Diffraction by a Semi-infinite Screen. 53 



however, that is in the neighbourhood of the planes defined 

 by <b = 7T — (f>' and <£ — 7r + <// 7 the difference in the magnitude 

 of the two components is generally quite negligible. For, 



in the neighbourhood of the first plane, — — — — T is nume. 



cos -2 

 rically very large compared with i _ ? and similarly in 



cos ^ r 



1 

 the neighbourhood of the second plane , __ , / is very 



cos — - -£ 

 1 ^ 



large compared with . ,*i . Accordingly, in the neigh- 



bourhood of these two planes, it is ordinarily sufficient to 

 retain one of the two terms and neglect the other in the 

 expression for tbe amplitude of the diffracted waves, which is 

 thus numerically the same for both states of polarization, and 

 for the region considered is in substantial agreement with 

 that found from the approximate theory. But the preceding 

 argument fails entirely when <f>' is nearly equal to either it or 

 ,zero, that is when the incidence of the light at the screen is very 



oblique. For the two terms — and -. 77 are 



© + © © — © 



cos ' ^ cos ^ ^ 



then always of comparable magnitude, and have both to be 

 retained. It is thus clear that some special features are to 

 be expected when the incidence of light on the screen is very 

 oblique. 



We may now consider separately the two cases in which <f>' 

 is nearly equal to it and zero respectively, as they present 

 distinctive features. When <// is nearly e^ual to it (see 

 figs. 1 a and 1 6), by far the largest part of the field is 

 occupied by the region of transmission (marked II. in the fig.), 

 and the remaining part of the field is equally divided between 

 regions of shadow and of reflexion (marked I. and III. re- 

 spectively in the figure) which lie on opposite sides of the 

 screen and are completely separated by it. If we wish to 

 observe the phenomena in the neighbourhood of the boun- 

 daries separating the different parts of the field, we have 

 two distinct choices open to us. We may either study the 

 phenomena near the region of shadow which lies on one side 



