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
Dioptries of the Eye 
reduced eye.1 The double principal point of this eye is 2.3448 mm 
beyond the anterior surface of the cornea, and the nodal point (k in 
Fig. 44) is 0.4764 mm in front of the posterior surface of the lens, the 
focal points being unchanged. The optical behaviour of this reduced 
eye is equivalent to that of a single spherical refracting surface whose 
centre and vertex are at the nodal point and principal point, respec¬ 
tively, the first medium being air and the second medium the aqueous 
or vitreous humor. The radius of curvature of such a surface would be 
5.1248 mm. Many problems, in which only the size and position of the 
image are required, are greatly simplified by using this equivalent 
spherical surface. In Fig. 44 the surface is shown as the dotted arc ll, 
with its centre at k. 
Fig. 44. 
If, as often happens, we know in advance that the image is focused 
on the retina, and all we wish to do is to find the position of the image 
of a given point, the nodal points are sufficient for the purpose; and 
if it is permissible to regard the nodal points as coincident, as in the 
reduced eye, the position of the image may be located by drawing a 
straight line from the luminous point to the nodal point and prolonging 
it to meet the retina. A straight line drawn in this way may be called 
a line of visual direction. The nodal point considered as single is there¬ 
fore the point of intersection of all the lines of visual direction. The 
two parts of such a line that are in the air in front of the cornea and 
1 ^Listing’s reduced eye is very similar to the “simplified eye” imagined by Huygens 
in the first part of his Dioptrica (1652). (J. P. C. S.)


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