262 



Mr. A. S. Percival : Method of 



Whenever p = 0, there is either a cusp, as at the point F 

 in figs. 1, 2, 4, etc., or there is a stationary point (point 

 d'arret) as L in fig. 4, where the angle of incidence is the 

 critical angle and total reflexion occurs at all greater angles 

 of incidence. 



When the path of light is from the dense towards the 



rare medium - must be substituted for /jl in the given equa- 

 tions, as has been done in the planoconvex lens represented 

 in fig. 4. 



Beneath fig. 1 is a table of all the values required for 

 finding the position of the first focal lines when the angle of 

 incidence is 0, and 45°. SC or a is assumed to be 20, and 

 r 5 units, while /ul, as in all cases, is taken to be 1*523 which 

 is the ordinary value of /ju in American spectacle glass. 



Reflexion at a Spherical Surface. 

 As a simple example fig. 2 is given, which represents the 



Rk. 2. 



Reflexion. Plane Wave-front. 



0'. 



f~£-%n. j p=£p. 



I 

 30° 

 60° 

 90° 



2-5 

 2-165 

 1-75 

 







1-875 

 3-247 

 3-75 



reflexion of a plane wave-front at a spherical surface where 

 r=5. The adjoining table corresponding to four values of<£' 

 is sufficient to trace the entire caustic in three minutes. The 



