378 PHYSIOLOGICAL PHYSICS. [Chap. xxix. 



constants of Gauss enables one to find the path of 

 rays passing through the system, and to construct an 

 image of the object from which the rays have passed. 



The cardinal points or optical constants are as 

 follows : (1) two focal points ; (2) two principal points; 

 (3) two nodal points. 



The focal points are represented in the figure by F 

 and F'. P is the anterior and F' the posterior focal 

 point. Planes passing through these focal points 

 perpendicular to the axis are focal planes, oo the 

 anterior focal plane, and o'o' the posterior focal plane. 

 Now the feature of these points is, that all rays which 

 diverge from the anterior focal point F, and pass 

 through the refractive media, issue from the media in 

 a direction parallel to the axis ; and all rays, which 

 before entering the media are parallel to the axis, 

 issue from the media so as to converge to the posterior 

 focal point F' ; that is, F and F' are to the system 

 w r hat the principal focus is to a single refractive 

 medium. 



The principal points are represented in the figure 

 by P and P', and the relation between the two is such 

 that, both being in a transparent medium, a luminous 

 point in the medium, which, to an observer situated on 

 the left, seemed, owing to the refraction, to be at P, 

 would, to an observer situated on the right, seem to 

 be at P'. The two points, that is to say, are conjugate 

 foci, and therefore rays passing through one point will 

 pass through the other also. Through P and P' let vv 

 and vV be planes perpendicular to the axis ; they are 

 principal planes. Any point in the plane vv will 

 have a conjugate focus in vV, and thus any ray passing 

 through a point in one plane will pass through a 

 corresponding point in the other plane, situated at the 

 same distance from the axis, and on the same side. 

 The planes represent the two ideal surfaces of separa- 

 tion of the transparent media. The distance FP is 



