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Waves
 (2005-05-21)
Wave Propagation and Huygens' Principle
A helpful fiction to describe wave propagation.
(2007-09-09)
Diffraction
What occurs when a wave originates from a bounded source.
(2005-05-21)
Thomas Young's "Double Slit" Experiment
Demonstrating the undulatory nature of light.
(2005-09-29)
Celerity
The celerity of a wave is the product of its frequency by its wavelength.
The celerity u of a wave is always equal to the product
l n of its wavelength by its frequency.
When this celerity is constant, the medium is said to be
nondispersive. In a nondispersive medium, a planar wave
would retain its shape as it propagates.
This is not generally true in a dispersive medium.
(2007-09-09)
Standing Waves
Nodes and Antinodes.
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Ernst Chaldni
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(2008-04-13)
Chladni Plates & Chladni Patterns
Standing oscillations on a surface feature lines of nodes.
Ernst Chladni (1756-1827)
was a German physicist whose family hailed from the medieval mining town of
Kremnica
(Kingdom of Hungary, now in central Slovakia).
Chladni has been called the father of acoustics.
He obtained the speed of sound for several
gases and experimented
with vibrating plates peppered with sand to visualize node lines
(the sand accumulates wherever the motion of the plate is minimal).
Similar experiments now go by the name of Chladni plate
experiments and the intriguing patterns so obtained are dubbed
Chladni patterns.
Ernst Chladni was also an avid meteorite collector and he successfully argued
in favor of the celestial origin of meteorites.
(In English and in French, at least, his name is usually
pronounced like clad-knee.)
Chladni Patterns for Violin
Plates by Joe Wolfe (UNSW, Sydney, Australia)
Videos:
Chladni Patterns
on a Square Plate
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Holding a Chladni Plate
(and ruining a bow)
 (2008-01-12)
Snell's Law (1621)
Direction of a refracted wave. Total internal reflection (TIR).
By definition, a diopter is the surface (usually a plane or
a sphere) which separates two regions where specific waves (light, sound, etc.)
travel at different celerities (celerity = phase velocity).
Incidentally, the name "diopter" also denotes a
unit of curvature equal to the reciprocal of
a meter (m) which is used to rate an optical element by specifying the
reciprocal of its focal length.
Snell's Law applies not only to waves but also to other objects
at a boundary between two domains where the travelling speeds are proportional
to different values of a so-called index of refraction n.
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n1 sin q1
=
n2 sin q2
This law of refraction was discovered by
Thomas
Harriot in July 1601 and independently by
Snell
(1621) and
Descartes
(1637) who was the first to publish it.
The Dutchman
Christiaan
Huygens was instrumental in attributing the
Law to Snell (1678).
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Small angle approximation: Lens-maker's formulas.
1/f = (n-1) ( 1/R1 + 1/R2 )
Fermat's Principle of Least Time (c. 1655)
(2008-01-14)
Birefringence betrays polarization
(Bartholinus, 1669)
Birefringence of Iceland spar (optical calcite, CaCO3 ).
Some transparent minerals like Iceland spar exhibit a strange optical
property known as birefringence.
(2008-01-12)
Brewster's Angle (Malus 1808, Brewster 1815)
One angle of incidence makes the reflected beam 100% polarized.
The full polarization of light by optical reflection at a particular angle of incidence
q was first observed by the French mathematician Etienne-Louis
Malus (1775-1812) in 1808.
The dependence of that angle on the ratio of the two refractive indices involved
was specified by Sir David Brewster
(1781-1868) in 1815:
| q B =
arctan ( n t / n i ) |
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This expression can be derived from Fresnel equations by
imposing Rp = 0.
Snell's Law makes
this equivalent to the observation that Brewster's angle of incidence is
such that the relected and the refracted beam are perpendicular.
Apparently, Malus did not come up with this relation experimentally because
he focused on just the two cases of water and glass. It turns out that the
type of glass available at that time could have surface properties
unrelated to the index of refraction of its bulk.
Brewster was faced with the same puzzle but he could establish the above
general law by considering a variety of transparent minerals and (ultimately) disgarding
the exceptional peculiarities of glass.
(2008-01-12)
Fresnel Equations (1821)
How polarized light is reflected or transmitted by a
planar diopter.
Unlike Snell's Law,
the Fresnel Equations apply specifically to light and involve
the different polarizations of light which
Augustin Fresnel
(1788-1827) firmly established himself in 1821.
What Fresnel determined is that light is entirely a phenomenon of transversal
vibrations without any longitudinal component whatsoever.
This went against the opinion of Thomas Young (1773-1829) who held that light was mostly a
longitudinal phenomenon with only small transversal components.
The Fresnel equations
state quantitatively how the intensity of an incident (i)
light beam is split between a reflected (r)
and a refracted (t) beam.
Traditionally, the linear polarization of an electromagnetic wave
(light) where the electric field is parallel to the plane of incidence
is denoted by the subscript "p" whereas the perpendicular polarization
is denoted by the subscript "s" (the word
senkrecht means "perpendicular" in German).
The Discovery of Polarization
by J. Alcoz.
Fresnel Equations
(8.03
Vibrations and Waves) by Walter Lewin, MIT.
Fresnel
Relations (531
Optics) by Cass Sackett, University of Virginia.
 (2009-03-12)
Stokes Parameters (1852)
A standard description of the
state of polarization.
Wikipedia
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