IY. ON THE LIGHT REFLECTED AND TRANSMITTED BY 

 THIN PLATES. 



Transactions of the Royal Irish Academy, Vol. XXIV. 



THE problem of thin plates lias been completely solved for the 

 cases in which the incident light is polarized in either of the two 

 principal planes, and therefore also for the case of unpolarized 

 light, which, it is well known, may be regarded as composed of 

 two equal pencils, polarized respectively in these two planes. 



There is no difficulty in perceiving in what manner the theory 

 may be extended to light polarized in any plane ; but the results 

 become more complicated, from the necessity of including the con- 

 sideration of phase. When the incident light is polarized in the 

 plane of incidence, or in the perpendicular plane, we have only to 

 seek the magnitude of the resultant vibration, after the successive 

 divisions which it undergoes by reflexion and refraction at the two 

 surfaces of the plate. But when the light is polarized in any 

 other plane, the incident vibration must be resolved into two, in 

 the two principal planes ; and for each of these components we 

 must know the phases, as well as the magnitudes of the resultant 

 vibrations, before we can estimate their joint effect. These phases 

 are in general different, and therefore the resulting light is ellipti- 

 caHy-polarized. 



The preceding, and some other results of theory, were pointed 

 out by the author many years ago ; and the general formulir, 

 in which they are included, were at the time laid before tho 

 Academy.* In the present communication it is proposed to 

 develop these consequences ; and in particular, to deduce the law 



* fromiliiiffs of the Koi/nl Irish Academy, June 13, 1842. 



