Refraction for Electric Waves. 193 



Then y = f (a) (sin pt), where p is frequency; 



1/ = If [a + .r) (sin \pt - — - tt j ) 

 = — kf (a + #) smUi — J 



= — A/(a + d') -j cos— -smp/- sm ~T~ " cos P t \ ' 



To get from this the resultant intensity we must take the 

 square of the sum of the amplitudes of the sin jttf component 

 and add to it the square of the amplitude of the cos pt 

 component. 



I = {/(a)-* ./(<*+*) cos?p' }V { h ./(<• + «) sin xT 



27T7' 



= /(«)« + l*./«(a + i)-2A./(a) ./(a + *) cos ^. . (1) 



^4s a y?rs£ approximation let us assume ,? negligible in 

 comparison with a, which is nearly enough the case for the 

 first maximum. 



Then 



I =/(a) 2 { 1 + P-SA . cos^}, 



which has a maximum for 



27r.r 

 cos-- — = — 1 



A 



2tt£ 



In this position the reflector is distant j from the oscillator. 



This is in accord with experiment, and justifies the assumption 

 of a change of phase of 180° by the reflexion. This phase- 

 change is given by Hertz's theory. 



* The — tt is introduced to take account of the change of phase hy 

 reflexion. Its meaning is clear in what follows. 



