180 Lord Rayleigh on the Theory of Optical Images, 



and rises to a maximum at a point near u = ^7r, considerably 

 beyond the geometrical image at w = 0. Moreover, the value 

 of the maximum itself is much less than before, a feature 

 which would become more and more pronounced as the points 

 were taken closer. At this stage the image becomes only a 



Table III. 



7T 



/(«). 



4m 



7T 



/(«)■ 



— 1 



+ •00 

 +•36 

 + •60 

 + •64 

 + •48 

 +•21 



5 



-•05 

 -•21 

 -•23 

 -•13 



+ •02 







6 



1 



7 



2 



8..., 



3 



9 



4 







very incomplete representation of the object ; but if the forma- 

 tion of a black line in the centre of the pattern be supposed 

 to constitute resolution, then resolution occurs at all degrees 

 of closeness*. We shall see later, from calculations conducted 

 by the same method, that a grating of an equal degree of 

 closeness would show no structure at all but would present a 

 uniformly illuminated field. 



* These results are easily illustrated experimentally. I have used 

 two parallel slits, formed in films of tin-foil or of chemically deposited 

 silver, of which one is conveniently made longer than the other. These 

 slits are held vertically and are viewed through a small telescope, pro- 

 vided with a high-power eye-piece, whose horizontal aperture is re- 

 stricted to a small width. The distance may first be so chosen that 

 when backed by a neighbouring flame the double part of the slit just 

 manifests its character by a faint shadow along the centre. If the flame 

 is replaced by sunlight shining through a distant vertical slit, the effect 

 depends upon the precise adjustment. When everything is in line the 

 image is at its brightest, but there is now no sign of resolution of the 

 double part of the slit. A very slight sideways displacement, in my 

 case effected most conveniently by moving the telescope, brings in the 

 half-period retardation, showing itself by a black bar down the centre. 

 An increased displacement, leading to a relative retardation of three 

 halves of a period, gives much the same result, complicated, however, by 

 chromatic effects. 



In conformity with theory the black bar down the image of the double 

 slit may still be observed when the distance is increased much beyond 

 that at which duplicity disappears under flame illumination. 



For these experiments I chose the telescope, not only on account of 

 the greater facility of manipulation which it allows, but also in order to 

 make it clear that the theory is general, and that such effects are not 

 limited, as is sometimes supposed, to the case of the microscope. 



