Tracing Caustic Curves. 



267 



In fig. 5 it will be noticed that as before when p and p 

 carry the same sign Qf is measured in the same direction as 

 ON. When = 45° p is more than 56, so C is beyond the 

 limits of the diagram in the direction / 'C. 



Fig. 





\ 

 c 











Refraction at a plane surface. 







SO=5=4: /* = 1-523. 





p. 



¥• 



/*■ 



V- 



P- 











6-092 











45° 



27° 39' 50" 



13-5165 



3-5427 



56-0971 



Caustic formed by a Lens. 



In all cases it is necessary to know the axial thickness it), 

 the curvature of each surface, and the distance of the radiant 

 point either from the proximal surface or from its centre of 

 curvature. Formulae must then be obtained to determine in 

 terms of the data the length of the path (PiP 2 ) of any ray 

 within the lens, and the angle of incidence at each surface. 



We will consider first piano lenses. 



A (1) The plane surface facing the incident light. 



Fig. 6 represents a radiant point S on the axis of a plano- 

 convex lens. It will be necessary to find the values of fV l 

 and pi (due to the refraction at the plane surface) for the 

 axial and the extreme rays and one or two intermediate rays 



