[ 35 ] 
V. Observations on certain cases of Elliptic Polarization of Light by Reflexion. By 
the Rev. Baden Powell, M.A. , F.R.S., F.G.S., F.R.A.S., Savilian Professor of 
Geometry in the University of Oxford. 
Received November 10, 1842, — Read January 26, 1843. 
Introduction. 
The peculiar character impressed on light, originally polarized in a plane inclined 
to that of incidence and reflected from a metallic surface, discovered by Sir D. 
Brewster*, and named by him elliptic polarization, has been since shown to coin- 
cide with what, from a different analogy, is termed elliptic polarization in the undu- 
latory theory; and which is also exhibited by an interposed plate of mica, or by total 
internal reflexion, as in Fresnel’s rhomb. 
The most distinct experimental test of the existence of this property and a measure 
of its amount, is the well-known dislocation of the polarized rings, seen by a plate of 
calc-spar and a tourmaline, in light of this kind. And this, as in other similar cases, 
is represented theoretically by a formula for the intensity at any part of the plate, in 
the case of the rhomb , for circular polarization, as in Mr. Airy’s tract on the undula- 
tory theory (Art. 160.) ; and for elliptic, as in the same author’s paper on quartz -f\ 
A general formula for the rings in light of all degrees of ellipticity, not restricted by 
the peculiar conditions of the rhomb, has not been hitherto published : but I am in- 
debted to Mr. Airy for the communication of such a formula, which will be given in 
the sequel, as leading to some remarkable applications. 
With immediate reference to the experiments of Sir D. Brewster on thin Jilms\, 
Professor Lloyd, in 1841, investigated on the principles of the undulatory theory, the 
general case of light previously polarized in any azimuth, and reflected from a thin 
plate, at any angle ; and by generalizing the methods of M. Poisson, found expres- 
sions both for the intensity, the changes corresponding to different incidences, and 
the phase of vibration of the pencils reflected from the two surfaces, which in general 
differ in retardation and are polarized, one in the plane of reflexion and the other 
perpendicular to it : whence it follows that the resulting light should be in general 
elliptically polarized §. 
Professor Lloyd’s theory seems completely to explain the various phenomena ob- 
* Philosophical Transactions, 1830. t Cambridge Transactions, 1831. 
+ Philosophical Transactions, 1840. 
§ See Reports of British Association, 1841, Sectional Proceedings, p. 26. 
F 2 
