Appendix B 



597 



and refracted rays, Oy and 08 in Figure 1 ; drawing lines for the wave- 

 fronts is superfluous. 



From the point of view of mathematical theory, Snell's law describes 

 the simplest case of refraction possible. In analyzing lens systems, 

 including the eye, it is necessary to treat curved interfaces between two 

 media and curved wavefronts. The type of curved interface which is 



n=] 



n>] 



cc 



i^r::_' 



Figure 2. Refraction of a spherical wave at a plane interface. 

 A virtual image is formed at q due to the object at p. Curva- 

 ture of wavefront is changed because it does not all reach inter- 

 face at the same time. Image is virtual because wavefront 

 diverges as if it came from q; in other words, q is negative. 



simplest to treat mathematically is a spherical interface. Even this is 

 complex when used for an analysis of lens action ; only small sections of 

 spherical surfaces are simple to treat. Although insufficient for making 

 optical lenses, an analysis of refraction by small sections of spheres is 

 sufficiently complex to describe the action of the eye because the inter- 

 faces between the various media in the eye are very close to small 

 sections of spheres. 



A curved wavefront will, in general, undergo a change in curvature 

 when it is refracted. This is illustrated in Figure 2 for a plane interface. 

 The point p from which the incident wave diverges is called the location 

 of the object, whereas the point q to which the refracted wave converges 

 is called the location of the image. Objects are called real if they are on 

 the side of the interface from which the light is coming ; images are called 

 real if they are on the side of the interface toward which the light is 

 going. Objects and images which are not real are called virtual. 



For camera or eye action, it is necessary to have real final images. 

 In the following examples, only real initial objects, real final images, and 

 positive (converging) surfaces are illustrated. The convention is 

 adopted of treating distances as positive or negative, according to their 

 location relative to the lens or to the surface of discontinuity of index 

 refraction. Thus, a real object will be located at a negative distance p, 

 whereas a real image will be located at a positive distance q. 



