THE IMAGE-FORMING MECHANISM OF THE EYE 65 1 



of the cornea, an increase in curvature increases the 

 refracting power of the eye. 



When we want to know how a change in index 

 affects the refracting power of the eye, we have to 

 approach the matter from a different direction. If we 

 introduce a thin layer of air between the adjoining 

 media, this will create two surfaces for each surface 

 except the first, and each medium will be bounded 

 on both sides by air. Introducing such layers of air 

 would not affect the direction of the refracted rays. 

 Figure 6 represents an exploded diagram showing 

 each medium bounded on both sides by air. These 

 elements form plus and minus lenses except in the 

 ca.se of the lens nucleus where a biconvex lens is 

 formed, and in the case of the vitreous where we 

 must deal with a single refracting surface. This analy- 

 sis of the optical system makes it easy to visualize 

 what happens when the index of a given medium 

 changes. An increase in index will increase or de- 

 crease the total power of the eye depending upon 

 whether the refracting effect of the particular element 

 is plus or minus. 



Helmhollz Schematic Eye 



Hclmholtz (yg, p. 152) made use of a somewhat 

 more simplified schematic eye than that employed 

 by Gullstrand. In the Helmholtz schematic eye the 

 cornea represents a single refracting surface at which 

 the aqueous adjoins the air. Furthermore the lens is 

 treated as having a uniform index throughout (see 



fig- 7)- 



The value which Helmholtz selected for the radius 



of the front surface of the eye approximates the average 



front surface of the cornea in the adult human eye. 



The displacement of the lens from the front surface 



of the eye also approximates the distance from the 



front surface of the cornea to the front surface of the 



lens as measured experimentally. The thickness of 



the lens and the radii of curvature also appioximate 



the actual values. The value of 1.338 given to the 



CORNEA 



CORNEA I CORTEX | CORTEX | 



AQUEOUS NUCLEUS VITREOUS 



FIG. 6. Exploded diagram of the Gullstrand schematic eye 

 showing the various elements with air spaces between them. 



FIG. 7. The Helmholtz schematic eye 



index of the aqueous and vitreous for sodium light. 

 (589 m|t) approximates the true value. A value 

 of 1.455 ^35 been selected for the lens because, if 

 the lens substance is assumed to have a uniform 

 index throughout, it gives the lens approximately the 

 same refracting power as an actual lens immersed in 

 vitreous. The indices selected by Helmholtz have 

 been adjusted by Laurance (54) from 1.338 to 1.333 

 (or J--Q and from 1.455 to 1.45 in order to give the 

 eye primary and secondary focal lengths of — 15 and 

 20 mm, respectively, which are round numbers. 



The radii of curvature of the refracting surfaces, 

 their locations and the indices of the media constitute 

 the optical constants of the eye and are summarized 

 for the Helmholtz schematic eye in table i. All of 

 these values refer to sodium light (589 mix). 



Reduced Eye 



Helmholtz's schematic eye can be simplified still 

 further, as has been done by Laurance (54), by 

 using a single refracting surface as shown in figure 8. 

 The interior of this eye is filled with a medium which 

 has the same index throughout and is equivalent to 

 that of the vitreous of the Helmholtz schematic eye, 

 namely 1.333. The surface at which this medium 

 makes contact with the air in front of the eye is the 

 only refracting surface. The curvature of this surface 

 has been arbitrarily increased to compensate for 

 the absence of the lens so that the eye has the same 

 refracting power as the Helmholtz schematic eye. 



In the reduced eye the two principal planes coin- 

 cide and are tangent to the front surface of the eye. 

 The two nodal points coincide at the center of curva- 

 ture of the front surface. The focal lengths are the 

 same as in the Helmholtz schematic eye, and for 

 most purposes the reduced eye is equivalent to the 

 Helmholtz eye. It is very useful for visualizing certain 



