752 



BELL SYSTEM TECHNICAL JOURNAL 



Imagine, at the outset, a pair of perfectly plane and parallel mirrors, 

 onto which wave-trains of extended plane wave-fronts are falling 

 from every direction. The mirrors must of course be semi-transparent, 

 so that part of the light which falls first upon one — say, the upper — 

 is reflected from it at once, and part goes on to meet and be reflected 

 by the lower. Thus (as Fig. 3 shows more clearly than words) the 



Fig. 3. 



mirrors form out of each incident wave-train a first and a second 

 reflected beam, which travel back through the space above the mirrors 

 in the same direction, making according to the law of reflection the 

 same angle i with the normal as the incident wave-train did. In truth 

 there are not merely two reflected beams derived from each incident 

 one, but an infinity thereof, owing to the multiple reflections which are 

 indicated in the sketch. We need not however (as I shall presently 

 show) take account of more than two; by combining the second re- 

 flected beam with the first we can predict the most important features 

 of the interference. 



It is necessary to be somewhat more precise about the nature of the 

 mirrors. As good an example as any to begin with is that of the 

 "thin plate "^ — a slab of some transparent substance, glass for instance, 

 embedded in a transparent medium which I will take to be empty 

 space. The mirrors, then, are the upper and lower sides of the plate. 

 Denote by /i the ratio of the speeds of light in the environing medium 

 and in the substance of the plate, by i the angle of incidence of any 

 wave-train and by r the angle of refraction of its transmitted part; 

 then as heretofore we have 



s\m = IX sm r. 



(16) 



