Light from Transparent Matter. 91 



From (13) and (14), 



2^=X + Y=^« + ^|/+ztan^M(/. 2 -l)|^ 



2f = X-Y={^-^|'-aan^M(^-])}t r 



The quantities within the brackets are complex, and may be ex- 

 hibited in the forms Re ie , R'e 16 ' ; e and e' then denote the dif- 

 ference of phase between the incident and refracted, the reflected 

 and refracted waves respectively, and are given by 



COt e= M(/* 2 -l) &* COt ° + COt '\ 



= l C ot(0-0 y ); (15; 



by trigonometrical transformation, with use of relation 

 sin 0=//, sin t ; 



cote'= g \ — /* 2 cot 0+ cot t \ 



== __- CO t^+6> / ) . . (16) 



We have seen that when the vibrations are normal to the plane 

 of incidence there is no difference of phase between the incident 

 and reflected waves, unless the change of sign, when the second 

 medium is the denser, be considered such. Now what is observed 

 in experiments is the acceleration or retardation of the one po- 

 larized component with regard to the other, and is therefore given 

 simply by e—e'. The ambiguity must be removed by the con- 

 sideration that when the incidence is normal there is no relative 

 change of phase, though throughout Jamin's papers it is assumed 

 that there is in that case a phase-difference of half a period. I 

 am at a loss to understand how Jamin could have entertained 

 such a view, which is inconsistent with continuity, inasmuch as 

 when = the distinction between polarization in the plane of 

 reflection and polarization in the perpendicular plane disappears. 



The ratio of the amplitudes of the reflected and incident vi- 

 brations is given by 



B/ 2 _ (-^*cotfl+cotfl,j a + MV a --l) 8 



R 2 ~ {fJ? cot + COt 0,) 2 + M 2 (/* 2 - l) 2 



_ cot»(fl + fl,) + M« 



"cot^-^+M* Kn 



