# Bauhaus-Universität Weimar

### Volltext Helmholtz's treatise on physiological optics. Volume 2. Edited by James P. C. Southall. Translated from the 3rd German edition (2)

Titel:
Helmholtz's treatise on physiological optics. Volume 2. Edited by James P. C. Southall. Translated from the 3rd German edition
Person:
Helmholtz, Hermann von
PURL:
https://digitalesammlungen.uni-weimar.de/viewer/image/lit39650/100/
```88
The Sensations of Vision
[73.
Now, as a matter of fact, this latter equation will be always satisfied,
provided either Aa=0 or A6=0, that is, provided the intersecting
normals lie either in the 2/2-plane or in the xs-plane. And, finally, if at
the same time
d2c d2c _
~db2~ ~d^~ 9
the condition that adjacent rays shall intersect the ray A is satisfied
for all arbitrary values of A a and Ab; that is, all the adjacent rays
d2c
meet the ray A. Still supposing that = and then putting either
Aa = 0 or Ab =0, we find, as was mentioned above, the distance z of the
point where the adjacent rays meet the ray A by putting x=y = 0 in
equations (3).
For the rays in the xz-plane, A& =0; hence from equations (2) the
distance of the point of intersection from the wave-surface is
1
Z ~ C ~ H2c'
la*
The second of equations (2) becomes 0=0.
For the rays in the 2/z-plane, A a = 0, and
z — c
1
Hfl *
db2
Finally, if
tinction
d2c
da2
— = —, then for all adjacent rays without dis
db2 p
z — c = p .
Moreover, in this case the æz-plane and 2/2-plane are also the
principal sections of the surface for which the curvature has its maxi¬
mum and minimum values; and the values of the corresponding radii
of curvature are:
Pa
1
l?c
Pb =
1
da2 db2
and hence the focal points of the bundle of rays are also at the centres
of principal curvature of the wave-surface.
Constitution of an infinitely narrow bundle of rays that meets the
wave-surface in a circle. In order to get a clearer notion of the way the
```

### 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.