THE SENSE OF SIGHT. 609 



termination, either by calculation or geometrical construction, of the 

 path of the refracted ray, and the position and size of the image in 

 the last medium, of the object in the first. 



Every dioptric system can be replaced, as Gauss showed, by a 

 single system composed of six cardinal points and six planes per- 

 pendicular to the common axis e. g., two focal points, two principal 

 points, two nodal points, two focal planes, two principal planes, and 

 two nodal planes. 



Properties of the Cardinal Points. The first focal point, F v m 

 Fig. 284, has the property that every ray which before refraction passes 

 through it, after refraction is parallel to the axis. 



The second focal point, F 2 , has the property that every ray which 

 before refraction is parallel to the axis, passes after refraction 

 through it. 



The second principal point, H 2 , is the image of the first, H^ that 

 is, rays in the first medium which go through the first principal point 

 pass after the last refraction through the second. Planes at right 



FIG. 284. DIAGRAM SHOWING THE POSITION AND RELATION OF THE CARDINAL 



POINTS. 



angles to the axis at these points are principal planes. The second 

 principal plane is the image of the first. Every point in the first 

 principal plane has its image after refraction at a corresponding point 

 in the second principal plane at the same distance from the axis and 

 on the same side. 



The second nodal point , N 2 , is the image of the first, N l : a ray 

 which in the first medium is directed to the first nodal point passes 

 after refraction through the second nodal point, and the directions of 

 the rays before and after refraction are parallel to each other. In 

 Fig. 284 let A B represent the axis. The distance of the first focal 

 point, F v from the first principal plane, H v is the anterior focal 

 distance. The distance of the posterior focal point, F 2 , from the 

 second principal plane, H 2 , is the posterior focal distance. The dis- 

 tance of the first nodal point, N lt from the first focal point is equal 

 to the second focal distance. The distance of the second nodal 

 point, N 2 , from the posterior focal point is equal to the anterior focal 

 distance. It is evident, therefore, that the distance of the correspond- 

 ing principal and nodal points from each other is equal to the differ- 



39 



