314 Mr. G. U. Yule on the Passage of Oscillator 



id 



the denominator becomes pe 2. Writing 



Vfc-Js. .... , (11, 



@2 \/p 



as a further abbreviation we have 



ie 

 \=re2. 



A ' 



We can now proceed to rationalize the values of — ^ and 



B 2 . A i 



jr given in (8). Inserting our value of \, 



. , l — re* 1— rcosr: — %v sin ■* 



A/_ _ 2 2 



AT ~~~ *? — 6 '. 7~0' 



1 + re 2 1+r cos ~ + zV sin - 



Multiplying numerator and denominator by 



e . . e 



1 + r COS-r — 27" Sin £r, 



2 2' 



this becomes n 2 ~ . . 



1— r — Zw sin 7: 



2 



l + r 2 + 2r cos ~ 



and multiplying again by 1 — r 2 .4*2zV sin -, 



Ai'__ HV-2?* 2 cos0 



A, 



If then 



Ll f l + r 2 + 2» , coSn)fl— »-' 2 h2&Vsin-J 



It snir 

 tan<^ = i, (12) 



we have finally 



. , A/ = (l+r 4 -2^cosflj^ _,^ 



1 l + r 2 + 2r cos -~ 



that is, the ray reflected from the first surface of the plate 

 undergoes a phase-change of ( — i/r), the reduction factor or 

 ratio of the amplitude of the reflected to that of the incident 

 ray being 



6= _ (1+/ _ 2 , 2cos y (ig) 



1 4- r 2 + 2?' cos - 

 Z 



