Form of Newton's Rings. 219 



Part I. — Newton's Rings in Reflected Light. 



Section I. Calculation of the Relative Retardations. 



Suppose a plate of plane parallel glass to be in contact at 

 the point (fig. 1) with the surface of a lens, whose upper 

 surface is convex and of radius r. 



Fig. 1. 



Let d be the thickness of the glass, fx its refractive index. 



Let LABCDEG be the course of a ray incident on the 

 plate at A and reflected at the lens at C. 



Let U A! B' E ; G / be the course of a ray belonging to the 

 same incident wave-front and reflected at the lower face of 

 the plate at B'. 



Suppose the pair of rays so chosen that their directions after 

 emergence intersect at the point F. 



Let the interval between plate and lens be supposed to 

 contain the same medium (air) as the space above the plate. 



Let be taken as origin, the common normal to lens and 

 plate, drawn on the side towards the plate, as axis of z, and 

 let axes of x and y be taken in the lower face of the plate. 



Take 



as coordinates of F. 



B'. 

 Let 







*, 



V, 



? 







iu 



Vu 



?1 







& 



V2> 



?2 







u, 



v, 







I, 



m, 



n be the < 



h, 



m 1} 



n i 





V 



*', 



m' } 



n' 





yi 



V, 



v, 



V 





» 



n be the direction-cosines of AL or CB, 



BA or B'A', 



S 2 



CD, 

 DE. 



