Focal Lines of Cylindrical Lenses. 63 



the spherical surface they will intersect at the point n' on 

 the line joining the point/' to the centre qf of the spherical 

 surface. The point n' is at the extremity of the axial 

 focal line. 



If m!n! = l 3 and o'm' = v B we have from the triangles 

 fe'q' and n'm'q' (fig. 3), 



^3 — ^2 



or L = L 



(3) 



From the ordinary formula for spherical lenses 

 we have 



pWs 



(//,— i)t7 8 +r 2 ' 



and substituting this value o£ v i in (3) we get 



or the length of the axial focal line of a sphero-cylindrical 

 lens = axial aperture X distance of the line from the lens 

 x the glass to air power of the cylindrical surface. 



— - — = the glass to air power of the cylindrical surface ; 



or the power of a piano-cylindrical lens having a 

 cylindrical surface of radius r x ; or the difference of 

 the two principal powers of the sphero-cylindrical lens. 



(b) The tangential focal line. 



Two refracted rays symmetrical with respect to the hori- 

 zontal plane or the plane of fig. 4 are represented in elevation 

 by the lines a'n'p', and a"p\ and in plan by the line amp. 

 These two rays will intersect at a point p in the horizontal 

 plane, and this point will be at the extremity of the 

 tangential focal line pp corresponding to the aperture h 2 . If 

 the semi-length of this line = l A and its distance from o = v 4 , 

 we have from fig. 4, 



«3 



or 



k = h 



*>3 



. . (4) 



