704 



TEXT-BOOK OF PHYSIOLOGY 



refractive indices of the first and last media. Planes passing through the 

 focal points vertically to the axis are known as focal planes. 



From these properties of the cardinal points the position of an image in 

 the last medium of a luminous point in the first may be determined, and the 

 course of a refracted ray in the last medium be constructed if its direction in 

 the first be given according to the following rules: 



1. To find the image in the last medium of a luminous point in the first : Let 



A (Fig. 290) be this given point. Draw A B parallel to the axis until it 

 meets the second principal plane in B ; then B F 2 will be this ray after 

 refraction. Draw a second ray from A to the first nodal point; then 

 draw another ray, D E, from the second nodal point parallel to A C. 

 This will be the refracted ray in the last medium. Where the two re- 

 fracted rays, BF 2 and D E, intersect, the image of A will be A r l 



2. To find the refracted ray in the last medium of a given ray in the first 



medium: Let A B (Fig. 291) be the given ray. Continue this ray until 



FIG. 291. DIAGRAM TO FIND THE REFRACTED RAY IN THE LAST MEDIUM OF A GIVEN 

 RAY IN THE FIRST MEDIUM. 



it meets the first principal plane in C. Draw C D parallel to the axis. 



Now assume any point, such as , in the given ray, and find its image 



EI by the Rule i. Then D E l becomes the course of the refracted 



ray. 



The Schematic Eye. Accepting the system of cardinal points, Listing, 

 Donders, and v. Helmholtz have constructed " schematic" eyes to be sub- 

 stituted for the refracting system of the natural eye. 



For this purpose it is necessary to make use of the various estimates of 

 the indices of refraction of the different media, of the radii of curvatures 

 of the different refracting surfaces, and of the distances separating them, to 

 deduce an average eye as a basis for calculation. The most widely accepted 

 attempt is that of v. Helmholtz. The data he assumed are as follows : The 

 refractive index of air = i; of the cornea and aqueous humor, 1.3365; of the 

 lens, 1.4371; of the vitreous humor, 1.3365; the radius of curvature of the 

 cornea, 7.829 mm. ; of the anterior surface of the lens, 10 mm.; of the posterior 

 surface, 6 mm.; the distance from the apex of the cornea to the anterior 

 surface of the lens, 3.6 mm.; thickness of lens, 3.6 mm. From the above- 

 mentioned data v. Helmholtz calculated the position of the cardinal points 

 for the eye as follows (see Fig. 292) : The first focal point is situated 13.745 



1 If the point A is infinitely far from the eye, all the rays striking the eye will be parallel to 

 each other. The nodal ray must therefore be drawn, and the point where this nodal ray meets 

 the second focal plane will be the image of A, or A j where all rays parallel to the nodal ray will 



