DIOPTRIC MECHANISMS OF THE EYEBALL 591 



and also with the axis CQ (a to a 5 ) ; and the rays proceeding from r pass into 

 the first medium parallel to each other, but not parallel to the axis OQ (as c to 

 c a ). (3) All rays, which in the second medium are parallel to each other (6 to 6 6 ) 

 and with the axis OQ, reunite in a point in the first medium (p) called the first 

 focal point ; of course, the converse of this is true. A plane in this point perpendi- 

 cular to OQ is called the first focal plane (AB). The radius of the refractive 

 surface (ma:) is equal to the difference of the distance of both focal points (p and 

 p 1 ) from the principal focus (x) ; thus mx = px px. 



In compound systems composed of several refractive media with spherical 

 surfaces of contact, such as the eye, we may proceed from medium to medium 

 with the same methods as those just described. Since, however, such a procedure 

 would be very tedious, the method first proposed by Gauss is usually adopted. 

 Gauss showed that if the several media are ' centred ' i.e. if all have the same 

 optic axis then the refractive indices of such a centred system may be repre- 



FIG. 260. The position of the cardinal points in the schematic eye. (HELMHOLTZ.) 

 h /f h /f , principal points ; k t , k,,, nodal points ; F x/ , posterior focus. 



sented by two equally strong refractive surfaces at a certain distance apart. 

 The rays falling upon the first surface are not refracted from it, but are regarded 

 as projected forwards parallel with themselves to the second surface. Refrac- 

 tion is then considered to take place at the second surface just as if that were 

 the only surface present (represented by the dotted line II in Fig. 260). 



All such systems possess three pairs of cardinal points, viz. two 

 principal foci, two principal points, and two nodal points. These points 

 may be defined by the following principles : 



(a) Rays which pass through the principal focus are, after refrac- 

 tion, parallel to the optic axis. 



(6) Rays which pass through the first principal point, after refrac- 

 tion, pass through the second. 



(c) Rays which pass through the first nodal point, after refraction, 

 pass through the second, and the direction of the refracted ray is 

 parallel to the direction of the incident ray. 



In Fig. 260 the situation of these cardinal points is shown in the 



