Energy Distribution of Diffraction- Gratings. 889 



constant, the first class minima move out and presently the 

 spectra of the third and sixth orders disappear. 



Groing back now to the echelette grating we find that in 

 the ideal case, in which the reflected fronts build up an 

 unbroken surface (i. e. with no inoperative or dark regions 

 between them) we should expect all of the light in one 

 spectrum, namely the one lying in the direction in which 

 the reflected wave-fronts are travelling, the case being- 

 analogous to the reflecting grating with infinitely narrow 

 opaque lines ; except that in this case we find the light in 

 a spectrum instead of in the central image. We must 

 remember, however, that in this case we have chopped up 

 the wave-front into linear strips, and that our reflected wave- 

 front is built up of strips obtained from successive waves, as 

 can be seen from fig. 1, in which we have the reflexion of a 



Fig. 1. 

 \kEir el-ion of- Incident' 

 'Wives. 



train of four waves, numbered 1, 2, 3, and 4 from the 

 echelette grooves. It is very questionable whether the 

 upper wave-front 4, 3, 2, 1, will behave as a plane- wave, 

 i. e. travel out without diffraction, for each one of the 

 elements of which it is composed has had to travel one or 

 more wave-lengths before uniting with its neighbour. 



This is a question, however, which can be best answered 

 by experiment. In the paper on the Echelette grating the 

 opinion was expressed that a concentration of light could not 

 be obtained in a region narrower than that covered by the 

 diffraction range from a single reflecting element*. Further 

 consideration shows that this is not the case, for in the ideal 

 case shown in fig. 1 the maxima of the first class coincide 

 in position with the minima of the second class, and vice versa. 

 In the case figured the reflected waves are travelling in the 

 direction of the first order spectrum, and the path-difference 

 between the successive elementary wave-fronts is X, 

 * Supra, p. 777. 



Phil. Mag. S. 6. Vol. 20. No. 119. Nov. 1910. 3 N 



