DIOPTEIC INVESTIGATION BY GAUSS 

 substituting in (8) 



whence 



"' = , , ,^ 



b'=y Y + m (hu .X-OK) ; 

 m"=k Y + m (lk X O X) ; 



A-i/(X-oX) 



_/. (x-ox T ^ ' *' = fj Y + ^ m "~ 1c ^ 



Xow sul)stituting in (4) the equation to the retracted ray 

 becomes 



or by (8) 



Y 



^O X) 



-- 

 _ ;, x - O 



0') 



First: If X be taken such that I /,' (X -< > X) = 1 . i.e. 

 X = < > X - LJ=0 E. suppose ; 



when 

 .,-=OV 







suppose. 



//=Y, or P and p are equally distant from the axis. 

 Also, if Y = 0. // = ; or if a ray proceed from E, it will after 



refraction pass through E'. Also m = 



m " _ 



,.- - = in", that is, 



,.- - 

 < 4- (X OX) 



the ray will be equally inclined to the axis before and after refrac- 

 tion. 



E and E' are called the principal points.' 



du' 



(a' //) il a n' 



Secondly: If m" = 0, or the ray be parallel to the axis after 

 refraction, we have from (8) 



!>=. -. m, and the equation to the incident ray become- 



K 



+ . in = in (x O X). or // = m ( x - 



K \ 



< > X - 



