COLOKS OF THICK TLATES. 187 



In these explanations wc have isupposcd the incidence pcrpenclicular, and 

 have regarded the faces of the laminae as parallel. In the case of Newton's 

 rings, neither of these snppositions is usually true ; and the second can never 

 be so. The inclination of the faces is not, however, great enough sensibly to 

 aifect the conclusions. In the case of oblique incidence, it is obvious that no 

 ray reflected from the second surface can return to the same point of the first 

 surface (supposed parallel) at which it entered. But the loss occasioned by 

 this deviation is made good by the reflected component of some other ray 

 parallel to the first, in the plane of incidence and on the other side of it rela- 

 tively to tl:o point of emergence. 



It will thus be seen that the colors of thin plates, for which, on the theory of 

 emission, it is difficult to assign a cause which docs not introduce as many dif- 

 ficulties as it removes, arc all necessary consequences, on the undulatory theory, 

 of the simple principle of interference. The hypothesis devised by Newton to 

 account for them has not been presented, since it is now generally abandoned, 

 and the limits of these lectures would not allow its introduction. 



The colors of thick plates, of which some examples were noticed in the intro- 

 ductory lecture, depend on causes similar to those above explained. In the 

 case iKustrated in Fig. 8, whicli we here introduce again for the sake of the 

 explanation, if the light entering at o be composed of rayrf 

 perfectly parallel, and be rciurned from the spherical sil- 

 vered glass mirror, by a perfect specular reflection, to the 

 perforated screen c, placed at the centre of curvature, it 

 will all of it pass through the perforation toward o, and 

 no rings will appear ; or at least only such as might be 

 due to the diffraction of the aperture, very much eniecbled 

 by the reflection. But if the first surface of the glass bo 

 imperfectly polished, the specular reflection will not be perfect, but there will 

 be a reflected cone of scattered light at the first incidence. This has nothing 

 to do with the phenomenon. There will, however, be also a transmitted cone 

 of scattered light, which will become at the second surface a reflected cone, 

 having a virtual apex behind the mirror. Moreover, the light transmitted and 

 subsequently reflected regularly, will, at its emergence after reflection, form a 

 second scattered cone, the rays of which will have a virtual origin behind the 

 mirror, though the apex of this cone is at the first surface. The condition of 

 the light of these two cones is easily seen to be such as to produce interference; 

 hence the formation of the rings observed in the experiment. 



Fi-. 8. 



TLcat is to say, the brightness of these trausmitted viiags^is eqiial to that of the incident light. 

 In the second case, the equation ibr the tirst svuface is, 



z'=^{\ — f2).(t; — i;3-)-c5 — rP ad inf.) 



This may be separated into two equations, thus : 



I'ut v'^w-\-tc' . 



Also jc=(l— »2).(j,+r5-fi-n-f-i,i^...fl^ h)f.) 



And id'={V^—1).{v"-\-v'-\-c'^'^-{-v^^ ad inf. ) 



^ , — r« -, , , , {i—v') 



Themc^-^^; ^^''- :qrr ' "^d u•^-^. =. -..^^-_^-^^. 



This value is positive, and shows that the rings by reflection at these thicknesses \vill be 

 bright. 



At the second surface, for the same thicknesses, we shall have, 

 u'—{l— €-).{]— v''~-\-o-^—c'^ - .. -ud inf.). 

 And, bv proceeding as before, 



Showing that the rings seen at those thicknesses by transmitted light are obscure, but not 

 dark, because m', which embraces all the light trtmsmitted, has still a value. 



