19 



r 



2 



Setzt Dian ( 9 ) für die drei Linsen nacheinander M, M, und 



M„ , so ist : 



A — M-\- 1 



A' = 1/, (1 -f 2m6) 2 + 1 = iW, [1 - 2m (1 — <?)] 2 -fl 



A" == M„ (1 + 2m6) 2 + 1 = M„ [1 - 2m (1 — d)] 2 + 1 



sonach ist die Bedingungsgleichung des Aplanatismus: 



p, (üT, [1 - 2u (1 - *)]* 4- 1) = (i (Jf + 1) (1 - <f) 2 m3 4- 

 4- m" (M„ [1-2m(1 - ďj] 2 + l) + ( mV-j-m^" ) (l-M (!-<?)) (1 - Ů) 

 H'M, - 4p'M' u (1-4)4- 4?í2 **' i¥ ' d— ď ) 2 ~h ^ — ww3 ( M + 1) (1— d Y~\- 



4- m„ Jf„ - 4ttf*" if- (i— *)4- 4m 2 w „ jf w {i-df 4 P « 



-f^v' + fiVOwil- d) — (>V4-m'V')m 2 (1— d) 2 



IL'M, —fi"M„ -f m' — m" — [fiu* (M-\- 1) — 4u 2 (i'M, + 4u 2 ii"M" — 



— (mV -j- m'V) m 2 ] (1— d) 2 - [4m ((i"M" — m' ilf') — 



-{řiV-f^í/")íí](l-d) 

 t u'ili,-M".M;, +m'-m" _ J 



fiu 3 (M-\- 1) — 4m 2 Q»'Ji; — p"Mf) (p'v! 4 m'V') m 2 u ' _r 



[4M (ft'Jf — M">i,,) 4 (mV-J-m'VOm] (1— Ö) 



4 



um 3 (Jf 4- 1) — 4m" {p'M' - [i"M") — (mV 4- w' V) m 2 



p'(jf, + i) — f*"Ä4- 1) -(i_rf) 2 4- 



WM 3 (jf 4 1) — 1 4 (ft'if, — p"jtf") 4 mV 4- f*' V } M- 

 4 (m'í¥ ' — ii "M") -\- p'v' + p"v" 

 «m 2 (M-fl) — { 4 (ji<3P — M"Jf") 4- mV 4 m'V J m 



^ = (i-df4-~(i-tf), wo^^m'W + d-m"^^!); 



5 = (i (i¥4 1) m— 4 [m'i¥, — y,"M" 4- ftV4-ft'V'} und 

 C=z 4 (w'itf, — M"J!;f") 4- mV 4- ft'V 



' 2uB -\ tfB + 4&m 



* x - C'+ f±AB + C 2 C , 1 1/-. , 4^ 



2* 



