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/lit39649/105/
64, 65.] 
§9. Laws of Optical Imagery 
81 
The Cardinal Points of a Compound Optical System, Composed of Two 
Systems with Axes in Same Straight Line 
The two component systems are designated in Fig. 38 by A and 
B. The focal points and principal points of system A are designated 
by P*, p// and a>, a>>, respectively; and the focal points and principal 
points of system B are designated by 7r>, 7v and a>, a>>, respectively. 
Let d denote the distance of the first principal point of system A from 
the second principal point of system B; this interval being taken as 
positive when, as in Fig. 38, the point a> lies beyond the point a>>\ 
The focal lengths of the first system are a'p>=f> and a-p" =/", and 
A B 
F!g. 38. 
those of the second system are a>T>=(p> and a-7t" = Evidently, 
the first focal point (w) of system B is the image of the first focal 
point (L) of the compound system as formed by system A. Hence, a 
ray which in the first medium crosses the axis at t> will, after traversing 
system A, cross the axis at %> and emerge finally in the last medium 
along a straight line parallel to the axis; because by definition this 
must be the case with a ray that crosses the axis originally at the first 
focal point of the compound system. Since a-?T"=d — 

, we have: a.t, = £r*J)J1......(11a) d-ip—f" Similarly, the second focal point (t") of the compound system is the image of the second focal point (p>>) of system A in system B. Hence {d-f"), r>> are the principal points of the compound system. If s is the image of r> in system A, and if r>> is the image of s in system B, then r>> is the image of r> in the compound system. This is one of the conditions that these points must satisfy; the other condition being that object and image in the principal planes must be equal in every way. Suppose, therefore, that an object of height ß> is set up at the

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