Appendix B 



599 



and turning the handle of the algebraic crank several times leads to the 

 final relationship 



ru 



2LZJ3 (9) 



q p r K J 



Several aspects of Equation 9 should be emphasized because they are 

 characteristic of all lens systems. For simplicity, only the case in which 

 (n 2 — n x )jr is greater than zero will be con- 

 sidered. It is possible then to construct 

 Table I. The point —f x is called the back 

 focal length, whereas f 2 is the front focal length. 

 Objects more than 10^ behind the inter- 

 face will produce real images within 10 per 

 cent of/ 2 - This is the case for most objects 

 focused by the eye. 



The implications of Equation 9 for the 

 refraction of spherical wavefronts at a 

 spherical interface can be represented by a 

 ray diagram, as shown in Figure 5. Just as 

 in the illustration of Snell's law, the ray diagram 

 makes detailed drawings of the wavefronts 

 superfluous. In Figure 5, the optic axis passes 

 through the center of curvature r of the inter- 

 face and the central point of the interface o. 

 Another line labeled (a) is drawn from the end 

 of the object, located at —p, parallel to the 

 optic axis until it reaches the interface. 

 Because this ray is parallel to the axis, it is 



TABLE I 

 Objects and Images for Equation 9 



Values above valid if/1,/2 > 0. 



