602 



Appendix B 



A ray diagram for the thin lens is illustrated in Figure 6. Note that 

 because the front and back focal lengths are equal, the center r as defined 

 by Equation 10 is at 0. 



Object 



Figure 6. Ray diagram for a thin lens. The lens is shown as 

 a straight line because it is thin. The plus sign indicates /is 

 positive. 



B. Thick lens with same medium on both sides : In this case, it is no longer 

 possible to neglect t. However, if one defines P, Q, and F as 



P = p - a (22) 



then Equation 19 becomes 



(23) 

 (24) 



(25) 



This is completely analogous to Equation 20, except that now the object 

 distance and back focal length are measured from a plane called the 

 first principal plane, which is normal to the optic axis and intersects it at 

 the point called the first principal point, which is at a distance a from the 

 first surface. The image and front focal length are measured from the 

 second principal plane, located at a distance /? from the second surface. 

 The ray diagram describing the thick lens is illustrated in Figure 7. 

 Note that if one imagined that the space between the two principal 

 planes did not exist, the diagram would be essentially the same as 

 Figure 6. 



C. Thick lens separating two different media: For this case, one can use 

 Equations 22 and 23 to simplify Equation 19 slightly to yield 



Hi 



Q 



<D 



(26) 



This is identical in form to Equation 9 for refraction at a single spherical 

 surface, provided one interprets (n 3 — n x )0 as an equivalent radius. 



