# Bauhaus-Universität Weimar

### Volltext Helmholtz's treatise on physiological optics. Volume 1. Edited by James P. C. Southall. Translated from the 3rd German edition (1)

Titel:
Helmholtz's treatise on physiological optics. Volume 1. Edited by James P. C. Southall. Translated from the 3rd German edition
Person:
Helmholtz, Hermann von
PURL:
https://digitalesammlungen.uni-weimar.de/viewer/image/lit39649/123/
```79, 80.]
§10. Optical System of the Eye
99
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 )
(1)
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)
(la)
The interval (a) between the two principal points is indeed of the
third order of smallness, namely :
d*An........(lb)
nr
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
humor.
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
```

### Nutzerhinweis

Sehr geehrte Benutzer,

aufgrund der aktuellen Entwicklungen in der Webtechnologie, die im Goobi viewer verwendet wird, unterstützt die Software den von Ihnen verwendeten Browser nicht mehr.

Bitte benutzen Sie einen der folgenden Browser, um diese Seite korrekt darstellen zu können.

Vielen Dank für Ihr Verständnis.