(iv.) 

 (v.) 



Tracing Caustic Curves 

 Hn o _ C *N r 2 sin <ft 2 



273 



/Fi + FiP 2 — r 2 cos^ 2 ' 



fC 2 or a 2 = C 2 N cosec 6 2 . 

 Mar. 9. 



In the diagram all the magnitudes are positive except 

 a x (or SCi) and </> 2 , so the signs of these symbols must be 

 changed in order to make the above formulae universally 

 true when the symbols cary direction signs. 



For a plane wave-front at normal incidence 6± and 

 d\ do not appear. These changes have been made in 

 Table IV. 



In fig. 10 an example is given of a biconvex lens of the 

 same power as that of the previous planoconvex ; in this 

 case r 2 ~ —r Y = 9*4552 and, as can be readily found, the 

 second principal plane passes through the point H" where 

 H' / B = 1*0416. From the table of values below the diagram 

 it is seen that when </>i = and a or fC 2 (i.e. /P 2 — r 9 ) is 

 -33-9892, v or F"B= -8*5186, and therefore F"H"= 

 — 9*5602 as in the case of the planoconvex in fig. 4 and in 

 fig. 9. 



The symmetrical biconvex oives the smallest caustic when 

 the lens is midway between the object and its real image. 

 Fig. 10 represents the case when parallel rays are incident ; 

 if provided with a diaphragm to reduce its aperture to that 

 of the planoconvex in fig. 4 the caustic is fairly small, as 

 is shown by the full lines. Even when used with its full 

 aperture the caustic does not quite touch the surface of the 

 lens. 



Phil. Mag. S. 6. Vol. 43. No. 254. Feb. 1922. T 



