THE IMAGE-FORMING MECHANISM OF THE EVE 



649 



actual eye a schematic eye such as Gullstrand's (79, 

 p. 392) which is illustrated in figure i . 



The front and back surfaces of the cornea, the 

 front and back surfaces of the lens and the front and 

 back surfaces of the nucleus of the lens are the refract- 

 ing surfaces and constitute the refracting mechanism. 

 The spaces bounded by these surfaces are assumed 

 to be filled with homogeneous transparent media, 

 but differ from each other in having different indices 

 of refraction. The si.\ refracting surfaces of Gull- 

 strand's .schematic eye are assumed to be spherical 

 and centered on a common optic a.xis. 



Ffirmation of Image by Refracting Meehanism 



The refracting mechanism forms images of objects 

 placed in front of the eye. The simplest kind of object 

 that can be .so placed is a monochromatic point 

 source of light as shown in figure 2. The point source 

 Q. gives off rays which are incident at the cornea. 

 Because these rays diverge from the point Q_ this 

 point represents the focus of the incident rays. These 

 rays are said to exist in object space and the point 

 Q. is called an object point. 



The pupil admits into the eye a certain number of 

 the rays diverging fron the point Q_, and after these 

 rays emerge into the vitreous they are said to exist in 

 image space. They converge at the point ()' which 

 represents the image point which is conjugate to Q_. 



One can locate the image point corresponding to 

 a given object point by tracing two or more rays 

 through the refracting surfaces. Each ray entering 

 the eye is refracted or bent at each surface in accord- 

 ance with .Snell's law of refraction, illustrated in figure 

 3. The ray in the first medium which is incident to 

 the refracting surface makes an angle a with the 

 normal to the refracting surface at the point of inci- 

 dence. After it emerges into the second medium as 

 the refracted ray, it makes an angle a with the 

 normal. .Snell's law states that 



n sin a = n' sin a' 



where n represents the inde.x of refraction of the first 

 medium and n' the index of the second medium. 



This method of locating an image point which in- 

 volves tracing rays from surface to surface is tedious, 

 and it is much simpler to locate first the so-called 

 cardinal points and planes and then use these to 

 locate the image point. For Gullstrand's schematic 

 eye one may compute for any given wavelength a 

 pair of nodal points N and N' , a pair of principal 

 points H and H' and planes, and a pair of focal 

 points F and F' and planes (.see fig. 4). The signifi- 

 cance of these points and planes will become obvious 

 as the discussion proceeds. 



A ray incident to the front surface of the eye which 

 is directed through the first nodal point emerges into 

 the vitreous directed through the second nodal point 

 and parallel to the incident path of the ray, as shown 

 in figure 5. A second incident ray which passes 

 through the primary focal point F emerges into the 

 vitreous parallel to the optic axis. The emerging ray 

 is also directed through the points V and (". This is 

 true because an incident ray which is directed 

 through the point V in the primary principal plane 

 must emerge into the vitreous directed through the 

 point I' in the second principal plane which lies on 

 a line through V parallel to the optic axis. This is a 

 consequence of the fact that the principal planes are 

 the conjugate planes of unit magnification. A third 

 incident ray parallel to the optic axis emerges into the 

 vitreous directed through the secondary focal point 

 F'. All three of these rays which emerge into the 

 vitreous converge at the image point Q'. It is obvious 

 that once the cardinal points and planes are located 

 we can predict the location of the image of any object 

 point. 



The cardinal points bear fixed relations to each 

 other so that once the principal points and one of 

 the focal points are given, the locations of the other 

 points can be immediately determined b>' means o 



FIG. 2. Conjugate foci in object and image space. 



