Highly Magnified linages. By J. W. Gordon. 



25 



practical use a more serviceable form of diffractor could easily be 

 devised. Indeed, diffractors which really work upon this principle 

 are already in extensive use in the form of spot-lens apparatus for 

 producing oblique illumination. But the art and science of oblique 

 illumination must be classed among the matters which are at 

 present ill understood for want of a sound and comprehensive 

 optical theory of the Microscope. 



Note. — It may, I trust, be open tome, without breach of that respect 

 which is due — and of which I am most deeply sensible — to Sir George 

 Airy, and to the other distinguished men Avho have adopted his calcula- 

 tion, to suggest that some closer approximation to the true value of the 

 light amplitude curve of the antipoint is desirable than his method of 

 solving the problem affords. The difficulty may be illustrated in this 

 way. Let the cone A A 77 in fig. 21 represent the 

 principal or dioptric beam, and the other cone 

 A x A x -q x one of the diffracted beams transmitted 

 by the same aperture. Now, according to Sir 

 George Airy's way of viewing the matter, these two 

 cones have a common middle point at C, where, of 

 course, the undulation in both cones is in very 

 nearly the same phase. Also, the surface A C A is 

 monophasal — a wave-front focussing on the point 

 77 in the focal plane. The surface A x C A : is, on 

 the other hand, polyphasal, and focussed in the 

 point 77^ Airy determines the light amplitude at 77 

 by integrating over the surface A C A, and in like 

 manner he determines the amplitude at rj x by in- 

 tegrating over the surface A x C A : . 



Let us now consider the resultant light phase 

 at the point P in the diagram. This point is one 

 point among many common to both cones, and here, therefore, the 

 phase must be to a large degree common to them both. But it is quite 

 ■obvious that such is not the case upon Airy's method of calculating. 

 For, considered as a part of the diffracted cone A x A t 77^ the retardation 

 of its phase is determined in relation to the contemporary phase in the 

 wave-front A C A by the distance C P. But, considered as a part of the 

 dioptric cone A C A, its retardation is determined by the shorter distance 

 A P, and the phase difference of these paths may, by slightly varying 

 the position of the point P, be made to run through the complete cycle 

 of possible values, while the phase value at P throughout its movement 

 remains substantially constant. It is evident, therefore, that Sir George 

 Airy's two results — that is to say, the calculation of amplitude at the 

 focal point, and that of amplitude at the point rj^ — are incompatible with 

 one another, and some more consistent mode of reckoning the light 

 amplitudes in different parts of the antipoint is desirable. 



The criticism suggests the alternative mode of computation. It is 

 plain that all the diffracted light which escapes from the dioptric beam 

 and lights up the disc of the antipoint must pass through the bounding 



Fig. 21. 



