Curvature Method of Teaching Optics. 487 



Hence i _A' + B'U'-i 



Consequently, since these equations were proved to hold 

 for two surfaces, and have now been shown to hold for an 

 additional surface, they must hold generally. 



It may be of interest as a conclusion to this section to 

 exhibit the three methods in a comparative form. 



Comparative Table of Formulae for Heft acting Systems. 



Galss Method. Deviation Method. Curvature Method. 



Surface ... — ■ - — = F 



Interval 1 ... u^ = i\' -+- // 



Surface 2 . . . — ■ — — F 



Interval 3 ... «/ = v.J + t./ 



&c. &c. 



FA 



1 - _i 



h 2 -7^ = ^/(7, 

 <T./ — <T l / = F.J/ 

 h r h. 2 = t 3 '<T :i 



&e. 





W+l 



V/-TJ-F, 

 V' 



u 



3 W+i 



&c. 



Eesults 



referred to 



first and last 



surfaces. 



Results 



referred to 



principal 



planes. 



2n + r 



1 _ 

 m ~~ 



Q«+D 

 Aw+B 



Aa + B 



AD-BC=-1 



*2»=C*o+ I ><-] 



7 2«+i = A/ '-'"t' Bo ''-i 

 1 M !) +B(r' 

 m a' 



A+BTJ'_ j 



_; 



AD -EC: 



V 2»+i-C+DU , _ 1 

 1 = A+BU'_, 

 m ~ U'—i 

 AD-BC=-1 



1__ 1 _ 1 

 */' uf ~ A 



« y/ 2«+l~ (7 -l= A ** 



2)1 + 1 



F' = A 

 V'-U'=A 



* A is here the height of intersection with the principal planes. 

 Aberrations. 



The subject of aberrations will have to be treated in a 

 separate paper ; but to show how the curvature method lends 

 itself to aberration problems, we will here take the case of 

 oblique refraction in thin lenses. Just as we started the 

 ordinary theory of thin lenses by considering the retardation 

 produced by a plate, we may here commence with oblique 

 refraction by a similar plate. 



