[Phys-L] Re: Travel distance in a waveguide.

[David Bowman <David_Bowman@GEORGETOWNCOLLEGE.EDU>]

Regarding BC's response to Mike's questions:

> Very quick answer:  (others will probably criticize and amplify.)
>
> My understanding is that th fiber does work like a wave guide.  I
> suspect this is true if the relative dimensions are the same.  A
> quick search of the webb will reveal the truth or falsity.  [aside,
> I think the graded N is so total internal reflection will occur at
> shallower angles than the Brewster's (right word?) determined for
> 1.5]
>
> The chase:  the formula for the group speed down the guide is v sub
> g = C sqrt[ 1- (frees space wavelength/2*waveguide dimension)^2];
> the wave guide dimension is for a rectangular guide with E
> perpendicular (lowest mode).
>
> Berkeley Phys. Lab. B 10 explores this including deriving the group
> and phase speeds.
>
> bc who suspects the experiment is a fraud.   A less fraudulent
> experiment is to use coaxial cable driven by the pulse generator.
> Compare the predicted from the cable's Z w/ measured.

In a real sense *any* experiment that purports to actually measure c
is a 'fraud'.  This is simply because c is a defined quantity--not a
measurable one.  Experimentally determining c is like experimentally
determining the numerical value of a dozen.  Since 1983 the meter has
been *defined* to be 1/299792458 of the distance light travels in a
vacuum in 1 sec.  Any experiment that advertises itself as measuring
c really is either measuring the quality of the calibration of the
time and/or distance standards used in the experiment, or measuring
the size of the systematic errors/corrections in the measurement
(such as the accuracy of the value of the refractive index).

In our Modern Physics lab course at my college we usually do perform
an experiment that ostensibly claims to measure c by measuring the
time of flight delay in a AM modulated signal riding on a laser beam
that is split with a beam splitter with one beam being reflected off
of a mirror a few 10's of meters away compared to the reference beam
having a short total path length of a fraction of a meter.  The
modulated signals from the short path beam and from the long path
beam are compared using a 2 channel o-scope after each beam is sent
to its respective photodetector.  I warn the class that the
experiment really measures a combination of the calibration of
the claimed time-base sweep rate of the scope, some contamination
effects from some internal crosstalk between the signals in the
common electronics of the detectors/preamplifiers apparatus for both
channels, and the ability of the students to eyeball the delay time
between the sine wave modulation signals on the scope.

In this experiment the actual distance measurements involved are not
the accuracy-limiting quantities in the experiment (even though the
*meter* is actually defined via the defined value of c and the prior
Cesium definition of the duration of a second and) even though they
mostly involve the low-tech methods of counting floor tile squares
to the distant mirror and measuring the path length of the short
beam using a meterstick and visually checking that the cable lengths
from the detectors to the two scope inputs are equal by laying them
side by side and looking at them.  The typical accuracy of the
'measurement' is about 3 - 4 % which is much worse than the accuracy
of the relevant distance measurements involved, and mostly reflects
a combination of a mis-calibration of the scope time-base and some
contaminating signal crosstalk in the apparatus electronics
(presumably via the common power supply).

David Bowman