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 
borders of the field that is not shaded off by the mutual action of the 
source of light and the pupil, we obtain corresponding formulae, 
namely : 
p — q 
X=-, B A = X T pA. 
The intensity of the light of the illumination system depends on the 
area Pn of the useful pupil, the intensity of illumination on the retina 
being equal to 
where e denotes the specific intensity of the source of light. In order 
to find the useful pupil, the image of the source of light and the hole in 
the mirror must be projected on the pupil from the point of fixation of 
the eye as centre of projection. According as the projection of the 
image of the source of light is smaller or greater than the pupil, the 
area of the projection of the hole in the mirror must be subtracted from 
the area of the former or from that of the latter, respectively. Accord¬ 
ingly, Pn is the same as the smaller of the two values given by the 
following expressions; 
7T f P 1 7T f q2 P 
' P'n= — ]P2---, P"n = — \------- 
4 {1 + dAy 4 [l + (c+d)A]2 (1+dA)2 
By auxiliary optical appliances the position and size of the image 
of the source of light in the mirror can be arbitrarily modified. But as 
one of the prime factors in the practical employment of the simple 
ophthalmoscope is the unhampered movement of the mirror, any 
combination of it with lenses, which (entirely aside from limitations of 
space) requires complicated manipulation for changing the direction 
of the incident light, is ruled out in advance. It is only in certain 
electrical forms of ophthalmoscope when the lamp and mirror are 
rigidly connected that such combinations as are referred to here are 
really practical. Generally speaking, therefore, the form of the mirror is 
the only optical method of influencing the image of the source of light. 
If it is a question of getting the largest possible field with the best 
possible brightness, evidently the lamp and mirror should be as near 
together as possible. 
Now the ratio — =IG depends merely on the 
size of the source of light and its distance, and not on the form of 
the mirror, since, in both the tangential and the sagittal imagery, the 
principal points coincide at the surface of the mirror. Hence, starting 
with the value of K' that is practicable, we must see how the field and 
the intensity of the light are altered when c is varied. The simplest 
method to use for this purpose is that of differentiation; although the


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