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



may be called an astigmatic collimator. The emergent wave front 

 n this case will be cylindrical. 



By rotating M, the principal planes of the emergent wave front 

 emerging from an astigmatic lens L can be turned about the axis 

 of M*. 



The principal planes of the emergent wave front due to a 

 luminous point at K are perpendicular and parallel to the axis 

 of the cylindrical surface of L. We will denote by i/f^ the inclination 

 of the first of these planes to XON, the horizontal plane of incidence 

 of the chief ray upon the zone plate; then the inclination of the 

 other principal plane is tp-^ + ^tt. If, in place of a small hole, a slit 

 is used, its inclination to the horizontal plane through OX must 

 be j/»i or ifj^ + Itt, when 6 = 0. When 6 is not zero and i/r^ is not 

 zero, no sharp focal line will be formed unless the slit is inclined 

 to XON at one of the two angles S and S -f ^tt. To find the angle 

 8, first find the focal lines formed at Q and R on OX by the system 

 of lens and zone plate, when a luminous point is placed at A'. 

 Next place a luminous point at Q; the direction of that focal line 

 which lies in the plane of K gives one of the required directions 

 of the slit. When the slit is placed in this position and is illuminated, 

 there will be a long sharp focal line at Q. If the slit is turned through 

 ^7T, there will be a long sharp focal line at R. If we carry out this 

 process mathematically we can calculate S. In practice it is easy 

 to adjust the direction of the slit so that the images formed by 

 focal lines are sharp. 



§ 7. First practical example. In this experiment the results of 

 § 3 were tested. 



A vertical slit was used in the collimator 31 (Fig. 5), and the instrument 

 was adjusted so that the slit was accurately at the focus of a converging lens 

 of 3-5 dioptre power. The rays falling on the zone plate came, in effect, from 

 an infinitely distant slit, and thus l/u=0. The real images for p= +1 and 

 the virtual images for p= -1 were observed by aid of a telescope. The real 

 and virtual horizontal focal lines did not change their positions when 6 was 

 increased from zero. Since b, the distance of the vertical focal line from the 

 zone plate is positive or negative Avith ^J, the product bj) is always positive. 

 The values of bp given for ^ = 15° are the means of those found" for ^ = 15" 

 and 6= - 15°, and similarly for the other angles. By (2), since l/u =0, bp sec^ B 

 is constant. 



* The appliance (Fig. 5) for rotating the wave front may be used with advantage 

 in the experiment described in § 10 of "Experiments with a plane diffraction grating " 

 {Proc. Camb. Phil. Soc. Vol. xx. p. 105). In the method there described, the angle 

 between the vertical and the cross-icire is erroneously taken to be V'l, whereas, in 

 the theory, the angle between the vertical and the' generators of the cvlindrical 

 surface of the lens is i/zj. These two angles are not generally identical. In the actual 

 example given, the difference was small. When the experiment was done, I had 

 not the appliance shown in Fig. 5 above. 



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