THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FOURTH SERIES.] 



MARCH 1873. 



XX. On the Optics of Mirage. By Professor Everett, M.A., 

 D.C.L., Queen's College, Belfast*. 



PROPOSE in the present paper to investigate some of the 



principles which govern the formation of images in a medium 



of continuously varying index of refraction, with special reference 



to the phenomena of mirage and atmospheric refraction. 



I. I shall first establish the following proposition : — 



In a medium in which the absolute index of refraction varies 



continuously, the path of a ray will in general be curved; and its 



curvature - at any point is given by the formula 

 P 



1 _ 1 d/ju __ dlog /jl 



p~ji~dN~~ ~W~' 

 N denoting distance measured along the normal towardsthe centre 

 of curvature, and therefore -^ denoting rate of increase in the 



direction of the centre of curvature. 



The simplest proof of this important proposition is derived 

 from the principle that fi varies inversely as v the velocity of 

 light. 



Draw normal planes to a ray at two consecutive points of its 

 path. Then the distance of their intersection from either point 

 will be p, the radius of curvature. But these normal planes are 

 tangential to the wave-front in its two consecutive positions. 



* Communicated by the Author. 

 Phil. Mag. S. 4. Vol. 45. No. 299. March 1873. M 



