330 Dr Searle, Experiments on focal lines formed by a zone plate 



Experiments on focal lines formed by a zone plate. By Gr. F. C, 

 Searle, Sc.D., F.R.S., University Lecturer in Experimental 

 Physics. 



[Read 28 February 1921.] 



§ 1. Introduction^ . In the usual theoretical investigation of the 

 properties of a zone plate, the luminous point is taken to be on the 

 axis of the zone plate, and in the practical measurements, such as 

 those which have been made at the Cavendish Laboratory for many 

 years, the incident rays are not inclined at more than small angles 

 to the axis of the zone plate. When, however, the luminous point 

 is not on the axis, the zone plate gives rise to two focal lines, as 

 a thin lens does under similar circumstances; the positions of these 

 focal lines are investigated in the present paper. The theory has 

 been extended to the case in which any non-spherical wave front 

 falls upon the zone plate at any angle of incidence, and the positions 

 and directions of the focal lines of the emergent wave front have 

 been found. The experiments illustrating the theory were made with 

 the kind assistance of Mr Gr. S. Clark-Maxwell of King's College. 



§ 2. Theory of zone pilate. Let OG^G^, ... (Fig. 1) be the section 

 by the plane of the figure of an infinitely thin plane opaque screen, 

 and let X'OX be' the normal to the screen at 0. Let the spaces to 

 the left and right of the screen in Fig. 1 be called the object and 

 image spaces respectively. On the screen take a point 6^i near 

 and let OG^ = p-^. Let G2, G^, ... be other points on the screen 

 such that OGn^ = p,^^ = p^^ + (n — 1) k^. Let narrow circular slits 

 be cut in the screen with as centre and passing through G^^Gi, .... 

 This system of screen and slits forms a theoretical zone plate f. 



1G4 



* When this paper was read, I did not know that the general theory of the 

 action of a diffraction grating or of a zone plate upon a wave front of any form had 

 been indicated by Sir J. Larmor in "The Dioptrics of Gratings," Proc. Lond. Math. 

 Soc. Vol. XXIV. p. 166 (1893). 



t To obtain strong images, the widths of the slits through (^^ ,(?,,... are increased, 

 so that the edges of the nth slit have the radii a-„,T„, where a„- =pj - s-, T„^=p„^ + z^. 

 Zone plates are made by photography from large scale drawings, and the attempt 

 is generally made to make z- = lk^. If this were accurately done, no images of even 

 order would be formed. The zone plate used in the experiments is a "phase-reversal" 

 plate made by Prof. R. W. Wood and given by him to the Cavendish Laboratory. 



