170 Lord Rayleigh on the Theory of Optical Images, 



cone corresponding to the aperture of the lens and illuminate 

 a circle CD in the plane of the image, whose centre is B. 

 The first lateral spectrum S : is formed by rays diffracted from 



Fig. 1. 









$^4 





L' 



the grating at a certain angle ; and in the critical case the 

 region of the image illuminated by the rays diverging from 

 S x just includes B. The extreme ray S t B evidently proceeds 

 from A, which is the image of B. The condition for the 

 co-operation at B of the first lateral spectrum is thus that 

 the angle of diffraction do not exceed the semi-angular 

 aperture a. By elementary theory we know that the sine of 

 the angle of diffraction is \/e, so that the action of the lateral 

 spectrum requires that e exceed A/ sin a. If we allow the 

 incidence upon the grating to be oblique, the limit becomes 

 itysina, as in (1). 



We have seen that if one spectrum only illuminate B, the 

 field shows no structure. If two spectra illuminate it with 

 equal intensities, the field is occupied by ordinary interference 

 bands, exactly as in the well known experiments of Fresnel. 

 And it is important to remark that the character of these 

 bands is always the same, both as respects the graduation of 

 light and shade, and in the fact that they have no focus. 

 When more than two spectra co-operate, the resulting inter- 

 ference phenomena are more complicated, and there is 

 opportunity for a completer representation of the special 

 features of the original grating *. 



* These effects were strikingly illustrated in some observations upon 

 gratings with 6000 lines to the inch, set up vertically in a dark room 

 and illuminated by sunlight from a distant vertical slit. The object-glass 

 of the microscrope was a quarter inch. When the original grating, 

 divided, upon glass (by Nobert), was examined in this way, the lines 

 were well seen if the instrument was in focus, but, as usual, a compara- 

 tively slight disturbance of focus caused all structure to disappear. 

 When, however, a photographic copy of the same glass original, made 



