276 



Method of Tracing Caustic Curves. 



9 , and G 2 P 2 T is (/>/. The line P 2 T meets the final caustic 

 atV. 



Fig. 11. 



Virtual Caustic formed by a meniscus where SA = 4, and r 1 = 15 

 r 2 = 5; fl4 = -rll; t=3; /* = 1-523. 



B x . 



0i- 



0i'- 



/Pi- 



02- j 2 '- 







30° 

 45° 







21° 30' 37" 

 31° 14' 5" 



j 5-3464 

 13° 55' 50"! 6-1856 

 19°54'21"j 7-3463 







-15° 37' 38" -24° 13' 17" 

 -24° 50' 22" — 39°46'31" 





PiPa. 



/P 2 . 



2 . ff 2 . 



v. 



p 2 . 



p. 



3 



2-2735 



1-2527 



8 3464 

 8-4590 

 8-5985 



3-3464 

 20° 17' 10" 3-8848 

 27° 20' 52" 4-5721 



1 



12-8411 

 14=7693 



25-5068 







2-0513 



3-1989 



o 



6-6197 

 3-4034 



Now although this caustic is very large, as Q is the con- 

 jugate focus of S, the longitudinal aberration is very small 

 being only QT, Avhile the lateral aberration is the short 

 vertical line above Q, and the radius of the least circle of 

 aberration is indicated by the minute vertical line between 

 Q and T. If an eye, or a camera of very small aperture, 

 were placed behind the lens in the direction P 2 R and were 

 focussed for the point Y, the radiant point S would be repre- 

 sented by a focal line at right angles to the plane of the 

 paper, but if placed in the direction AB and if focussed for 

 the point Q, 8 would appear as a minute circle. 



It has been previously pointed out that in most cases it is 

 advisable to determine the angle -\fr 2 or BTP 2 . From the 

 figure it is seen that 



B0 2 P 2 = BTP 2 + C 2 P 2 T = AT'P 2 + C 2 P 2 T' 



or 



^2 + 4 > 2= y l r l + c f>2' 



