of Refraction, Reflexion, and Extinction. 283 



into vacuum, seemingly from the surface of the hody. Hence, 

 if the reflected wave be 



E*=A*e^+«*+?) (3) 



(where A* will be supposed to be real), we get 



A# 2ttNA< 2 > 



A ^- ?WTT ) W 



To connect A* with A (1) it is only necessary to resort to 

 equation (5) of § 5 ; the result may be expressed 



A*=-^^A< 1 V^-^, .... (5) 



which gives the well-known relations, applicable in the case 

 of external reflexion : 



A(1) cos%-p)=- ( --- 2T -, . . (6 a) 



^ ) sinn( ? - i .)= + ^ + - ) ' C s + - 8 . . . (6 6) 



It may be easily verified that the component along y of 

 the magnetic field of the reflected wave is 



_A* e init±az+q) /y\ 



In concluding this subject it may be well to consider in a 

 similar manner the refracted wave, propagated within the 

 material medium (~>0). In order to represent this wave, 

 we write 



E**=A*V'<'-^+ r ) ...'.. (8) 



supposing A** to be real; having regard to (6), § 5, we 

 obtain 



1 vr a(2) 



t(6V-lJ V ; 



By (5), § 5, used in (9) we dedu-e 



?A (1) • , 



A ** = -^ r>,(p-r) .... (10) 



bc+ 1 

 and therefore we find 



—.cosn^^)^^^^, . . (Ha) 

 5urSinn(r-;>) = ^ + 1)i + iBi . ■ • (U « 



