38 
On the Limits of the Oj)ticaI 
^ Let 77 be the relatively narrowest aperture, and (c) its middle 
point, B the portion of the optical system immediately behind this 
aperture, and let a be the image of the axis point a of the object ; 
further, let a /3 be its image lying in the medium 7 7' and fh 
the image formed by B in the last medium. 
^ When light proceeds from a, and is viewed through the aperture 
77' whose radius is p, interference fringes will appear around a, 
in which the distance S between each two neighbouring maxima 
(excepting the two first) will be according to known laws, if, as 
before, a represents the divergence angle cay, which by assumption 
is very small. 
(a c) A A 
If N be the- amplification of the image hfin comparison to a 
the breadth of fringe B' of hf will be 
S' = N 5 = I N ^ [8] 
or as N = when a' expresses the divergence angle of the 
emergent ray, n' the refractive index of the last medium, n that of 
the medium at (c). 
If ^ = n, then the form in which this value of the breadth of 
fringe of image hf is expressed is exactly analogous with that for 
a y6, 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 7 (X 7, or, in other words, 
through the ocular image of narrowest aperture. 
The above demonstration presupposes 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. 
