( 218 ) 



XVIIL ON THE PROBLEM OP TOTAL REFLEXION. 



[Proceedings of the Royal Irish Academy, VOL. n. Bead November 30, 1841.] 



PROFESSOR MAC CULLAGH communicated to the Academy a 

 very simple geometrical rule, which gives the solution of the 

 problem of total reflexion, for ordinary media, or for \iniaxal 

 crystals. 



First, let the total reflexion take place at the common sur- 

 face of two ordinary media, as between glass and air, and let it 

 be proposed to determine the incident and reflected vibrations, 

 when the refracted vibration is known. It is to be observed, 

 that the refracted vibration (which is in general elliptical) can- 

 not be arbitrarily assumed ; for, as may be inferred from what 

 has been already stated,* it must be always similar to the sec- 

 tion of a certain cylinder, the sides of which are perpendicular 

 to the plane of incidence, and the base of which is an ellipse 

 lying in that plane, and having its major axis perpendicular to 

 the reflecting surface, the ratio of the major to the minor axis 

 being that of unity to the constant r. The value of r, as deter- 

 mined by the general rule in p. 191, is 



IT- ^ 



\ n 2 sin 2 f 



where i is the angle of incidence, and n the index of refraction 

 out of the rarer into the denser medium. The ellipse is greatest 



* Proceedings of the Academy, VOL. n. p. 102 (supra, p. 192). 



