240 Prof. A. McAulay on Reflexion and 



First, let H be in the plane of incidence, i. e. let the incident 

 light be polarized in the plane of incidence. Fig. 6 indicates 



Fig. 6. 



Reflected unzve su/f. 



Refracted wave svrf. P 

 I?ici<Jent mze^e surf. 



the nature of the reflected and refracted light. The plane of 

 incidence is the plane of the paper, i the angle of incidence, 

 and r the angle of refraction ; p, p ! , p" are the vectors of ray- 

 velocity of the incident, refracted, and reflected light. H is 

 drawn in the incident wave- front and in the plane of incidence. 

 It will be seen that if H' and H" be also drawn in the refracted 

 and reflected fronts and in the plane of incidence, as indicated 

 in the figure, three mechanical forces H, — H', H" may be made 

 to be in equilibrium, i. e. to reduce to a (null) couple whose 

 plane is parallel to the face. By the sine rule for the 

 equilibrium of three concurrent forces, we have 



TH TH' = TH" 



sin (i + r) ~ sin ~2i sin (i — r)' 



in which it is to be remarked [eq. (5) above] that the inten- 

 sities are proportional to the squares of the numerators and 

 therefore to the squares of the denominators. 



Fig. 6 also serves for the case when the light is polarized 

 perpendicular to the plane of incidence. H, H', and H" are 

 not then as indicated in the figure, but instead they act at 

 the points P, P', and P" of the wave-surfaces perpendicular 

 to the plane of the paper. In order that in this case the 

 system may reduce to a couple parallel to the face, H and H" 

 must have a resultant equal and parallel to H' at the same 

 distance as H' from the face and on the same side of the face. 

 Since the distances of P, I 3/ , and P" from the face are 



OT cos i sin i, OT cos r sin r, and OT cos i sin i 



