Dr Searle, Experiments on focal lines formed by a zone plate 341 



The mean value of bp sec- 6 is 6608 cm., and the corresponding "power" of 

 the zone plate for images of the first order is 



F^ = 1/66-08 cm.-i =-015133 cm.-i = 1-5133 dioptre. 



§ 8. Second practical example. The results of § 5 were tested in 

 these experiments. 



The lens L (Fig. 5) was built up of a spherical lens of 2-5 dioptres in power 

 {2-o D) and a piano-cylindrical lens of powers and ID. The axis of the 

 cylindrical surface will be called the axis of L. When this axis is vertical, 

 •»/^i =0. In each set of observations, 6 was made 45° and -45°, and the mean 

 results for the two positions are given. In the first set, the sUt was vertical 

 when \/^i =0. Then ifj was gradually changed from to ^tt, and at the same 

 time the direction of the sUt and the position of the telescope were changed 

 so as to keep the slit in view throughout. The image of the sUt, formed by focal 

 lines, was very sharp if the direction of the slit was very carefully adjusted. 

 Tlie table records B.,, the reciprocal of the distance of the focal Une from the 

 zone plate, expressed in dioptres. Thus the reciprocal of 40 cm. would appear 

 as 2-5 D. 



The axis of L was again made vertical and the slit was made horizontal. 

 Then t/^j was changed step by step from to ^tt. The reciprocal of the distance 

 of this focal fine from the zone plate is C^, . 



In each case the virtual focal line of the first order was used, and thus 

 jBo and C^. were both negative and ^ = - 1. From the values given in the table 

 we have, in dioptres, 



52°= -2-9976, 5.//'^ =- 3-9002, C'aO^ -2-4201, CV 



r/2. 



1-5006. 



Since (28) gives two expressions for X, F.^, tan^ 6 and B^^-C^, we take the mean 

 in each case. Thus 



X= -I (5-4177 +5-4008) = -2-7046, 



Fp tan- e= -I (1-4970 + 1-4801 ) = - 1-4886, 



Bi -C\=i (-9026 + -9195) =-9110. 



Hence 7"= -0-2888, Y 



-1-1998, and Y is, therefore, taken as negative 



for all values of \//i . Using the values of F„ tan- d and of B^ - C\ just found, 

 Y was calculated for \/^i = 15°, ... by (25). There is good agreement between 



X + Y and the observed value of B, and between X ^^ —^ ^' v.^-..,..^^ 



value of C'2 . 



The distance OL was approximately 10 cm. 



Y and the observed 



