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 
[156, 157. 
difference between curve A and curve B is that the latter becomes 
perpendicular to the Æ-axis at the point /, corresponding to the actual 
position of the boundary. That is, for x = 0, the derivative 
2 Bb 
2 vV2 —x2+log nat P | 
r |_r+ Vr-xzj ) 
becomes infinite. This sudden drop in intensity enables the eye to 
recognize the position of the edge, even if some light does extend 
beyond it. In the case represented by curve A, however, the falling 
off is more gradual, so that there is nothing to indicate exactly where 
the edge is. 
If it were possible to take into account the diminishing brightness 
of the colours towards the ends of the spectrum, the curve B would be 
found to follow more nearly the dotted line drawn adjacent to it. 
That is, the intensity would approach its normal maximum value more 
rapidly inside the edge, and would fall off more rapidly outside, than 
curve B indicates. 
It will be clear from these considerations why the distinctness of 
visual images is so little affected by chromatic aberration. A combina¬ 
tion of lenses intended to correct the chromatic aberration of the eye 
does not produce any appreciable improvement of the visual acuity, 
according to the writer’s experience. A concave flint glass lens of 
15.4 mm focal length, taken from the objective of a microscope, was 
found suitable for this purpose. It was combined with convex crown 
glass lenses so as to produce a system with a negative focal length of 
about 2.6 ft; which was adapted for the writer’s eye so that he could 
discern distant objects through it clearly. On looking through this 
arrangement with half of the pupil covered, no coloured fringes ap¬ 
peared at the boundary between light and dark. The same was true 
even with the eye imperfectly accommodated; so that the lenses 
evidently rendered the eye practically achromatic. There was, how¬ 
ever, no apparent improvement in definition. 
The chromatic aberration in the eye was known to Newton, who 
mentions the coloured fringes that appear when the pupil is half covered.1 
Newton made the mistake of supposing that the dispersion of all transparent 
media is proportional to their refraction; and hence he concluded that an 
achromatic combination of lenses was impossible. Curiously enough, Euler,2 
starting from the false premise that the eye is achromatic, argued that 
Newton must have been wrong as to his theory of dispersion and thence 
deduced the correct conclusion that an achromatic combination of lenses was 
possible. d’Alambert3 took exception to this reasoning, by pointing out 
that the chromatic aberration may not necessarily become noticeable in the 
1 Optics. Lib. I. P. II. Prop. VIII. 
2 Journal Encyclop. 1765. II. p. 146. — Mém. de VAcad. de Berlin. 1747. 
3 Mém. de VAcad. de Paris. 1767. p. 81.


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