184
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
dH
db
2 Bb
N{N-1)
2 vV2 —x2+log nat P |
r |_r+ Vr-xzj )
(9)
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.