Dr Searle, Experiments on focal lines formed by a zone plate 3'39 



b, c respectively, while v is the distance from of the image when 

 ^ = 0, we have 



- + -=i^,, - + ] = F,sec'e, l + l = F,. ...(31) 



u V 'ii b u c 



The distances u, v or c, and b are measured. The accuracy of the 

 second formula is tested by finding the value of {1/u + 1/6) cos'^ 6 

 for various values of d. 



The experiment is improved by substituting for the small hole 

 a pair of slits cut in a metal plate and intersecting accurately at 

 right angles. To obtain sharp "images" of the slits formed by focal 

 lines, one slit must be vertical, the other horizontal, since the focal 

 line at P due to a luminous point at Q is vertical, and the focal line 

 at P due to a luminous point at R is horizontal. 



When ^ = 0, the zone plate forms images of the crossed slits. 

 We can use the multiplicity of focal lengths to produce an apparent 

 image of the crossed slits when 6 is not zero. With ^ = 0, the 

 telescope is set on the image of the second order (p = 2). Then 

 l/u + l/v = F.2. If 6 is now made ^tt, the horizontal focal line of 

 the second order is given by l/u + 1/c = F^. The vertical focal 

 line of the first order for 6 = ^tt is given by 



llu+ llb = F.sec^TT^ 2F^. 



But Fo = 2F^ , and hence b for the first order equals c for the 

 secondorder. The two focal lines will thus be at the same distance 

 from 0, and the observer will have the impression that he sees 

 a true image of the slits. If, however, a small hole is used in place 

 of the crossed slits, two focal lines will be seen. 



For testing the results of § 5, additional apparatus is required. 

 A horizontal tube M, arranged with a draw tube for adjustment of 

 length, turns in bearings A, A (Fig. 5) and carries a vertical divided 

 circle V, which is read by the index E. A lens L is fixed to the 

 end of the tube nearer 0. At the other end is a plate K pierced 

 by a small circular hole, by one slit or by a pair of slits crossed 

 at right angles. This plate can be turned in its own plane about 

 the axis of M and thus a slit can be given any desired direction. 

 The plate K is held against a flange at the end of the tube by 

 three nuts working on three studs carried by a plate on the other 

 side of the flange. The tube passes through a hole in the latter 

 plate with an easy fit. (The plate with the hole P is removed.) 



If L has spherical faces, the length of M can be adjusted so 

 that K is in the focal plane of L. The system then forms an ordinary 

 collimator. If L is an astigmatic lens, spherical on one face and 

 cylindrical on the other, and if M is adjusted so that KL equals 

 one of the two focal lengths of L, one of the focal lines formed when 

 a small hole is used in A' will be at infinity, and the arrangement 



