THE REFRACTION OF THE EYE 531 



relatively low intensity on top of this. Under these conditions it is found 

 that quite well denned images are produced. Thus, with a pupil of 2 mm. 

 diameter, approximately 70 per cent, of the light falls in an area of 

 0'005 mm. diameter. Further it may be shown that a lens system such as 

 the eye, which suffers from chromatic aberration, produces an image that 

 is only just appreciably worse than one that is perfectly corrected, when 

 the effects of diffraction are taken into account in both cases. But since the 

 effects of chromatic aberration increase as the pupil enlarges, while those 

 caused by diffraction decrease, it is clear that the larger the pupil the more 

 does chromatic aberration tend to spoil definition. But as this is accom- 

 panied by decrease in diffraction, the two changes taken together have the 

 effect of leaving the actual definition practically unchanged. This important 

 conclusion will be referred to again more fully in the last section. 

 Beside effects on definition, chromatic aberration causes small bright 

 points of light on a dark ground to form images which are largely 

 composed of yellow rays, and on the other hand small black objects 

 on a bright ground to be purple in colour. The reason for these colours 

 being unnoticed in ordinary circumstances is due to the recognition by 

 the eye of the presence of the complementary colour which forms a fringe 

 round the central point. 



SPHERICAL ABERRATION OF THE EYE. The employment of 

 spherical surfaces to bound optical media leads to a difference in the 

 position of the foci of rays that have passed through the centre of 

 the lens and those that have passed through the more peripheral parts. 

 The latter usually form a focus nearest to the lens. Since the eye is 

 bounded by nearly spherical curves it has been assumed that this aberra- 

 tion must be present in this organ. It should be remembered however 

 that the crystalline lens has a structure quite different to that found in 

 e lens systems of optical instruments. For the presence of a graduation 

 f optical density, culminating in a nucleus of relative great curvature, causes 

 ys passing through the centre of the eye to be refracted to a greater 

 extent than more peripheral rays, or in other words exactly the opposite 

 effect to that produced by spherical aberration. Measurements on the eyes 

 of different individuals therefore show the presence both of small amounts 

 of under correction (when the correcting effect of the lens nucleus has not 

 been enough) and also actually of over correction (when the lens nucleus 

 has had too big an effect). In quite a number of cases the amount 

 of spherical aberration is negligible even with pupils of 4 mm. diameter. 

 With larger pupils there is probably a certain amount of under correction, 

 but this again is less than would be found in the case of spherical surfaces 

 because the more peripheral parts of the cornea are flattened and therefore 

 refract less (as Gullstrand has shown). We may say therefore that in every- 

 day life the effects of spherical aberration are altogether negligible, compared 

 with those of diffraction and chromatic aberration. 



tn 







