842 FORMATION OF RETINAL IMAGES. [Book hi. 



of several surfaces and media centred on one optical axis may be 

 treated as if it were a more simple system consisting of two sur- 

 faces only. In such a simplified system each of the two (ideal) 

 surfaces has its own nodal point and its own principal f6ci, an- 

 terior and posterior ; moreover, the two points where the two 

 surfaces cut the optic axis are called principal points (and ver- 

 tical planes drawn through those points principal planes), first, or 

 anterior, and second or posterior. Hence the cardinal points of 

 such a simplified complex system are six in number, namely, the 

 anterior and posterior principal foci, the anterior and posterior 

 principal points, and the anterior and posterior nodal points. 

 (When such a system is, by removal of surfaces and media, con- 

 verted into the still more simple system of one surface separating 

 two media, the two nodal points become coincident in one point, 

 namely, the centre of the sphere, and the two principal points 

 become coincident in one point, namely, the point at which the 

 optic axis cuts the surface.) 



In order to effect such a simplification of a complex optical 

 system, it is requisite to know: — (1) The refractive index of 

 each medium. (2) The radius of curvature of each surface. 

 (3) The distance along the optic axis between the first surface 

 on which the rays fall and the succeeding surfaces. These can 

 be and have been determined for the human eye, and the follow- 

 ing table gives the several values usually adopted with some re- 

 cent corrections, the latter being placed in brackets. 



Refractive index of aqueous or vitreous humour 1-3376 (1-3365) 



Mean refractive index of lens 1-4545 (1-4371) 



Radius of curvature of cornea 8 (7-829) mm. 



" " of anterior surface of lens 10 " 



" " of posterior " " ... 6 " 



Distance from anterior surface of cornea to ante- " 



rior surface of lens 4 (3-6) 



Thickness of lens 4 (3-6) 



.. 



By means of these measurements the optical system of the 

 eye may be simplified into an optical system of two surfaces. In 

 this 'schematic, or diagrammatic, eye of Listing,' as it is gener- 

 ally called, the two (ideal) surfaces, and the principal points 

 where these cut the optic axis (Fig. 141, p 1 , p 2 , the two surfaces 

 being indicated by dotted lines), lie close together in the front 

 part of the aqueous humour, and the nodal points, n\ n 2 , lie, also 

 close together, in the back part of the lens. 



Further, the two principal surfaces lie so close together that, 

 for practical purposes, no serious error is introduced, if instead 

 of two such surfaces we assume the existence of one surface lying 

 midway between the two. In this wa} r we arrive at the ' reduced 

 diagrammatic eye,' or 'the reduced eye ' as it is called, in which 



