78 Mr. A. Whitwell on the Lengths of the 



Now 



— ly? a, a^v* 



= or v z e = — , 



v 3 — u u 



1 1\ , VJlo 



All's l7 Z 1 M . ^ 



M V'3 /2/ /l 



or 



A 1^8 W 3 /ig 



These lines are shown on fig. 16 by ng and nh. 



When CL\ is made = — « x we get the equations of lines m</, 

 w £ (fig. 16). 



The intercepts on the axis of y are ±_a x and those on the 

 axis of x are 



«i f\ ft 

 a\f\±hf2 

 Fig. 16 shows that if we have two sources of light at a 



© © 



distance 2a apart the tangential focal lines will be distinct if 

 their distance from the lens is less than 



or greater than 



© 



o* = 



°9 



aifi + hfz 



a \f\fa 

 "ifx—hf* 



but will overlap if they are formed anywhere between these 

 two distances. 



8. The image produced by a sphero-cylindrical lens of an 

 object consisting of narrow parallel horizontal and vertical 

 bands or slits of light. 



(1) The images of the horizontal bands. 



Let the distance between the centres of the object bands 

 be a and the width of the bands be w. Each point of each 

 horizontal band will produce an axial and a tangential focal 



