350 Messrs. Bdser and Senior on the Diffraction of 

 find a position of the point E such that 

 AP + A=/a.DE+EP, 



where A is the wave-length of the incident light. In this 

 case the wavelets from A and E reinforce each other at P, 

 their phases differing by 27r. If, then, we stop out the rest 

 of the surface, so as to intercept the wavelets which would 

 ordinarily interfere with those from A and E, light will 

 arrive at P. We may go further and stop out portions of 

 the surface AC, leaving a number of clear spaces from which 

 the wavelets arrive at P in phases differing by multiples of 

 27r. In this case we have virtually described a zone plate 

 on the refracting surface, and light is diffracted into the 

 rarer medium. Since there is only a superficial disturbance 

 in the rarer medium when the surface is free, it follows that 

 the zone plate must be in optical contact with the surface. 



The particular case which is most readily verified experi- 

 mentally corresponds to the location of the point P at an 

 infinite distance from A. In this instance the zone plate 

 takes the form of an ordinary diffraction-grating, the lines 

 being placed perpendicular to the plane of incidence. If $ 

 represents the sum of the widths of a space and a ruling, 

 then for the diffracted rays to reinforce each other at infinity, 

 in a direction making an angle 6 with the normal to the 

 surface, we must have 



&(fju sin i — sin 0)=n\, 



where n is an integer. Using white light as an illuminant, 

 we shall obtain diffraction spectra similar to those ordinarily 

 observed by the aid of a grating; but when fi sin i>l, the 

 central undiffracted image (corresponding to ??. = 0) will be 

 absent. Further, for large angles of incidence, the number 

 of lines per centimetre must exceed a certain value, other- 

 wise the smallest possible value for n will correspond to a 

 diffracted spectrum of such high order that the latter will be 

 too faint to be seen ; for here, as in the ordinary case, the 

 intensity of a diffraction spectrum varies inversely as the 

 square of the order, to a first approximation. Let the light 

 be incident at an angle of 45° on the grating, and let yot=l-5. 

 Then if the 8th diffraction spectrum for \ = "00006 cm. is to 

 be seen along the surface (0 = 90°), we must have 



. 8 x -00006 mQ _ 

 o=--— r — -—='0096 cm. 

 1*05 — 1 



Thus the grating must possess more than 100 lines per centi- 

 metre, or more than 250 lines to the inch. For the first 



