30 



Light and the Eye \1 : 2 



The use of geometrical optics to describe the properties of thick lenses 

 is outlined in Appendix B. The details will not be pursued here. 

 Rather, it is hoped that readers interested in geometrical optics will turn 

 to this appendix where the behavior of light at surfaces of refraction 

 (lenses) is discussed. 



In the eye, the luminous energy passes through a series of curved 

 surfaces of refraction. All of these surfaces may be approximated by 

 sections of spheres whose centers lie on a common line. This general 

 case has been shown to be mathematically equivalent to a single thick 

 lens, which separates two media of different indices of refraction. It is 

 not possible to relate the image and object distances by as simple an 

 expression as that for a thin lens, such as Equation 10 of Appendix B. 



Object 



Image 



Figure I. A thick lens immersed in different media on its two 

 sides. F x and F 2 are focal points. Note that F x does not 

 equal F 2 . The principal points are H ± and H 2 , and the nodal 

 points are N x and N 2 . Rays a, b, and c are drawn as in Fig- 

 ures B-6 and B-7 of Appendix B. 



However, six cardinal points completely specify the lens action. These 

 consist of two focal points, two principal points, and two nodal points. 

 This general case is illustrated in Figure 1. The cardinal points are 

 denned in Figure 1 ; they will be used in the next section to describe the 

 eye. 



The strength of a lens (or its power), L, is defined as the reciprocal of 

 the focal length / measured from the corresponding principal plane ; 

 that is 



'V 



(3) 



When /is measured in meters, L will be expressed in diopters. A lens 

 with a shorter focal length can produce a real image for closer objects 

 than a lens with a longer focal length. Thus, the lens produces a 

 greater algebraic change in curvature of an incident light front. In this 

 sense, a lens of shorter focal length is indeed stronger. In any case, 

 increasing the radius of curvature of a converging surface will increase 



