Tracing Caustic Curves. 



275 



Fig-. 10. 



Refracti on of a plane wave-front by a biconvex lens. 

 r= -9-4552; r 2 =9*4552 ; t = 3; p = 1*523. 



0i- 



*'. 



f?, 



02- <p2> i P,?,. i 



1 







15° 

 30° 







9° 47' 4" 

 19° 9' 56" 



I a 



-27-534 



-26-1429 



-22-4396 





 -18° 50' 19" ! -29° 27' 28" 



-40° 9' 55" -79° 12' 45" 



! 



3 ; 



2-4207 | 

 •5098 ! 



/*»• 



9. 2 . 



a 2 . 



v. 



Pv 



P- 



-24-534 



-23 7222 

 -21-9298 







- 5° 20' 20" 

 -11° 48' 52" 



- 33-9892 

 -32-8131 



-29-7865 



-8-5186 

 -6-4323 

 - -2435 





 4-6499 



9-2881 





 -16-0049 



- 8-3388 



The virtual caustic in fig. 11 is interesting. To avoid 

 confusion in the diagram only the lines which have a relation 

 to the extreme ray SPi are indicated ; ASPi = #i or <±5°, 

 C 1 PiS = ^ 1 , C l P l T = (f) 1 ', and P:P 2 is the path of the refracted 

 ray through the lens, and o£ course the angle AT'P 1 = *^r 1 or 

 Oi — cfri + </>/• It will be noted that i£ PjT' be produced it will 

 touch the end of the caustic in dotted lines of which the 

 lower limb only has been drawn ; this is the caustic form?d 

 by the first refraction. For the second refraction C 2 P 2 T' is 



T 2 



