106 Dr Searle, Experiments with a plane diffraction grating 



in a hole in the board D. A circular scale is attached to D and P 

 has a pointer J which indicates its angular position. Only one wire 

 is used in the measurements, but the second wire is useful as 

 identifying E. The wires are illuminated by the sodium flame F. 

 A lantern projection lens L is placed so that E is at its principal 

 focus; for the best results, that end of L should face E which faces 

 the lantern slide. Beyond i is a cylindrical tube Q, resting in 

 two F's, V, V, and against a stop C/, and thus having only one 

 degree of freedom. A piano-cylindrical lens A is attached by its 

 plane face to one end of Q. A lens of about + 2-5 dioptres, such 

 as is used in spectacles, is suitable. The grating, centre 0, is 

 placed at G. A ground glass screen H can slide on the main optical 

 bench, which also carries G, Q, L; if possible, D should be carried 

 on the bench. On a short auxiliary bench slides a second screen K; 

 the angle between the benches is cf), where sin cf) = i\ld. The 

 ground sides of the screens face 0. 



Suppose, for a moment, that E \^ & luminous point. Then E^ 

 at the focus of L, gives rise to a parallel beam falling on the 

 cylindrical lens A. This lens converts the plane wave front into 

 a cylindrical front. If the "power" of ^ is + i^ dioptres, a "real'' 

 focal line, parallel to the generators of A'b surface, will be formed' 

 100/i'' cm. from A. This focal line can be received on the screen H, 

 By § 4, the diffracted front is cylindrical and there is only one 

 focal line at a finite distance. This focal line can be received on 

 the screen K. If A is turned by turning Q on its axis, the focal 

 line of the diffracted beam will turn about the axial ray and the 

 distance of the focal hue from will change. The experiment tests 

 the relation between the linear displacement of K and the angular 

 displacement of A. 



When a wire is used instead of a luminous point, images of the 

 wire will be formed on H and K when the generators of A are 

 parallel to the wire. If the pointer J is set in any position, a sharp 

 image can be obtained by turning Q. 



When the adjustments of § 11 have been made, H is set to 

 receive the image of the wire, and HO is measured. As a correction 

 we may add tj ^i, where t is the thickness and ix the index of the 

 plate covering the grating. A line ruled on H is made vertical by 

 aid of a set square and a level, and P and Q are adjusted so that 

 the image is vertical and ^j = 0. Then K is set so that the diffracted 

 image is in focus on it, and the reading of K on its bench is taken. 

 Then P is turned by steps of 10° or 15°, Q is turned in response, 

 and K is adjusted in each case so that the image is focussed. When 

 P has been turned through 90°, so that ifj-^ = ^tt, the image is hori- 

 zontal, and, by (14), since i/r^ = \tt, its distance from is equal to 

 the measured distance OH. When the image is vertical, j^i = or it. 

 Since B-^-^ = OH, B^-^ = OK, we have, by (14), 



