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
[91, 92. 
§10. Optical System of the Eye 
ness of the lens as found by measurements of dead eyes are occasionally more 
than half a millimetre greater than the writer found for the same distance in 
the eyes of three live individuals.1 The method of measuring the distance 
between the pupil and the front of the cornea was explained in §3. The 
anterior surface of the lens is close against the edge of the pupil, and so the 
thickness of the lens can be found as soon as the distance of the posterior 
surface of the lens from the cornea is obtained. 
The cornea and lens are represented in Fig. 50 by AA and B, respectively. 
Light comes to the eye along some direction such as Cc, and, after refraction 
first at the cornea and then at the anterior surface of the lens, is partially 
reflected at i at the posterior surface 
of the lens. The reflected ray emerges 
by the path idD, so as finally to enter 
the eye of the observer. If now the 
source of light C and the observer’s 
eye D are interchanged, the light will 
again proceed along the same path, 
only in the reverse direction, DdicC, 
being reflected, as before, at the same 
point i on the posterior surface of the 
lens. The patient’s eye is directed 
steadily towards a point of fixation and 
the straight line Gg represents the 
visual axis of his eye. These things 
having all been previously determined 
by suitable measurements, we can find 
the angles between the lines Cc, Dd 
and Gg. In order to locate the points c and d on the cornea, suppose the 
observer’s eye is at D, and let a small source of light be so adjusted at a place 
E in front of the eye that the observer at D will see the reflex of this light 
in the anterior surface of the cornea and at the same time the reflex from C 
in the posterior surface of the crystalline lens. This coincidence occurs when 
the ray Ed is reflected to D, that is, when the bisector de of the angle EdD 
is normal to the cornea. Now if the angle EdD or the angle between Ed and 
Gg has been found by suitable measurement, it is easy to calculate the angle 
between ed and Gg; and hence, from the form and curvature of the cornea, as 
obtained by previous measurements, the length of the arc dg can be found, 
that is, the position of d with respect to g. The position of the point c is 
ascertained in the same way. Thus, the positions of the points c, d and the 
directions of the lines Cc, Dd are known; and the point h where these lines 
meet is the apparent place of the reflex image in the posterior surface of the 
crystalline lens, that is, the place where it appears to be as seen through the 
intervening ocular media. * 
In making the measurement the sources of light C and E are arranged on a 
horizontal graduated bar several feet from the eye under examination. The 
source C should be as large and bright as possible, but E should be small and 
coloured by a blue glass to facilitate observing its reflection. The observer 
looks through a small telescope, which is also mounted on the grauated bar to 
enable him to locate its position. The telescope and lamp C can then be 
interchanged, as desired.2 
The mean apparent position of the posterior surface of the lens, as found 
by observations of this kind with three different eyes, was not far in front of 
the centre of curvature of the cornea. The displacement produced by the 
1 v. Graefes Archiv, für Ophthalmologie. Bd. I. Abt. 2. S. 56. 
2 The details of this method are described in Graefes Archiv. I, 2, p. 51. 
Fig. 50.


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