Focal Lines of Cylindrical Lenses. 69 



and substituting the values of / and k we get 



54 ~ ^ sin 2 0, 4-/1 sin 2 ^ 2 * 



If F 2 be the principal iangential focal length of the 

 combination, we have from fig. 8, 



F 2 = os; 



h 



Now 



h 



JL 



Fi 



1 

 F 2 



^ JL 



Fi 





1 



sin 2 gi sin 2 fl 2 

 /1 + A 



/l 



t 



A J 



COS 2 # 2 



1 



cos 2 6 \ 



1 /« 



1 



/, ' 



sin 2 X 

 /1 



+ 



sin 2 69 



cos 20] 



- + 



cos 26> 2 



and 



f 2 /, ' /, 



(b) Secondly, we will take the light diverging from a point 

 at a distance — u from the point o (fig. 10). 



(1) The axial focal line. 



Figs. 9 and 10 are end and front elevations respectively, 

 being similar views to figs. 7 and 8, the letters/], / 2 , h ly h 2 , 

 l5 2 having the same meaning as before. Consider first a 





\CO 



o'-b 



oh^l* 



^-—^~" 





c X 



V 



I / 



fy* 





P 



r 



t 

 k 









A 









1 



1 



FIG. 



3. 







X 



. 



V, 



FIG. 



/<?. 



V3 



ray incident at a. This ray, after emerging from the first 

 lens, will be represented in end view by the line as (fig. 9), 



