Appendix B 



601 



surfaces is denoted by t, the distance from the second surface to its 

 object p' is 



P' = q' ~ t 



Hence, one can find the location of the final image q by applying 

 Equation 9 again to yield 



Tlr. 



no - ric 



(13) 



(12) 

 q q' -t r b V 



Tedious but straightforward algebraic manipulations of Equations 1 1 

 and 1 2 allow one to eliminate q', arriving at 



q - j8 " p - a" O 



where q is the image distance from surface b 



— p is the object distance from surface a 



7 

 n 3 f b t 



y 



n 2 fafb 



y 

 y = n 2 (f b -fa) - t 



fa = 



L = 



n x - n 2 



(14) 



(15) 



(16) 



(17) 

 (18) 



(19) 



n 1 - n 2 



The form of Equation 13 can be simplified in various fashions. Three 

 different cases will be considered. 



A. Thin lenses: In this case, one may neglect /. Then a and /3 are 

 both zero. If, in addition, n x and n 3 are equal and one denotes by n the 

 ratio 



n = — 

 n x 



then Equation 13 reduces to 



111 



~q P~ f 



whereas Equations 16 through 19 become simply 



/ Va V 



/ 



(20) 



(21) 



