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
79, 80.] 
§10. Optical System of the Eye 
and the object observed through it, the reduction in the size of the 
image could not be detected with the ophthalmometer. Whatever 
change may have occurred in the appearance of the image, it was so 
slight as to escape notice. 
In order to get an idea as to what extent the actual refraction of the 
eye differs from what it would be if the index of refraction of the 
cornea were really equal to that of the aqueous humor, the optical con¬ 
stants of the cornea may be calculated by equation (12), §9, by putting 
rii = 1, nz=n, ri2=n-\-An, r1=r, r2 = r — Ar, where the magnitudes de¬ 
noted by An, Ar and the thickness of the cornea (d) must all be regarded 
as very small in comparison with n and r. Substituting these values, 
at the same time neglecting the higher powers of the small quantities, 
we find for the focal lengths : 
1 r 
F1=-F 2= -r 
n n — 1 
. (n — l)d — nAr\ 
1 — An--~7~—tt-> 
n(n —l)r ) 
The difference between this and the value --, obtained by putting 
71 — 1 
An = 0 is a small magnitude of the second order. Likewise, the distance 
(a?) of the first principal point from the anterior surface of the cornea 
calculated as above turns out to be 
d. An 
X n(n — 1) 
The interval (a) between the two principal points is indeed of the 
third order of smallness, namely : 
For calculation of images, therefore, it is accurate enough to assume 
that refraction occurs simply at the anterior surface of the cornea and 
to put the index of refraction of the cornea equal to that of the aqueous 
The second part of the optical system of the eye is composed of the 
crystalline lens, bounded by the aqueous humor in front and the 
vitreous humor behind, The indices of refraction of these two humors 
are so nearly the same that the difference may be ignored. In an opti¬ 
cal system surrounded by the same medium on both sides, the principal 
points coincide with the nodal points. Thus, just as in an ordinary 
glass lens surrounded by air, these two pairs of points in the optical 
system of the crystalline lens are identical. But the crystalline lens 
differs essentially from a glass lens because the density of its substance 
is not uniform but increases from the outside towards the central part. 
Being ignorant of the exact law of this increase, we are not in position


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