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
Dioptrics of the Eye 
[199, 200. 
contained in the retinal image of the pupil of the observer’s eye, no 
matter whether this image is clear-cut or blurred. 
Notes: 1. This proposition is true not only when the light proceeds 
directly from the source to the illuminated eye and thence into the observer’s 
eye, but also when any lenses or mirrors are interposed along the way. Inci¬ 
dentally, this fact affords a convenient way of showing experimentally how an 
ophthalmoscope acts in one’s own eye. The light used for illumination is 
adjusted and the instrument arranged in the same position in front of the 
observer’s eye as it in front of the patient’s eye; then the part of the 
field that is bright corresponds to the part of the retina that is illuminated. 
It is possible to tell whether this bright field is large or small, and whether it is 
uniformly illuminated or whether there are dark places in it, and how dark 
they are. Then the source of light is transferred behind the instrument where 
the observer’s eye would naturally be, so that the light shines through the 
peephole. Whatever is illuminated now in the field of view is comprised in the 
part of the retina that the observer will be able to see. This is the simplest and 
easiest way of getting a clear idea of the effects of various combinations of 
flat and curved mirrors and of convex and concave lenses in ophthalmoscopes; 
without having to make complicated geometrical constructions that are oft- 
times more confusing than helpful to the unintiated. 
2. The effect of the mode of illumination described in this section is easily 
regulated by the above rule. Everyday experience teaches us (as can be 
proved also by a simple construction of the procedure of the light) that the 
blurred image of a distant object cannot cover the sharp image of a nearer 
object that is seen distinctly, but that the blurred image of a near object may 
cover the sharp image of a more distant one. In the experiment with the 
perforated mirror the blurred image of the peephole which must be adjusted 
as near as possible in front of the patient’s eye overlaps the image of the more 
distant source of light which is perhaps sharply in focus. If no mirror is 
employed, so that the observer looks past the light into the patient’s eye, the 
flame and the observer’s eye seem to the patient to be near together, and 
when his eye is not nicely accommodated for them, their blurred images are 
fused together. With illumination by a transparent plate of glass, both the 
image of the light and that of the pupil of the observer’s eye may be sharply 
in focus. The former is seen reflected in the plate and the latter is seen through 
the plate, so that they come together on each other. Accordingly, it is best 
for the patient himself to adjust the glass plate so that his eye looks luminous 
to the observer. All that he has to do is to be careful that the observer’s eye 
appears to be covered by the reflected image of the source of light. 
A reciprocity law similar to that given above for light proceeding 
in opposite ways over the same path may also be formulated for the 
amount of light transmitted to and fro. In this connection, let us 
state here, first, the following 
Fundamental Law of Photometry. 
Suppose a and h are the areas of two tiny elements of surface in a 
transparent medium at the distance r apart; and let the brightness of 
the luminous element at a be denoted by H ; then the quantity of 
light received by h will be 
H.ab cos a cos ß


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