the Pressure of Radiation. 165 



It is interesting to verify by this method the case of perfect 

 reflexion ; for then p approaches the value given by 



^= i- [a^^ + /3^2 + y2 + Y-^ + Z^-X2] . . . . (40) 



OTT 



Let the angle of incidence be 6, and let the amplitude of the 

 incident and reflected waves be given by 



Xi = Aisin^; X2 = A2sin^ \ 



Yi = AiCos6'; Y2=-A2Cos6>i. . . . (41) 



Zi=^i; Z2 = B2 } 



Then the corresponding magnetic forces are 



ai = — Bi sin ^ ; a2=~B2sin^ "j 



/3i=-BiCos6'; ^2= B2 cos (9 V . . . (42) 



7i= ^1: 72= A2 j 



At the surface Y and Z are zero ; giving 



Ai-A2 = 0; Bi + B2=0 (43) 



Hence from (40) 



i^=^(Ai^ + B,^)cos2^ 



= 2EiCos2 6l (44) 



Avhere Ei is the mean density of total incident energy. 



For radiant energy incident equally in all directions, we 

 have 



Total incident energy = lEi^z<; = 27rEi. 

 Total pressure = 1 2Ei cos^ 6 dw 



i 



= ^2Ei cos' 6>. 27r sin 6>^6> 



= |.27rEi. 



Thus the total pressure is two-thirds of the whole incident 

 energy ; and as there is perfect reflexion, this is equal to one- 

 third of the total energy, incident and reflected, in front of 

 the surface. And this is the form which is generally used in 

 thermodynamic applications. 



