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
G. 303, 304.] 
II. 3. The Optical System of the Eye 
A reduced eye corresponding to the exact schematic eye and having 
an index of refraction of 4/3 would have a radius of curvature of 5.7 mm. 
According to the accuracy demanded in any given case, one or the 
other of these models can be employed. With regard to the simplified 
schematic eye, it should be expressly noted that, due to neglect of the 
aberration, the total index of the lens is greater than its actual be¬ 
haviour indicates, as its value in the exact schematic eye is only 1.4085; 
and, consequently, this latter eye should be used in case it is desired 
to trace the rays through the lens exactly. In the simplified schematic 
eye it may be said that we are never concerned with calculating the 
refraction at the single surfaces of the lens, but the lens is always to 
be treated as a single unresolvable optical system. 
In the schematic eye both the décentration of the refracting surfaces 
and the obliquity of the line of sight (Visierlinie) are left out of account 
entirely, because the décentration is doubtful in amount, and more¬ 
over seems to be variable in extent. As we have already seen that the 
anterior surface of the cornea does not have any exact vertical plane 
of symmetry, obviously, the reflex images of infinitely large objects 
cannot determine any precise centering of the optical system. However, 
in Helmholtz’s experiment illustrated in Fig. 51 the effect of the 
asymetry of the cornea is eliminated as far as possible by basing it on 
the osculating ellipse, and there would seem to be hardly any doubt 
as to the fact that this experiment proves that the lens is decentered 
with respect to the axis of this ellipse. But since, by virtue of the 
asymmetrical structure of the cornea, it is not certainly established 
that the calculated axis of the ellipse is a normal to the cornea, it is 
not proved by the experiment that the axis of the lens does not in 
general coincide with the normal to the cornea that passes through the 
centre of the pupil. Investigations carried out by Tscherning’s1 
method afford just as little proof of this. If, in observing the reflex 
images in the surfaces of the lens, the axis of the telescope and two 
lights, preferably Ophthalmometrie Nernst lamps, are adjusted all in 
one vertical plane, then, supposing there was a vertical plane of sym¬ 
metry, a position of the eye can be found for which all six reflex images 
would be seen lying in one straight line. But generally this is not the 
case. When the patient’s eye looks right into the telescope, the reflex 
images in the anterior surface of the lens are on the nasal side of the 
reflex images in the cornea, and those in the posterior surface of the 
lens are on the temporal side. If then the look is directed in towards 
the nose, in most cases, first, the reflex images in the posterior surface 
of the lens turn into line with the reflex images in the anterior surface 
1 Beiträge zur Dioptrik des Auges. Zeilschr. f. Physiol, u. Psychol, d. Sinnesorgane. 
III. 1892. S. 429 and elsewhere.


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