76 

 or 



Mr. A. Whitwell on the Lengths of the 



y 



r, + 



but 



_1 



u 



+ 



1 _ 



r 2 



1 



or 



1 



u 



_1 



1 



7v 





,-. 



y 





V+ 



a - 



av 2 

 'ft' 



• • 



(15) 



This is the equation o£ a line which forms the upper limit 

 of the focal line as its distance from the lens varies. It is 

 represented in fig. 14 by the line ag. The intercept on 



the axis of x = oa = 



a/1/3 

 afi — hfs 



of y=-oa- 



a. 



W 



r and the intercept on the axis 



/l 



If in equation 15 we put /i x = — /i x we get the equation of 

 the line ak, fig. 14, which forms the lower limit of the focal 



line. The intercept on the axis of y = a and that on the axis 

 a/1/3 



of x = o& = 



a/. + Va- When «"»=/* ^ fl 



*h. 



If in equation 15 we put a=—a and h 1 = h 1 and — /^ we 

 get the equations of the two lines — ag and — ak which 

 form the limits of the focal lines when the source is at —a. 



Fig. 14 shows that if we have two sources of light at a 

 distance 2a apart the axial focal lines will coincide at the 



principal focus, their lengths being =2h{^, and will overlap 



/1 



if their distance from the 



lens 



lies between the values 



og = ^Ml^ and oh= _?hk 



