Tracing Caustic Curves. 269 



oc' with the axis of the lens. The caustic will appear as if 

 rotated about C through the angle a.' from the axis of the 

 lens. If the emergent light be received on a small vertical 

 screen, the flare, of light seen on it is of course the coma. 



The difficult subject of coma can be simply introduced to 

 the student by getting him to trace the caustic of such a lens 

 due to a plane wave-front incident at some angle a. With 

 the help of the table below fig. 4 it can be done in three or 

 four minutes. On then drawing a vertical line through the 

 cusp, parallel to the plane surface of the lens, he will find 

 that the rays, which are symmetrical above and below the 

 axis of the lens, when produced beyond the caustic will 

 intersect on this vertical line below the cusp if a be positive. 

 This vertical line presents an edge view of the intersecting 

 comatic circles that produce the flare below the cusp. 



A (2) The curved surface facing the incident light. 



The construction of fig. 7 requires no explanation ; S is 



the radiant point, SC = cr, sin cj) 1 = sin 1 as before, and 



fF l is found by Table I. As the second surface is plane 

 /O represents SO in fig. 5 or b in Table II.; since /is the 

 radiant point for the second surface, its angle of incidence 



is 2 = CTP 2 (or O/P 2 ) = 0! -</>! + (/>!'. 



Fiar. 7. 



It is required to find PjP 2 and/O in terms of the known 

 quantities. From the diagram it is obvious that 



PiP 2 cos (j> 2 = t — r vers ($! — #i), 

 and /O or 6=/P 2 cos $ 2 . 



In the figure all the magnitudes are positive except] r, so 

 the sign of r must be changed in the above to give the 

 general formulae in Table III. (V is not shown.) 



