THE SENSE OF SIGHT 



703 



common axis e.g., two focal points, two principle points, two nodal points, 

 two focal planes, two principal planes, and two nodal planes. 



Properties of the Cardinal Points. The first focal point, F^ in Fig. 

 289, 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, Hj that is, 

 rays in the first medium which go through the first principal point pass after 



k 



FIG. 289. DIAGRAM SHOWING THE POSITION AND RELATION OF THE CARDINAL POINTS. 



the last refraction through the second. Planes at right 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, -ZV\: a ray which in 

 the first medium is directed to the first nodal point passes after refraction 

 through the second nodal point, and the direction of the rays before and 

 after refraction are paralled to each other. In Fig. 292 let A B represent 

 the axis. The distance of the first focal point, F L , from the first principal 



FIG. 290. DIAGRAM TO FIND THE IMAGE IN LAST MEDIUM OF A LUMINOUS POINT IN 



THE FIRST. 



plane, H lt is the anterior focal distance. The distance of the second focal 

 point, F 2 , from the second principal plane, H 2 , is the posterior focal distance. 

 The distance of the first nodal point, N v from the first focal point, F v is equal 

 to the posterior focal distance H 2 F 2 . The distance of the second nodal 

 point, N 2 , from the second focal point, F 2 , is equal to the anterior focal 

 distance, H l F r It is evident, therefore, that the distance of the corre- 

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

 ences between the two focal distances. Also the distance of the two 

 principal points from each other is equal to the distance of the two nodal 

 points from each other. Finally, the focal distances are proportional to the 



