vi DIOPTEIC MECHANISM OF THE EYE 289 



Index of lens us a whole . .... 1-43 



Radius of curvature of cornea . . . 7-82 mm. 



Radius of anterior surface of lens .... -10-00 ,, 



Radius of posterior surface of lens . 6-00 



Distance of anterior surface of lens from cornea . . : 3-6 



Distance of posterior surface of lens from cornea . 7-2 



From these figures, and by applying the rules and calculations 

 of Gauss to determine the position of the cardinal points on the 

 axis of the total dioptric system of the eye, Helmholtz arrived at 

 the results set out in the following table, in which the figures 

 show the distance in millimetres of the cardinal points from the 

 apex of the cornea : 



First principal point, (/') . . .1-75 mm. 



Second principal point (P) . . . 2-1 



Anterior focal distance (F) . . . 15-5 



Posterior focal distance (F') . .20-7 



First focal point (P) . 13-75 



Second focal point (P') . . . 22-79 



First nodal point (N) . 6-96 



Second nodal point (N') . . . 7-32 



Diagranimatically considered, therefore, the eye represents a 

 convergent or collecting system with unequal anterior and 

 posterior focal distances. The refractive index of the eye, measured 

 from the posterior focal distance, amounts to 64'6 D. 



As shown by Fig. 128, magnified three times from Helmholtz' 

 figures, the two principal points (P, P'} and the two nodal points 

 (N, N'} are so close together that there is practically no great 

 error in taking the intermediate point p as the only principal 

 point, and the intermediate point n as the only nodal point in the 

 entire system. By this we arrive at the so-called " reduced eye," 

 which consists of a simple convergent system, limited by a 

 spherical surface p with a radius of curvature of 5 mm., which 

 divides the air (refractive index = 1) from the vitreous body 

 (refractive index = 1'33). The nodal point of this simple system 

 lies close to the posterior surface of the lens. The refractive 

 power of this reduced eye would be 66'67 D., which differs little 

 from the average normal eye. 



By means of this diagram it is easy to follow the course of the 

 luminous rays that enter the eye, and to understand the forma- 

 tion of real images of external objects upon the retina. When 

 the inverted image of a flame is formed, it must be assumed that 

 each luminous point of the flame sends a bundle of divergent 

 rays through the pupil, which, in consequence of refraction, con- 

 verge at a corresponding point on the plane of the retina. 



Fig. 129 indicates the course of the rays abc, a'b'c' from the 

 extreme ends of the object. The lines XX and YY from these 

 two points, which cross at the nodal point n of the reduced eye 

 and are projected, unrefracted, on to the retina after crossing, are 



VOL. IV U 



