Phenomena of Reflection of Light. 



415 



6 moves to the right and as before, at the Polarizing Angle 14 

 becomes zero. Fig. 3 is drawn for light incident at 30° upon 

 a glass (n=l-53) — air surface. 



= == -.185, R.= =.528 



R = 



12 



34 



As the angle of incidence is still more increased, 16 A 2 exceeds 

 15 = — and 65 = C 2 2 becomes negative, and hence C 2 is imagin- 

 ary. At the point where 6 is at 5, A 2 = — - or the emerging 



2 

 waves, travel parallel to the surface and the angle of incidence 



is the Critical Angle. Beyond this angle, conditions are repre- 

 sented by fig. 4, which may be taken as typical of total reflec- 

 tion. Since 62 (=0 1 C 3 ) and 64 are mean proportionals of 65 

 and 63 and C 3 is imaginary, 2 and 4 must lie on a circle whose 

 diameter is 53. Evidently numerically, . 



XV 



~ = 1 = R s = R p , and the angle between 12 and 14 gives 



the phase difference between the two components and the angle 

 between 32 and 34, the phase difference between R s and the 



4 



incident, perpendicular, component. The latter phase difference 

 is evidently zero when total reflection begins and tt at grazing 

 incidence. The difference of phase between the two compo- 

 nents, angle 412, is seen to be zero at both extremes and a 

 maximum when 12 and 14 are tangents. For this case, by 

 geometry, 



_ 2 _ 2 _ l l 



52 : 23 = 56 : 63 = 15 : 13 = — 



V „ V . 



52 : 23 = V 1 : >K 2 



the maximum ancde 412 = -tr — 4 angle 235 = tt — 4 tan" 



Am. Jour. Sci. — Fourth Series, Vol. XXIV, No. 143. 

 29 



-November, 1907. 



