Focal Lines of Cylindrical Lenses. 



75 



distance ou——u from the lens, and let the semi-aperture 

 = h i . Consider first the refraction by the piano-cylindrical 



lens alone. The part of the lens above the line a b will 

 produce a focal line he of length (h l — a) : ^ at a distance 

 ov l — v l from the lens. The part of the lens below the line 



ab will produce a focal line bd of length (/ti+aW. The 



Vi J 1 



total length of the line is 2A 2 ^-. 



Consider now the refraction by the piano-spherical lens. 

 A pair of rays, symmetrical with respect to the plane of the 

 paper in fig. 13, converging to the point c, fig. 13, will be 

 refracted in such a way that their point of intersection 

 will be at e on the line oc, the distance of e from the 

 lens being = ov 2 or v 2 . Similarly a pair of rays converging 

 to d will, after refraction by the spherical lens, intersect at / 

 on the line od. The axial local line will therefore be ef. If 

 its total length =2Z l5 we have from fig. 13 



2k 

 v. 



2h v 4 



h 



1 or l 1 =j 1 r 2 , 



/i 



that is the length of the line is the same as when the point a 

 or the source of light is on the optic axis ou. 



If the length of that part of the line above the axis ou be 

 called y we have 



y_ J a 





(H) 



h .4. a 



