/nt/i the Incident Light. By 

 Robert B. Sangster*. 



THE greater part o_ this paper is taken up with the 

 investigation of formulae derived as consequences of 

 Fresnel's Reflexion of Light Theory. 



We have first, however, to deal with some trigonometrical 

 relations connected with reflexion which are required later. 

 The investigation is restricted to media which are homo- 

 geneous and isotropic, and as frequent reference will be 

 made to the first and the second medium, either of which may 

 be the denser, it is as well to state now that these terms 

 indicate that the progress of the light is from the first to the 

 second. 



Let S (space) represent the volume generated in the first 

 medium by a plane wave-front in unit time, and S' the 

 volume generated in unit time in the second medium by the 

 same plane wave-front, the transfer taking place at a plane 

 interface. Also, let i be the angle of incidence, r the angle 

 of refraction, and /x the refractive index of the second 

 medium with respect to the first. To remove possible 

 ambiguity, /_ = V/V, where V and V are the velocities of light 

 respectively in the first and second media. 



Two obvious ratios of S to S' exist. At normal incidence 

 S = /aS' and at grazing incidence S/S' = or oo : It may 

 not be quite so obvious that at the incidence of maximum 

 polarization S = S'. To show this, in fig. 1, suppose the 

 plane of incidence to coincide with the plane of the paper, 



* Communicated by Dr. C. Chree, F.E.S. 

 Phil. Mag. S. 6. Vol. 22. No. 128. Aug. 1911. X 



