CARDINAL OPTICAL POINTS. 



747 



but are essentially projected forwards parallel with themselves to the second surface. Refraction 

 takes place first at the second surface, just as if only one refractive surface was present. In 

 order to make the calculation, we must know the refractive indices of the media, the radii of 

 the refractive surfaces, and the distance of the refractive surfaces from each other. 



Construction of the refracted ray is accomplished as follows : Let a b represent the optical 

 axis (fig. 530, I.) ; H, the first focal point determined by calculation ; h A,?the principal plane ; 

 H, the second focal point ; h x , h lt the second principal plane ; k, the first, and k x the second 

 nodal point ; F, the second focal point ; and F x , F l5 the second focal plane. Make the ray of 

 direction p k x parallel to m x , n x . According to proposition 2, p, k x and m x , n x must meet in a 

 point of the plane F x Fj. As p k x passes through unrefracted, the ray from n x must fall at r ; 

 n x r is, therefore, the direction of the refracted ray. 



Construction of the focal point. Let o be a luminous point (fig. 530, II.), what is the 

 position of its image in the last medium ? Prolong from o the ray of direction o k, and make 

 o, x parallel to a b. Both rays are prolonged in a parallel direction to the second focal plane. 

 The ray parallel to a b goes through F ; m, k x as the ray of direction passes through unrefracted. 

 0, where n, F, and m k x intersect each other, is the position of the image of o. 



386. DIOPTRICS RETINAL IMAGE OPHTHALMOMETER Position 



of the cardinal points. The eye surrounded with air on the anterior surface of the 

 cornea, represents a concentric system of refractive media with spherical separating 

 surfaces. In order to ascertain the course of the rays through the various media 

 of the eye, we must know the position of both principal foci of both nodal points 

 as well as the two principal focal points. Gauss, Listing, and v. Helmholtz have 

 calculated the position of these points. In order to make this calculation, we 

 require to know the refractive indices of the media of the eye, the radii of the 

 refractive surfaces, and the distance of the latter from each other. These will be 

 referred to afterwards.^ (1) The first principal poi?it is 2*1746 mm.; and (2) the 

 second principal point' is 2*5724 mm. behind the anterior surface of the cornea. 

 (3) The first nodal point, 0*7580 mm. ; and (4) the second nodal point, 0*3602 mm. 

 in front of the posterior surface of the lens. (5) The second principal focus, 

 14*6470 mm. behind the posterior surface of the lens; and (6) the first principal 

 focus, 12*8326 in front of the anterior surface of the cornea. 



Listing's reduced eye. The distance between the two principal points, or the two 

 nodal points, is so small (only 0*4 mm.), that practically, without introducing any 



Fig. 531. 



great error in the construction, we may assume one mean nodal or principal point 

 lying between the two nodal or principal points. By this simple procedure we gain 

 one refractive surface for all the media of the eye, and only one nodal point, 

 through which all the rays of direction from without must pass without being 

 refracted. This schematic simplified eye is called " the reduced eye " of Listing. 



Formation of the retinal image. Thus, the construction of the image on the 

 retina becomes very simple. In distinct vision, the inverted image is formed on 

 the retina. Let A B represent an object placed vertically in front of the eye (fig. 

 531). A pencil of rays passes from A into the eye; the ray of direction, A d, 



