Modification of Newton's Rings. 287 



observation; and it proves therefore that B is > B*; a conclusion 

 of some importance, as shewing that plane-polarized light reflected 

 at a metallic surface becomes elliptically polarized, and as con- 

 necting these phaenomena with those of a very different kind 

 discovered by Dr. Brewster. It appears here that the phases of 

 vibrations in the plane of reflection are more retarded, than those 

 perpendicular to that plane. 



If cos (« + <) is positive, that is, if the angle of incidence is less 

 than the polarizing angle, it appears that upon increasing a the 

 diameters of the rings ought to decrease. But it is easily seen 

 that the change ought to be much less than in the former case. 



2tt / „, , B + B' 



is 



For in the former case, if one value of — (2 7 , cos<' + 



XV 2 



«7T+/3, when a=0, then, upon increasing a to 90°, -~ (2 T cos «' + — i — ) 



changes through «7r + 90° to mtt + 180 -/3, and the whole change is 



therefore 180° - 2/3. But in the latter case ^ (zToost' + B+ 2 R ) 



changes from wtt+/3 through mtt to «tt-/3, and the whole change 

 is therefore 2/3, which is exactly supplemental to the former whole 

 change. Now in Newton's rings formed between two lenses, /3 

 is 0; from the general similarity of the rings formed by a metal 

 reflector when a = 0, it is certain that /3 is small ; consequently 

 though the dilatation of the rings in the former case depending 



on the increase 180° — 2/3 in ~ (2Tcosi + — - — ) is considerable, 



the contraction in the latter case (depending on the decrease 2/3) 



* If B were < B', the rings would contract instead of expanding; and if B were = B', 



the diameters of the rings would not alter, but their intensity would diminish to 0, when 



, A' cos (i — <') . . „ . . , ,11 



tan' a = — - . ' ' , and rings or the opposite character would then appear. 



