Form of Newton's Rings. 



'. «i=f+j(f-«iO; 



+ €i-(f— Oj +-2^ (& — 2 ), 



241 



r r r 



Again, 



(yii.) 



r 6 cos yjr = f: l = !: (d 



T n k + 2 



-?) +^±i (d-fib+J +V - ({* + Ci+i), 



Wijfc+2 



Wfc+i 



«i+l 



A = l WA 



Hviii.) 



A=& 



nth 



Using the values already found in (v.) for the direction- 

 3 0sines, we have 



, u g — 8/ I f lux + mvj g — 8 2 / 



/>cos^= -* — e f 2 fe+i 



2 e 2fc + l 



/ 



= ^-2r 



1 K — & 1 _ 7, f?_ ow + ffljg — 8 2 , 1 «_ f 2 7, _ 7_~| ^ 2 + ^ 

 7* y 2 r t* 2 7 L w-yj r 2 



y~ r r y l /-ty 



5 _ M ??Z^_o,l»Ji±^?=8a + i^r«-il!^ 2 



f> sin-^ = - — 2k 



' r rv 



ind 



^ r ' 2 y L""' yu,y'J r 2 



+ 



^ (ix.) 



</>* 2 =<£ 2 -2A 



yr r 2 



r 2 r 2 r \ yy / r 



[ 



' J 



2A- 



and 



/xy J y^ 

 c/> 2 is obtained by putting 7i = 



yr 



,2 • 



<£ ,2 is obtained by putting k = as well as h = 0. 



If a plane be drawn through B perpendicular to B'A' and 

 BA, and cutting the former in H, the points B, H are in 

 the same wave-front which is incident in the direction LA. 



