DIOPTRIC LAWS. CONSTRUCTION OF RETINAL IMAGE. 



829 



APPLICATION OF DIOPTRIC LAWS TO THE EYE. CONSTRUC- 

 TION OF THE RETINAL IMAGE. THE OPHTHALMOMETER. 



ERECT IMAGES. 



The eyeball represents a centered system, composed of several 

 refracting media separated by spherical surfaces, the anterior surface 

 of the cornea being in contact with the air. In order to determine the 

 course of the rays through these media, it is necessary to know the posi- 

 tion of both principal foci. Following the simplified solution of Gauss 

 previously discussed, Listing and v. Helmholtz in particular have 

 estimated the position of those points. In order to make this calcula- 

 tion, a knowledge of the indices of refraction of the ocular media, the 

 radii of the refracting surfaces, and the distance between them is neces- 

 sary. These will be taken up later. According to this calculation : 

 (i) The first principal point lies 2.1746 mm., and (2) the second principal 

 point 2.5724 mm., behind the anterior surface of the cornea; (3) the 

 first nodal point is 0.7580 mm., and (4) the second nodal point 0.3602 

 mm. in front of the posterior surface of the lens; (5) the second 



FIG. 279. 



principal focus is 14.6470 mm. behind the posterior surface of the lens, 

 and (6) the first principal focus is 12.8326 mm. in front of the anterior 

 surface of the cornea. 



As the distance between the two principal points and between the 

 two nodal points is so small (only 0.4 mm.), a point in the middle of 

 each pair may be adopted instead of the two separate points, without 

 committing much error in the construction. In this way there is 

 only one refracting surface for all the media, and only one nodal point, 

 through which all of the axial rays coming from without must pass un- 

 refracted. Such a simplified eye is known as the "reduced eye" of 

 Listing. 



The construction of the image on the back of the eye is now simple. 

 The inverted image is formed on the retina with distinct vision. Let 

 A B (Fig. 279) represent an object standing perpendicularly before the 

 eye. From A a pencil of rays enters the eye; the axial ray A d passes 

 through the nodal point k without being refracted. As the image of A 

 must lie on the retina, all the rays from A must come to a focus at d. 

 The same is true for the rays from B, and of course for the rays coming 



