Tin- Theory of Optical Images. By Lord Rayleigli. 45 9-' 



pose that the aperture is rectangular and that the points or lines ; 

 are twice as close as before, the geometrical images being situated 

 at u = — ^7r, u = 0. The resultant amplitude is represented by 

 f(u), where 



f(v \ _ sin v _ sin O + fe) n 7^ 



The values of / (u) are given in Table III. They show that the 

 resultant vanishes at the place of symmetry u = — \ir, and rises 

 to a maximum at a point near u = \tt, considerably beyond the geo- 

 metrical image at u = 0. Moreover, the value of the maximum 

 itself is much less than before, a feature which would become' 



Table III. 



more and more pronounced as the points were taken closer. At 

 this stage the image becomes only a very incomplete representa- 

 tion of the object; but if the formation 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, 



* 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, provided with a high-power eye-piece, whose 

 horizontal aperture is restricted 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 side- 

 ways 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, t« 

 the case of the microscope. 



