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
166, 167.] 
§14. Monochromatic Aberrations 
at 6; but between b and q it will be elliptical with the major axis of the 
ellipse perpendicular to the plane of the diagram. The ellipse gets 
smaller and more elongated, the nearer the cross section is to q ; and at 
q the cross section of the bundle of rays is a horizontal straight line 
perpendicular to the plane of the diagram. Beyond this point the 
cross section is again an ellipse with its major axis perpendicular to 
the plane of the diagram, which soon becomes more and more round 
and is actually circular about midway between q and s; then it becomes 
an ellipse again with its major axis in the plane of the diagram, which 
collapses into a vertical line at s. Beyond this point it gradually gets 
broader again and becomes more and more circular. 
The results are similar when a narrow bundle of incident rays 
encounters a spherical refracting surface obliquely. Suppose that the 
curve bch in Fig. 76 is the section of a spherical surface and that the 
straight line pc represents a ray incident on it at a finite angle of in¬ 
cidence. We know (cf. Fig. 32) that rays proceeding in the plane of 
the diagram and incident on the surface in the immediate vicinity of 
the point c do not intersect each other in a point on the axis pq after 
refraction, but at a point off the axis which lies on the caustic surface. 
Suppose t is this point. Conceive now that the whole figure is rotated 
around ap as an axis; so that the ray pc will come in succession into 
the positions of all rays from p that cross the axis at the same angle. 
The corresponding refracted ray cq will also describe a ray-cone with 
its vertex at the point q. Consequently, whereas the rays immediately 
adjacent to pc in the plane of the diagram intersect it at t, those ad¬ 
jacent to it on either side of that plane intersect at it q. Finally, it 
may be added that other adjacent rays do not intersect pc at all. 
Another question to be asked about this subject is, What is the 
effect of diffraction of light at the edge of the pupil on the monochro¬ 
matic aberrations? And this suggests a further question as to whether 
the star-like form of the small blurred patterns may not be due to the 
minute indentations in the edge of the pupil. In fact, if a luminous 
point is viewed through an opening smaller than the pupil, the edge of 
which is not perfectly smooth, a more extensive star-shaped figure will 
be seen; although, as a rule, such patterns consist rather of very fine 
hair-like brightly coloured rays, similar to the hair corona of the eye 
which was described above and which is seen around any brilliant 
point-source even without using an artificial opening. When the 
opening is rotated around its centre, the entire corona turns with it; 
which shows that the effect is due to the contour of the aperture. 
The writer could not be sure of perceiving in his own eye the indica¬ 
tion of any diffraction of light due to the fine fibrous structure of the 
crystalline lens. When a small luminous point is observed through a


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