20 Mr. T. K. Ohinmayara on the Flow of 



the reflected wave at Q. The expression (p\p + r 2 )% will 

 in the rest of the paper be denoted by k. The resultant 

 magnetic intensity at P is 



H = COS Tilt J + « COS ! Jilt j 4-7T > . 



Let now & 1} k 2 be unit vectors at P in the direction of the 

 incident and the reflected rays respectively. The flow of 

 energy is determined by the Poynting vector S where 



X /fi cosnN- — j +Jc 2 [iccos(nt— -H-ttJ X 



or 



4ttS 



hi [cos 2 % + kgosx cos %'] + k 2 [k cos %cos %' + k2 cos 2 %'] 



1/ 



here ^=Kii -) and % L =n It ) +7r. 



The time-mean S of the flow of energy is given by 

 4tt>> 



6' 

 87rS 



= i*l[l + K COS (%'-^)]+P 2 [« 2 + ^ COS (%'-%)], 



if a 1 =l + A;cos(% / — %) and a 2 = « 2 + /ccos (%' — ^). 



If </> be the angle which the . direction of S makes with 

 that of the incident rays, it can be easily shown that 



. a 2 sin 20 2a 2 Q 



tan © = — ^ = approx. 



a 1 -{-a 2 cos lo a x ^-a 2 x L 



Thus ^ M*+.™(x!-g L .... (17) 



^ 1 + 2/e cos (% — x) + K 

 Now x X— "^ ^+7r= 2r 2 v l -\-ir approx. 



Hence (17) becomes 



20 | k 2 -*; cos *2r 9 0*\ 



~~ • • • (18) 

 l + * 2 -2A;cos-2r 2 2 



c 



