438 LIMITS OF OPTICAL CAPACITY OF THE MICROSCOPE. 



a' =JV^=i N~ (8) 

 a 



or as JV= — j—f "when a' expresses the divergence-angle of the 



emergent ray, n' the refractive index of the last medium, n that of 

 the medium at (<?). 



w-^ («^) 



If n = n' then the form in which this value of the breadth of 

 fringe of image 5/ is expressed is exactly analogous with that for 

 -a j3, and shows that the fringes in the last image are of just the 

 same dimensions as if seen through the aperture which 

 determines the divergence-angle a' of the cone of rays y a y 

 or in other words, through the ocular image of narrowest 

 aperture. 



The above demonstration pre- supposes that the relatively 

 narrowest aperture of diaphragm is situate where the divergence 

 angles of the pencil of rays are very small. It may however be 

 situate at any part of the instrument. With an immersion micro- 

 scope this condition is indeed not fulfilled when the surface of 

 front lens is the relatively narrowest aperture. But it would 

 be fulfilled if the aperture were situate on the upper side of the 

 second or third lens. Thus if there were no lateral outspread of the 

 advancing rays on their passage through the front lens of the 

 objective where the pencil is still diverging strongly, then from the 

 point where the divergence is weak, or convergence commences, its 

 lateral limitation, whether occasioned by a diaphragm actually 

 situate at the place, or only conditioned by the previous course of 

 the rays, must nevertheless produce a diffraction. 



As regards the final result, it makes no diff'erence whether the 

 aperture at the circumference of the pencil of rays be supposed to 



