Appendix B 



603 



All of the interpretations of Equation 9 apply also to Equation 26, 

 provided one measures distances from the appropriate principal planes. 

 For example, there will be a back focal length — F x , given by 



-F 1 = ni <& 



and a front focal length F 2 , such that 



F 2 = /2 3 



A ray diagram for this case is shown in Figure 1 of Chapter 2. By 

 analogy with Figure 5, the ray from the object labeled (c) must intersect 



Figure 7. Thick lens ray diagram. Notice in this figure that 

 F, P, and Q_ are all measured from the planes P x and P 2 . 

 These planes at which the rays a and b change direction are 

 called principal planes and their intersections with the axis of 

 symmetry are called principal points. Likewise, the points at 

 which ray c proceeds toward and then away from are called 

 nodal points. If the media on both sides of the lens are the 

 same, the nodal and principal points coincide. The case of 

 different media on the two sides of the lens is illustrated in 

 Chapter 2, Figure 1. 



the optic axis at a point called the first nodal point, which is at the distance 

 (n 3 — n x )<b from the first principal point. This ray then runs along the 

 optic axis to the second nodal point, located at the distance (n 3 — w^O 

 from the second principal point. Thereafter, the line (c) must pro- 

 ceed to the image, running parallel to the first part of (c). Thus, the 

 image subtends the same angle about the second nodal point as the object 

 about the first. 



The six points, namely, two foci, two principal points, and two nodal 

 points, describe the refraction due to any pair of lens surfaces 1 to the 

 extent that the approximation developed in Figure 3 is valid. These 



1 Actually, only four of the six points are necessary. 



