THE OPTICAL CONSTANTS OF THE EYE 



511 



If through these points two planes be drawn perpendicular to the axis of 

 the system, then every point in the plane e will have its image in the plane e*, 

 and the image will be on the same side of the axis and at the same distance 



from it. In short an object in the plane e has an erect image of the same size 

 in the plane e*. 



These two planes are called the principal planes of the system and the points 

 at which they cut the optical axis are called the principal points. 



All distances in general are calculated from the principal points, those which 

 concern the incident ray from the first, those which concern the refracted ray 

 from the second. 



Now what will be the relation between an object, whose rays are transmitted 

 by a system of this kind, and its image? The answer is, just the same relation 

 as between the object and image of a simple system. 



If e. g., in Fig. 208, which represents a simple optical system an object, 

 sp, be transmitted by a simple refracting surface, the size of the image, tr, will 

 be to the size of the object as ar is to pa (from the similar geometrical figures 

 asp and art). The point a of such a system is called the nodal point. 



So also in Fig. 209 where EE* are the principal points and F and F* the 

 focal points, there will be two points K and K* so situated (at equal distances 

 from E and E*) that the size of the object PA will be to the size of its image 

 P*A l as the distance AK is to the distance A,K*. These two points are called the 

 nodal points of the system. They may be defined as the two points so situated 

 that a ray directed toward the first will be directed toward the second after 

 refraction, the rays before and after refraction being parallel. 



It is evident that if we can locate accurately the nodal points of the eye 

 and know the size and distance of any object, we can estimate the size of its 

 image in the eye. Moser was the first (1844) to make use of theoretical 



FIG. 209. 



results obtained by Gause and Bessel and on the basis of these to calculate 

 the position of the two nodal points. Somewhat later Listing gave an esti- 

 mate of the numerical values according to the best measurements completed 

 at that time. Since his time the designation of schematic eye has been applied 

 to an eye whose optical constants correspond approximately to the mean value 



