Bauhaus-Universität Weimar

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/lit39649/104/
80 
Dioptrics of the Eye 
[63, 64. 
If equation (9) is applied to the nodal points we must put a, = am +1} 
and thus we obtain: 
Th,'Y> m+1* 
Hence, we see that the linear dimensions of object and image lying in 
the nodal planes are likewise inversely proportional to the indices of 
refraction of the first and last media. 
Since the size of the image is proportional to its distance from the 
second focal plane, this distance can be found, provided the size of the 
image is given. If the image lies in the second principal plane, it has 
the same size as the object and its distance from the second focal point 
is F2. On the other hand, if the image is formed in the second nodal 
plane, its size, as has just been shown, will be 
T"+1=^T" 
If (r2 denotes its distance in this case from the second focal point, then 
v _Fi 
y m+l G 2 
and therefore by equation (9c), 
G2 = —F,=Fl......(10a) 
nm+i 
Accordingly, the distance between the second principal plane and the 
second nodal plane is 
0,2 = F 2 — t?2 
~ F 2 F 
The nodal planes are a pair of conjugate planes; and if oq denotes the 
distance of the first nodal plane from the first principal plane, that is, if 
o\ — Gi F l, 
then by equation (8a), we have: 
di 02 
hence 
0\ — 02 = F 2 — F1 
Gi = F 2........(10b) 
and 
G\_7ïm+i 
G2 ni 
(10c)
        

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