SUhjle-Piece Lenses. 523 



The line is therefore (h-awn parallel to the axis of y and 

 at a distance —.V from it. 



The condition that the focal lenoth shall be infinite is 



H 









^ — 



1 



/ = 















— 



>s- 



-I'l. 









/^ 



1 









1^ 



— 



i 







— 





, or 





if 



^ = 



i-5 





^J^ 







.J) 









ence i/ — a- : 



This straight line is shown upon the diagram and is called 

 the •• Telescope Line.'' 



The condition that the focal length shall not change for 

 small variations in the value of the index is of course found 



bv formino^ the equation ~ =0. 



This condition is given by the equation 



Hence y^- — 1 5 ... 



y—x='—-^-, or - it /x=l-o. 



This line is marked '' Focal Length a minimum,'^ and is 

 of course parallel to the Telescope Line. All lenses upon this 

 line possess a high degree of achromatism. 



A rav mav so pass throuo-h a lens that it encounters the 

 two surfaces in such a way as to receive equal deviation in 

 the same direction at each surface, and therefore on the 

 whole minimum de^■iation, as in the symmetrical passage of 

 a ray through a prism. I have shown elsewhere how this 

 can take place for all the rays of a pencil emanating from 

 any point on the axis of a lens. 



If the point is at an infinite distance the condition is 



'l—fjb r.2'\- h*-i\ + (■*■ — ld = 0. 

 Hence 'I^^iy + ^.v + tx — l =0. 



and if ^t=l'5 this becomes 



The line is marked upon the diagram " minimum deviation 

 for rays from infinity.'^ 



It passes through the sphere point .27= — J, j/ = -^ as all such 

 lines must. 



The curve which results from making the position of the 



