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318 THE PHYSICS TEACHER ◆ Vol. 41, September 2003
Letters
by a factor of 10,000, we reduce the
impedance by a factor of 10,000.
With that impedance mismatch, the
vibrations of the bell are not coupled
to the air, and if there were sound in
the air it would not be coupled to the
jar (or microphone).
An easy demonstration of imped-
ance matching is to stretch a rubber
band between thumb and forefinger.
If you pluck the rubber band, you
will hear very little sound. But
stretch the band over a drinking glass
set on a table, and you have the be-
ginning of a violin. Not a Stradivar-
ius, perhaps, but at least your imped-
ances are beginning to match.
1. Dejun Han, “Improved bell-in-a-
bell-jar demonstration,” Phys. Teach.
41, 278–279 (May 2003).
Clifford Swartz
Physics and Astronomy Department
SUNY
Stony Brook, NY 11794
Sun Pillars and Ice
Crystals
Dan Quinn contributed a beauti-
ful photograph of a sun pillar, which
he correctly attributed to the reflec-
tion of sunlight from falling ice crys-
tals.1However, the crystals do not
necessarily have to be the flat-plate
crystals that result in sundogs.2
Robert Greenler and his collabora-
tors showed that thin-pencil crystals
(see Fig. 1), which tend to fall with
their long axis approximately hori-
zontal, can also produce sun pillars.3
Quinn also posed the question of
why the sun pillar has a larger vertical
than horizontal extent. This is un-
derstood most easily for flat-plate
crystals. As Ron Edge explained,
these crystals tend to fall with their
axes approximately vertical and the
reflecting surfaces approximately
horizontal. Figure 2 shows how ice
crystals farther above the Sun must
be tilted farther to reflect light to-
ward an observer. The axes of ice
crystals to the right or left of the ob-
server (into or out of the plane
shown in Fig. 2) must have greater
tilts in order to contribute to the pil-
lar since they must also redirect the
light in the horizontal direction.
However, flat-plate crystals are not
likely to be tilted very far.
Unfortunately, it is difficult to tell
which type of ice crystals formed the
sun pillar in the photograph. Green-
ler notes that “the shapes do not dif-
fer greatly when the Sun is near the
horizon.” 3Also, there are no other
effects visible in the picture to offer
clues about the crystals. For exam-
ple, sundogs would be evidence that
flat-plate crystals were present in the
atmosphere.
1. Dan Quinn, “Photo of the Month,”
Phys. Teach. 41, 304 (May 2003).
2. Ron Edge, “Sundogs, ice crystals,
and Bernoulli,” Phys. Teach. 40, 522
(Dec. 2002).
3. Robert Greenler, Rainbows, Halos and
Glories (Cambridge, 1980), pp. 65–74.
Alan J. DeWeerd
University of Redlands
Redlands, CA 92373
alan_deweerd@redlands.edu
Grazing Incidence Reflec-
tion and X-ray Images
To Hasan Fakhruddin’s interesting
article about grazing incidence
(“Specular Reflection from a Rough
Surface” [Phys. Teach.41, 206–207
(April 2003)], I can add that NASA’s
Chandra X-ray Observatory is now
making high-resolution x-ray images
of celestial objects using the same
technique. Four nested cylindrical
mirrors are used, since the area of any
one mirror that is exposed to incom-
ing radiation is small at low angles of
incidence. See http://chandra.
harvard.edu for the fascinating results.
Jay M. Pasachoff
Astronomy Department
Williams College
33 Lab Campus Drive
Williamstown, MA 01267
jay.m.pasachoff@williams.edu
Comments on Deter-
mination of Absolute Zero
The March 2003 issue (Vol. 41,
No. 3) was a fascinating one, and I
would like in particular to compli-
ment Prof. Eugene Hecht on his pa-
per “On Morphing Neutrinos and
Why They Must Have Mass” (pp.
164–168). It made the mass ques-
tion and the matter of neutrino oscil-
lation reasonably clear to me for the
first time. I also found Dragia Tri-
fonov Ivanov’s paper “Experimental
Determination of Absolute Zero
Temperature” (pp. 172–175) both
useful and interesting. It presents an
elegant shortcut to obtaining this val-
ue, in contrast to the more lengthy
and pedestrian procedure described
in my laboratory textbook.1
Fig. 1.
Fig. 2. The formation of the sun pillar
at sunrise or sunset when the incom-
ing rays are horizontal.