The Theory of Optical Images. By Lord Baylcigli. 449 



In Prof. Abbe's method of treating the matter the typical object 

 is not a luminous jJoint, but a grating illuminated by plane waves. 

 Thence arise the well-known diffraction spectra, which are focussed 

 near the back of the object-glass in its principal focal plane. If 

 the light be homogeneous, the spectra are reduced to points, and 

 the final image may be regarded as due to the simultaneous action 

 of these points acting as secondary centres of light. It is argued 

 that the complete representation of the object requires the co- 

 operation of all the spectra. When only a few are present, the 

 representation is imperfect ; and when there is only one — for this 

 purpose the central image counts as a spectrum — the representation 

 wholly fails. 



That this point of view offers great advantages, at least when 

 the object under consideration is really a grating, is at once evident. 

 More especially is this the case in respect of the question of the 

 limit of resolution. It is certain that if one spectrum only be 



Fig. 117. 



operative, the image must consist of a uniform field of light, and 

 that no sign can appear of the real periodic structure of the object. 

 From this consideration the resolving-power is readily deduced, 

 and it may be convenient to recapitulate the argument for the case 

 of perpendicular incidence. In fig. 117 AB represents the axis, A 

 being in the plane of the object (grating) and B in the plane of 

 the image. The various diffraction spectra are focussed by the 

 lens LL' in the principal focal plane, S representing the central 

 image due to rays which issue normally from the grating. After 

 passing S the rays diverge in a 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 the grating at a certain angle ; and in the 

 critical case the region of the image illuminated by the rays diverg- 

 ing from Si just includes B. The extreme ray SiB evidently 

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



