Focal Lines of Cylindrical Lenses. 



01 



previous paper, above referred to, the point of intersection /' 

 of the lines a'g' and c'd' is on the focal line ; it is in fact 

 the uppermost limit of the focal line corresponding to the 

 semi-aperture h v 



If ef = li and o'e' = i\ we have from the triangle c'c'd' 



, = L or ?! = hA . 



/i! U — Ti \l« — T X J 



(1) 



Now by the ordinary formula for spherical surfaces we 

 have 



r 2 u \r x vj 



— I or u 



and substituting this value of w in (1) we get 





bnt 



/a-1 1 



where /i is the focal length of a spherical surface of radius r r 



k = 



_ ^i ?; i 



/i' 



or, the length of the axial focal line = axial aperture x distance 

 of focal line from the surface X power of the surface. 



(b) The line at right angles to the axis of the cylinder ; this 

 may be called the tangential focal line. 



Two incident rays symmetrical with respect to the 

 horizontal plane or the plane of fig. 2 are represented in 

 elevation by the lines a'd' and a"d' and in plan by the line 

 ad, and the corresponding refracted rays in elevation by the 

 lines a'g' and a"g' and in plan by the line ah. The two 

 refracted rays will intersect in the horizontal plane in the 

 point h which is at the extremity of the tangential focal line 

 corresponding to the semi-aperture h 2 . 



If hg = gk = l 2 and og = v 2 , 



we have from the triangles obe and ehg (fig. 2), 



i>2 — *>i 



or k = h ^ay, . 



CO 



