Bauhaus-Universität Weimar

Helmholtz's treatise on physiological optics. Volume 1. Edited by James P. C. Southall. Translated from the 3rd German edition
Helmholtz, Hermann von
Dioptrics of the Eye 
[82, 83. 
From the expressions above, it is evident that C increases and P 
decreases when n2 is increased, whereas (f'—p), which does not involve 
ra2, remains unchanged. Either increase of C or decrease of P results 
in diminishing ßa, and, hence, increase of the index of refraction causes 
reduction of the interval ßa. 
Thus far we have studied the effect of a single one of the lenses 
obtained by dividing the crystalline body in its layers. Suppose now 
that all these meniscus lenses on one side of the core are mounted 
together in their natural position and surrounded by aqueous humor 
introduced between each pair of adjacent layers of different densities 
in the crystalline lens; and isolate 
that part of it on one side of the 
nucleus; thereby obtaining a sys- 
tern like that represented in Fig. 46, 
where ab is the axis, and g and 
h are the two opposite vertices of 
the combination. Let a designate 
the position of a luminous point on 
the axis in front of the convex side. From what was proved above 
with respect to a single lens of this type, evidently the image of a in the 
first lens will lie in front of the second surface of this lens and therefore 
also in front of the first surface of the second lens. Similarly, the image 
of this image in the second lens will lie in front of the second surface of 
that lens, and so on for each lens in succession; and, consequently, the 
final image of a in the entire system will lie somewhere in front of the 
last refracting surface, at a, say. 
Evidently, too, as the point a approaches the vertex g, the point a 
will approach the vertex (h) of the farther surface. For the image of a 
real object in a simple negative lens is nearer the lens, when the object 
is nearer; and since the image produced by each lens of the system 
acts as object for the next lens, therefore when a approaches the first 
surface, its image moves along the axis in the same direction, and so on 
for each image in succession. 
The conclusion is that if the index of refraction of one of the 
layers were increased, the image a would thereby fall nearer h. Until 
the layer which is supposed to be altered is reached, there would be, of 
course, no change in the path of the rays or in the successive images; 
but the image in that layer will be nearer h than it would have been, 
and, consequently, the last image (a) will be nearer. If, therefore, this 
final image is to stay where it was originally before the index of one 
layer is increased, the object a must be moved farther back so as to 
increase the distance ag. 
Consider now the whole crystalline lens as composed of two such 
systems of meniscus lenses B and C (Fig. 47), with its double convex


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