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 \III. Proceedings of Learned Societies, 



ROYAL INSTITUTION OF GREAT BRITAIN. 



May 3, /^N Optical Phenomena produced by Crystals submitted 

 1872. ^^ to Circularly Polarized Light. By William Spottis- 

 woode, Esq., LL.D., M.A., Treas. R.S. and R.I. 



On a former occasion* I exhibited some phenomena depending 

 uj^on circular, or as it was then also called, successive polarizaon, 

 and in particular I adopted and explained a method for producing 

 circularly polarized light devised by Sir Charles Wheatstone. I 

 propose on the present occasion to pursue the subject into some of 

 its ulterior consequences. In terms of the wave theory, light is said 

 to be circularly polarized when the vibrations are circular, as distin- 

 guished from plane polarization (when they are rectilinear). And 

 further, it is known from mechanical principles that a circular vibra- 

 tion may always be produced by the combination of two rectilinear 

 vibrations, the amplitudes or extents of which are equal, and whereof 

 one is in advance or in rear of the other by one or by any odd 

 number of quarter wave-lengths. In the former of these cases the 

 circular motion will take place in one direction, say right-handed ; 

 in the latter in the opposite, say left-handed. The contrivance used 

 for producing circular polarization this evening is known by the 

 name of a ** quarter-undulation plate," and consists of a plate of 

 mica split to such a thickness that one of the two rays into which 

 plane-polarized light is divided on entering it is retarded by an odd 

 number of quarter wave-lengths behind the other. 



The optical phenomena produced by crystals when submitted to 

 polarized light are usually divided into two classes, viz.: — (1) those 

 arising from the use of parallel light, and consisting of broad sheets 

 of colour ; and (2) those due to convergent light, and consisting of 

 the rings and brushes, the general character of which is well known. 

 I propose to take a few specimens from each class, and to examine 

 the modifications which the known phenomena undergo when the 

 light is both polarized and analyzed circularly, i. e. when one 

 quarter-undulation plate is interposed between the polarizer (Nicol's 

 prism) and the crystal to be examined, and the second between the 

 crystal and the analyzer (Nicol's prism). 



In the first place, it is known that if a plate of selenite be placed 

 in an ordinary apparatus when the polarizer and analyzer are either 

 parallel or crossed, there are four positions at 90° apart in which the 

 plate will produce colour — and further, that if the analyzer be turned 

 through 90° the same result will be obtained, except that the colour 

 will be complementary to that first seen. The intensity of the light 

 at any given point is then given by the formula 



a 



cos'5 — sin 2 i sin 2(/ — s) sin'-^ -, 

 where i and 5 are the angles made with the original plane of polar- 

 * Phil. Mag. for May 1871, p. 398. 



