282 



PHYSIOLOGY 



CHAP. 



Of the six cardinal points the first two are represented by the 

 foci FF r . The posterior focus F' is, as we have seen, that at which 

 all parallel rays entering the system converge after refraction; 

 the anterior focus F is that at which all parallel rays converge on 

 leaving the system. The planes 00, O'O', which cut the foci 

 vertical to the optical axis, are the focal planes of the system. 



Between the two foci lie the two principal points PP. 

 Through these the two principal planes W and VV pass 

 vertical to the axis. 



Each incident ray that passes through P leaves by F ; each 

 ray that passes through any point of the plane W passes through 

 a corresponding point, equidistant from the axis, of the plane 

 V V. In other words, P' is the optical image of P, and the 

 several points of the plane V V are the erect optical image, equal 

 in size, of the corresponding points of the plane VV. The 

 distance FP is called the anterior focal, F'P' the posterior focal 



FIG. 122. Refraction of an incident ray passing througli a centred system, constructed from 

 the six cardinal points. 



distance. The position of the two principal points must be 

 calculated. . 



Between F and F' are the two nodal points, NN', the optical 

 centres for the two surfaces VV % W. The distance between 

 the two principal points is equal to that of the two nodal points ; 

 hence the distance FP is equal to the distance F'N'. The 

 nodal points are characterised by the fact that a ray which 

 passes from the first medium to the first nodal point J^also passes 

 through the second nodal point N' t the refracted and the incident 

 rays being parallel. 



(/) Course of a Refracted Eay in a Centred System. When a 

 system with differently refracting media is replaced by the six 

 cardinal points, it is easy to make a, diagram of the path of any 

 refracted ray. 



Let AB be an incident ray (Fig. 122) ; from point B draw a 

 parallel to axis XX, which cuts the second principal plane V V at 

 the point C ; then draw from the second nodal point, parallel to 

 the /incident ray AB, a line N'D, which cuts the posterior focal 

 plane O'O' at Z>; on joining C and D, the line CD gives the 

 direction of the refracted ray. The same result is obtained if the 



