MOTION MOUNTAIN

what is light? 135
Challenge 145 s
Ref. 96
Ref. 97
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The wave impedance of the vacuum of376.7Ω has practical consequences. If an electromagnetic
wave impinges on a large, thin, resistive film along the normal direction, the
numerical value of the film resistance determines what happens. If the film resistance
is much larger than376.7Ω per square, the film is essentially transparent, and the wave
will betransmitted. If the film resistance is much lower than376.7Ω per square, the film
is essentially a short circuit for the wave, and the wave will bereflected. Finally, if the film
resistance is comparable to376.7Ω per square, the film is impedance-matched and the
wave will beabsorbed.
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If the light emitted by the headlights of cars were polarized from the bottom left to the
upper right (as seen from the car’s driver) one could vastly improve the quality of driving
at night: one could add a polarizer to the wind shield oriented in the same direction. As
a result, a driver would see the reflection of his own light, but the light from cars coming
towards him would be considerably dampened. Why is this not done in modern cars?
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Could light have a tiny mass, and move with a speed just below the maximal speed possible
in nature? The question has been studied extensively. If light had mass, Maxwell’s
equations would have to be modified, the speed of light would depend on the frequency
and on the source and detector speed, and longitudinal electromagnetic radiation would
exist. Despite a promise for eternal fame, no such effect has been observed.
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A beam of light can be polarized.The direction of polarization can be changed by sending
the light through materials that are birefringent, such as liquid crystals, calcite or stressed
polymers. But polarization can also be changed with the help of mirrors. To achieve such
a polarization change, the path of light has to be genuinely three-dimensional;thepath
mustnotliein aplane.
Tounderstandtherotationofpolarization withmirrors,thebesttoolistheso-called
geometricphase.Thegeometricphaseisananglethatoccursinthree-dimensionalpaths
ofanypolarizedwave. The geometric phase is a general phenomenon that appears both
for light wave, for wave functions, and even for transverse mechanical oscillations. To
visualize geometric phase, we look at the Figure 87.
The left image of Figure 87 can be seen as paper strip or a leather belt folded in space,
with a bright and a dark coloured side. It is not a surprise that the orientation of the strip
at the end differs from the start. Imagine to follow the strip with the palm of your hand
flat on it, along its three-dimensional path. At the end of the path, your arm is twisted.
Thistwistangleisthegeometric phaseinducedbythepath.
Instead of a hand following the paper strip, we now imagine that a polarized light
beam follows the path defined by the centre of the strip. At the bends, mirrors change
themotionofthelight,butateachtinyadvance, the polarization remains parallel to the
polarization just before. One speaks ofparalleltransport.The result for light is the same
as for the belt: At the end of the path, the polarization of the light beam has been rotated.
In short,paralleltransportinthree dimensionsresultsinageometric phase. In particular,
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net