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
§11. Blur Circles on the Retina 
and hence 
If c designates the centre of the image of the pupil in the lens, that is, 
if be =ca, the point y where the straight line cp meets the retina is the 
centre of the blur circle. For since 
ac'.bc = ay :ßy 
ac = be, 
ay = ßyf 
Accordingly, the ray that proceeds to the centre of the blur circle is the 
ray in the vitreous humor that comes from the centre of the so-called 
exit-pupil of the eye. In the anterior chamber of the eye this same 
ray goes through the centre of the real pupil, and its prolongation in 
the air goes through the centre of the so-called entrance-pupil.1 
One result of this is, that if the centres of the blur circles on the 
retina corresponding to two points at unequal distances from the 
eye coincide, the ray proceeding from the centre of the exit-pupil to 
this common centre on the retina must belong to both bundles of 
rays. The part of this common ray which lies outside the eye must 
necessarily pass through both luminous points and its prolongation 
must go through the centre of the entrance-pupil of the eye. Even 
if one of the blur circles on the retina contracts to a single point at the 
centre of the other, the above statements will still be correct. 
When two points at different distances are aligned with each other 
as when we “sight” from one to the other, the image of one flails on 
the retina at the centre of the blur circle of the other; or, supposing 
both points are indistinct, the centres of their blur circles coincide. 
The straight line connecting such a pair of points is what we have 
already called a line of sight. As just explained, it must coincide with 
the ray that is aimed at the centre of the entrance-pupil, so that this 
centre is therefore the point of intersection of all lines of sight. 
This subject is closely related to the visual angle. When it is said 
that objects subtending equal visual angles have the same apparent 
size, the common vertices of the angles must be at the point of inter¬ 
section of the lines of sight. However, it is usual to assume that the 
vertex of the visual angles is at the point of intersection of the direction 
lines, that is, at the first nodal point. On the other hand, if the 
extremities of the object are viewed in succession one after the other, 
the vertex of the visual angle in this case should be taken at the centre 
1 ^Although the terms “entrance-pupil” and “exit-pupil” were suggested by Abbe long 
after the first edition of Hemholtz’s Optik was published, and, of course, do not occur in 
the original text, they are employed in the translation. Incidentally, it may be noted here 
that Huygens in his Dioptrica constantly makes use of the same ideas as conveyed by 
these terms. (J. P. C. S.)


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