Notes. 153 



The theory of diffraction teaches us that in a regular grating, 

 in which the slits are all of equal width, we need only draw the 

 light-intensity curve for one of the slits to be able to indicate 

 immediately the positions and relative intensities of the spectra or 

 maxima of the grating as a whole. 



The intensity curve for one slit may be represented by figs. 1 

 and 2.* From the highest point at the centre, A, it falls to zero 

 at B, and then alternately rises and falls. This indicates that in 

 the diffraction pattern which the slit forms, the points A, C, E will 

 be the middle of bright bands, the points B, I), F the middle of 

 dark bands. The width of the bands depends upon the width oi 

 the slits, being in inverse ratio. Thus, fig. 2 shows the intensity 

 curve for a slit half as wide as that of fig. 1. 



When, as in a regular grating, we have more slits than one, all 

 of the same width, all that we require to know to find the position 

 of the maxima of the grating is the relative width of the slits to 

 the bars, for the first maximum will occupy a position on A B 

 (i.e. the distance between the centre of the middle bright band and 

 that of the first dark band), such that its distance from A and B 

 respectively is in the same ratio as the width of the slits to that of 

 the bars. Thus, if the slits just equal the bars in width, the first 

 maximum will be equidistant from A and B (fig. 2) ; if the slit is 

 half as wide as the bars, it will be half as far from A as from B 

 (fig. 3) ; if twice as wide as the bars, it will be double as far from 

 A as from B (fig. 4) ; and so forth. Having found the distance of 

 the first maximum from A, we may mark off the same distance for 

 all the succeeding maxima, and it will be seen that as a necessary 

 corollary there are always just as many maxima formed between 

 A and B as the number of times the width of the bars divided by 

 that of the slit shows. Intermediate between the maxima of the 

 grating there will, of course, be the minima. 



The relative light-intensities of the maxima produced by the 

 grating depend on where they happen to fall with respect to the 

 intensity curve of their single slits, because they lie on a similar 

 curve. Thus, in figs. 3, 4, and 5, it will be seen that the relative 

 intensities of the maxima are just the same as for the corresponding 

 points on the single-slit t intensity curves, indicated by the dotted 

 lines. 



Now the point brought out by Mr. Conrady is, that in the case 

 of a single slit a change of half a phase-period occurs at each point 

 of zero intensity, and that the maxima from the grating, wherever 



* All the intensity curves shown in the figures are diagrammatic, their purpose 

 being merely to illustrate matters brought forward in this Note, and reasons of space 

 having precluded their being drawn to scale. 



t Tnia holds good even where a maximum happens to fall on a point where the 

 single-slit curve show3 zero intensity, for then the particular maximum in question is 

 absent. 



Apil 19th, 1905 m 



