INTERFERENCE OF LIGHT. 95 



It is a minimum, and equal to the difference of the amplitudes 



of the components, when cos (ai - o 2 ) = - 1, or 



/ 

 a, - 02 = (2n + 1) TT. 



Now a i - a 2 = 2ir I l ^ 2 ). Therefore the intensity of the 

 \ A / 



resulting light is a maximum, when 

 Xi - x. 2 = wA, 



or the difference of the lengths of the paths traversed by the 

 two waves is a multiple of the length of a wave. It is a 

 minimum, when 



#1 - ^2 = (n + J) X, 



or the difference an odd multiple of half a wave length. 

 When ai - a 2 = (2n + 1) -, cos (c^ - a 2 ) = 0, and 



and the intensity of the resulting light is the sum of the in- 

 tensities of the components. 



(112) The principle of interference furnishes the complete 

 answer to the difficulty suggested by Newton, and shows in 

 what manner the rectilinear propagation of light is reconciled 

 to the wave-theory. It had been objected, that if light con- 

 sisted in the undulations of an elastic fluid, it should diverge 

 in every direction from each new centre, and so bend round 

 interposed obstacles, and obliterate all shadow. To this the 

 reply is, that light does diverge in every direction from each 

 new centre, that it does bend round interposed obstacles ; 

 but that shadows notwithstanding exist, because the several 

 portions of this laterally-diverging light destroy one another 

 by interference, and no effect is produced, except by those parts 

 of the wave which are in the right line joining the luminous 

 origin and the eye. 



