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VI. On the Phenomena of Newton's Rings when formed 

 be f ween two transparent Substances of different refractive 

 Powers. By G. B. Airy, M.A. F.R.A.S. F.G.S. Late 

 Feltow of Trinity College, and Plumian Professor of Astro- 

 nomy and Experimental Philosophy in the University of 

 Cambridge*. 



N a paper communicated to this Society about four months 

 since, I stated my expectation (founded on Fresnel's theory), 

 that if a lens of a low-refracting substance were placed on a 

 plane surface of a high-refracting substance, and if light polar- 

 ized in the plane perpendicular to the plane of reflexion were 

 incident upon it, then so long as the angle of incidence was 

 less than the polarizing angle of the low-refracting substance, 

 or greater than that of the high-refracting substance, Newton's 

 rings would be seen with a black centre ; but if the angle of 

 incidence was greater than the first of these and less than the 

 second, Newton's rings would be seen with a bright centre. 

 I have now to announce the fulfilment of this anticipation. 



Before describing the method by which I have succeeded 

 in the examination of these phenomena, I think it right to 

 give a theoretical calculation of the intensity of light in the 

 rings ; as without this, the necessity for some of the precautions 

 will not be sufficiently evident. 



Conceive two nearly parallel plates of different media to be 

 separated by a plate of air whose thickness is T; and let the 

 vibration in the plane of reflexion, of an incident stream of 



light within the first medium, be represented by a sin — (vt— x) 



A 



where x is the equivalent in air to the actual distance of a 

 particle from some fixed point, (the light being supposed 

 polarized in a plane perpendicular to the plane of reflexion). 

 Let * be the angle of incidence on the last surface of the first 

 medium ; »' the angle of refraction, which is the same as the 

 angle of incidence on the first surface of the second medium; 

 and i" the angle of refraction in the second medium. A part 

 of the light will be reflected at the last surface of the first 

 medium; a part will reach the first surface of the second 

 medium, where it will be subdivided; and one portion will be 

 reflected to the surface of the first medium, where it will be 

 again divided ; and one of its parts will enter in the same 

 direction as that which was reflected at first. In this the 

 phase of the undulation will be behind that which was first 



* From the Transactions of the Cambridge Philosophical Society; be- 

 fore which body this paper was read, March 19, 1832, as noticed in the 

 Philosophical Magazine and Journal of Science, vol. i. p. 400. 



