Re: POLARIZATION

[John Mallinckrodt <ajmallinckro@CSUPomona.Edu>]

On Tue, 16 Jun 1998, brian whatcott wrote:

> > The *rms* amplitude (i.e., the only one that "really matters") of 
> > a transverse wave is always sqrt(2) times larger than that of its 
> > two equal amplitude component waves whether the wave is linear and 
> > the components helical or vice-versa.  This is a simple 
> > mathematical result and it (reassuringly) agrees with the dictum 
> > of conservation of energy since the intensity of a wave is 
> > proportional to the mean square amplitude.
> >
> > John
>
> It is certainly not difficult to frame an elementary rebuttal to 
> this curious post.
> If John admits the possibility of superposing waves of linear 
> polarization, then let him consider two waves of equal amplitude
> (rms or any other measure!) which are pi radians different in phase 
> but otherwise identical.
>  The simple result is cancellation.
> (Or at least this is my conclusion. Would John say it is in error?)

It's easy to "rebut" an argument by constructing strawmen.  A second
reading of my post, however, will surely reveal that I was referring to
two cases and two cases only: 

1  A linearly polarized wave constructed from two equal magnitude
   circularly polarized ("helical") waves 

2  A circularly polarized wave constructed from two equal magnitude
   linearly polarized waves

I suppose I might have bolstered my argument and better anticipated
brian's response by mumbling something about the nice properties of
orthogonal basis elements.  Nevertheless, a linearly polarized wave of
zero amplitude may be constructed from two (opposity parity) circularly
polarized waves of equal amplitude if and only if those amplitudes are
zero as well.  The same holds for constructing zero amplitude circularly
polarized waves from two (orthogonal) linearly polarized waves. 

John
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