Influence of Phase- Differences. By J. Rhcinberg. 53$ 



one grating interval on the stage, the zero maximum of the dif- 

 fraction spectra remains unchanged, the first maximum passes 

 through one complete phase period, the second maxima through 

 two complete phase periods, the third through three periods, and 

 so on. From which it is readily seen that if a grating has been 

 moved by exactly half a grating interval, the zero, second, fourth, 

 and every alternate maximum will have the same phase as before, 

 whilst there will be a difference in the phase of the first, third, and 

 every alternate maximum of exactly half a phase period. 



2. The phase-differences in the spectra of gratings, ivhich depend 

 on the relative ividth of the slits to the bars, as first pointed out by 

 Mr. A. E. Conrady. 



That in the diffraction spectrum arising from a star disk — and, 

 therefore, also in that of a single slit — there is a phase-difference 

 of half a period between consecutive maxima, was, it appears, first 

 shown by Sir George Airy. 



If we plot out the position of the diffraction maxima of a 

 regular grating on the curve of diffraction pattern of one of its slits,, 

 then the maxima which are situated between the first and second, 

 or between the third and fourth minima of the single slit pattern, 

 will differ by just half a phase period from those that are situate 

 between the two first minima, or between the second and third, or 

 fourth and fifth minima of the single slit pattern. 



The relative width of the slits to the bars determines the 

 position of the maxima of the grating on the diffraction pattern of 

 one of its slits. 



Whenever the slits are wider than the bars, then one diffracted 

 maximum only is formed between the centre and the first minimum 

 of the single slot pattern. From which it follows that in this case 

 the first maximum of the grating and the central, zero, or undif- 

 fracted maximum are alike in phase, whilst the second maximum 

 will differ by half a phase period. 



"When the bars are wider than the slits, then two or more of 

 the diffracted maxima of the grating fall between the centre and 

 first minimum of the single slit pattern. Such maxima will be in 

 the same phase as the central or zero maximum. 



In the photographs appended to my last note, an example is 

 seen of the effects which may be produced by these phase-differ- 

 ences, in the case of a reciprocal grating in which the ratio of the 

 slits to the bars is 1-2 in the upper, and 2-1 in the lower half. 

 Although in a reciprocal grating the position of the slits in the 

 upper half corresponds to the position of the bars in the lower half, 

 when all but the first and second maxima are blocked out in the 

 back focal plane of the objective, the image in the view plane 

 shows the slits in both upper and lower part of the grating coin- 

 ciding in position. 



Dr. Strehl's method of explaining this is as follows : — Pointing 



