Dr Searle, Experiments on focal lines formed by a zone plate 337 



Hence 



Z = 1 (5,0 + C,o) = 1 (B.//2 + Ci'%] 



F^ tan2 d = BJ>~ C/^^ = B^""^^ - C,", [ (28) 



The equation tan2i/r2 - 2 Tf 2/(^52- ^2) leads, by (11), to 

 2Tf 

 tan 2^2 = ^^-^ _ rr+ >;tan2*^ 



(^1 - CJ sin 201 

 ■ " (5i - Ci) cos 2^^! + jP,, tan2 ' 



which gives two values of ip2 corresponding to the two focal lines. 

 In practical work it is more convenient to use sin 2ifj2 ■ We have 



sm 202 = 5^ Z^ = 2 T ^ W '''' "^^ ' ^^^ 



where, as we may restrict ifti to range from to ^tt, we may specify 

 that I 02 1 < 2^- Equation (29) gives the value of 02 corresponding 

 to B2 ; the value corresponding to C, differs by hr from that given 



When 1=0, the two focal lines coalesce into a point image of 

 the luminous point. Unless B^ = C^, this can only occur when 

 lAj = or 01 = ^77. When this is satisfied, we must further have 

 k,- 1^ = 0, or," by (11), Fj, tan^ ^ = - (5^ - Cj) cos 20^, where 

 0j = or 01 = \tt. If d^ and 0"^^ are the required values of d, we 

 have 



tan2 ^0 = - [By - C,)/F„, tan^ 6''^^2 = {B, - Ci)/i^„. 



For real values of 6, p must have the values 1, 2, ... in one case 

 and— 1,-2, ... in the other. If^j — C^ is positive, jt) is — 1,— 2, ... 

 for 6^, and 1, 2, ... for 0"''^. If, however, B^ — Cg is negative, p is 

 1, 2, ... for ^", and - 1, - 2, ... for ^"'1 The value of tan^ d will be 

 the same in each case, viz. 



tan2^= I {B,-C,)/F,\ = \ {B,- C,)/p\.F,-\ ...(30) 



The image will be real or virtual according as the values of d and 

 p make X positive or negative. 



§ 6. Experimental details. In the experiments the apparatus 

 shown diagrammatically in plan in Fig. 5 was used. The zone plate 

 G is fixed, with its axis ON horizontal, to a table turning about 

 a vertical axis and carrying a horizontal divided circle H, which 

 is read by the pointers J, J. The adjustment of the zone plate so 

 that its centre lies on the vertical axis of the table may be 

 effected by aid of a long focus microscope or by simple mechanical 

 devices. It is convenient to mount the base of the revolving table 



