412 Mr green, on THE REFLEXION AND 



and, consequently. 



e = - e,, /3 = «, 



and 



a/A 

 tan e = + — — . 

 « A, 



This result is general for all fluids, but if we would apply it to 

 those only which are usually called elastic, we have, because in this case 



. fl/A rt/7/ 



tan e = — — = ' , . 

 «A^ ay' 



But generally 



(11) c= = 7;( - «;■-• + ¥) = r(a' + b^) ; 



and therefore, by substitution, 



i«ne= -^ = liX^i y u_ ^ ^^^^tan^^j - sec^0, 



«7" ay 



because ^ = — , and - = tan Q. 

 y a 



As e = — e , we see from equation (9), that 2e \s the change of phase 

 which takes place in the reflected wave ; and this is precisely the same 

 value as that which belongs to light polarized perpendicularly to the plane 

 of incidence ; (Vide Airy's Tracts, p. 362.) We thus see, that not only 

 the intensity of the reflected wave, but the change of phase also, when 

 reflexion takes place at the surface of separation of two elastic media, is 

 precisely the same as for light thus polarized. 



As a = ji, we see that when there is no transmitted wave the inten- 

 sity of the reflected wave is precisely equal to that of the incident one. 

 This is what might be expected : it is, however, noticed here because 

 a most illustrious analyst has obtained a different result. (Poisson, Me- 

 vioires de fAcndemie des Sciences, Tome X.) The result which this 

 celebrated mathematician arrives at is. That at the moment the trans- 

 mitted wave ceases to exist, the intensity of the reflected becomes 

 precisely equal to that of the incident wave. On increasing the angle 

 of incidence this intensity again diminishes, until it vanish at a certain 



