IMAGE FORMATION 641 



It is quite obvious that the eye, even considering only the three surfaces 

 above indicated, is a much more complicated optical apparatus than the one 

 described in the figure. It is, however, possible to reduce the refractive 

 surfaces and media to a simpler form when the refractive indices of the dif- 

 ferent media and the curvature of each surface are known. All of these 

 data have been very carefully collected. They are as follows : 



Index of refraction of aqueous and vitreous, .... 

 " " " " the lens, ....'.. 



Radius of curvature of cornea, 



" anterior surface of lens, 



" " " posterior " " ... 



Distance from anterior surface of cornea and anterior surface of lens 

 Distance from posterior surface of cornea and posterior surface of lens 



I-336S 

 I-437 1 

 7.829 mm. 

 10. o 

 6.0 

 3-6 

 7-2 



With these data it has been found comparatively easy by mathematical 

 calculation to reduce the different refractive surfaces of the different curva- 

 tures into one mean curved surface of known curvature, and the differently 

 refracting media into one mean medium the refractive power of which is 

 known. 



The simplified or so-called schematic eye, formed upon this principle, 

 suggested by Listing as the reduced eye, has the following dimensions: 



From the anterior surface of the cornea to the principal point, . = 2.3448 mm 



From the nodal point to the posterior surface of lens, . . . = 0.4764 " 



Posterior chief focus lies behind cornea, . . . . . = 22.8237 *' 



Anterior chief focus in front of cornea, . . . . . = 12.8326 ' 



Radius of curvature of ideal surface, . . . . . . = 5.1248 ' 



In this reduced or simplified eye the principal posterior focus, about 

 23 mm. behind the spherical surface, would correspond to the position of 

 the retina behind the anterior surface of the cornea. The refracting surface 

 would be situated about midway between the posterior surface of the cornea 

 and the anterior surface of the lens. 



The optical axis of the eye is a line drawn through the centers of curva- 

 ture of the cornea and lens, and when prolonged backward it cuts the retina 

 between the optic disc and the fovea centralis. This differs somewhat from 

 the visual axis which passes through the nodal point of the reduced eye to 

 the fovea centralis, and forms an angle of five degrees with the optical axis. 

 The visual or optical angle is the angle included between the lines drawn 

 from the borders of any object through the nodal point. It has been shown 

 by Helmholtz that the smallest angular distance between two points which 

 can be appreciated is fifty seconds, the size of the retinal image being 3.65 /*; 

 this practically corresponds to the diameter of the cones at the fovea centralis 

 which is 3 /*, the distance between the centers of two adjacent cones being 4 /*. 



The image of an object formed upon the retina may be considered as a 

 series of points, from each of which a pencil of light diverges to the eye, and 

 41 



