Bauhaus-Universität Weimar

Titel:
Helmholtz's treatise on physiological optics. Volume 1. Edited by James P. C. Southall. Translated from the 3rd German edition
Person:
Helmholtz, Hermann von
PURL:
https://digitalesammlungen.uni-weimar.de/viewer/image/lit39649/94/
70 
Dioptrics of the Eye 
[51, 52. 
Now by the conditions as to the size of the object, the angle a must be 
very small, and by putting cosa = l, we shall neglect only a small 
quantity of the second order of smallness ; and then we may write : 
If g>> denotes the distance from a of the image of the axial point p, 
then 
and hence 
9" 
= 1, 
X = grr 
(5) 
That is, the point r at the foot of the perpendicular tr is the image of p. 
Accordingly, the images of all points lying in a plane perpendicular 
to the axis at p are found to be approximately in a plane perpendicular 
to the axis through the image of p. Thus having first located the 
point r which is the image of the axial point p, the image of any other 
point in the object may be found by simply drawing a line from the 
given point through the centre of the spherical refracting surface, and 
the point where it crosses the transversal image-plane at r will be the 
required image. It follows from the principles of elementary geometry 
that the image and the object are similar. 
It is easy to find the ratio of the corresponding linear dimensions of 
the object and its image. For example, let the height of the object ps 
be denoted by ß>, and the corresponding length in the image rt by ß>>; 
then 
where the minus sign has to be inserted in the formula so that it will 
apply to the cases of both erect and inverted images. Combining this 
or 
(2c), (3a), 
(3b) and (3c), we find: 
0" 
G.. 
Grr-grr 
(6a) 
ß> 
~G'-gr 
G' 
ß" 
Fr 
F"—f" 
, (6b) 
ß' 
F•> 
When the refracting surface is plane, the focal lengths become 
infinite, and for this case equation (6b) becomes 
t 
ß' 
= 1 
(6c) 
Accordingly, the image in a plane refracting surface is exactly as large 
as the object.
        

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