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
G. 362, 363.] 
V. Monochromatic Aberrations of the Eye 
to be seen in the stigmatoscopic investigation of the given meridian 
plane are represented by the two symmetrical cusps. By measuring 
the difference of refraction between this section of the bundle and that 
which contains the cusp lying on the axis, the distance between the 
two sections can be found. In the writer’s own case this difference is 
4 dptr, and apparently this value is never exceeded. A higher value 
is frequently obtained with persons who are less expert, probably due 
to their inability to relax the accommodation completely. The diam¬ 
eter of the line R = 0 corresponding to the symmetrical cusps of 
Fig. 120 is measured by the diaphragm held in front of the eye. The 
serrated curve in the section of the caustic surface nearest the re¬ 
fracting system can be made to coincide in this way with the boundary 
line of the cross section of the bundle of rays. By this means the writer 
has obtained a diameter of 4 mm. Let d denote this diameter, D the 
difference of refraction to be used in the calculation, / the posterior 
focal length of the eye, and n the index of refraction of the vitreous 
humor; then the aberration-value is found by the formula: 
8 f4 D 
~ lOOOnd2 * 
the distances being expressed in millimetres and the value of D in 
dioptries. For / = 20 mm and w=4/3 (as in Donders’ reduced eye), 
the formula gives 240 mm for the aberration-value; whereas on the 
assumption that the refracting surface is spherical, the calculated 
aberration-value for this eye is 540 mm. The amount of the aberration- 
value found in the living eye proves at once that the bundle of refracted 
rays acquires a positive aberration in traversing the crystalline lens. 
This could be demonstrated by Helmholtz’s schematic eye; because 
by giving the surfaces of the lens in this eye a form such that the lens 
itself does not contribute to the aberration one way or the other, with 
spherical cornea and emmetropic focusing the value found for the 
aberration is 162 mm. Hence the writer infers that the variable index 
of refraction of the lens has little effect on the refraction of paraxial 
rays in the eye, and that, consequently, the chief significance of this 
peculiarity of the lens is probably in connection with the change of 
form of the lens in accommodation and possibly also for peripheral 
vision. This reasoning is completely sustained by the dioptrics of the 
lens; which likewise indicates that the lamellar structure of the lens 
is merely in the interest of the change of form in accommodation, 
since, as was proved above, the effect of this structure is to augment the 
astigmatism of an oblique bundle of rays. 
Again, if the posterior focal length of the exact schematic eye and 
the index of refraction of the vitreous humor are substituted in the


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