119 research outputs found
Generalized composition law from 2x2 matrices
Many results that are difficult can be found more easily by using a
generalization in the complex plane of Einstein's addition law of parallel
velocities. Such a generalization is a natural way to add quantities that are
limited to bounded values. We show how this generalization directly provides
phase factors such as the Wigner angle in special relativity and how this
generalization is connected in the simplest case with the composition of 2x2 S
matrices.Comment: Accepted for publication in Am. J. Phy
Composition law for polarizers
The polarization process when polarizers act on an optical field is studied.
We give examples for two kinds of polarizers. The first kind presents an
anisotropic absorption - as in a polaroid film - and the second one is based on
total reflection at the interface with a birefringent medium. Using the Stokes
vector representation, we determine explicitly the trajectories of the wave
light polarization during the polarization process. We find that such
trajectories are not always geodesics of the Poincar\'e sphere as it is usually
thought. Using the analogy between light polarization and special relativity,
we find that the action of successive polarizers on the light wave polarization
is equivalent to the action of a single resulting polarizer followed by a
rotation achieved for example by a device with optical activity. We find a
composition law for polarizers similar to the composition law for noncollinear
velocities in special relativity. We define an angle equivalent to the
relativistic Wigner angle which can be used to quantify the quality of two
composed polarizers.Comment: 23 pages, 9 figures, accepted for publication in Physical Review
The cosmological constant and the coincidence problem in a new cosmological interpretation of the universal constant c
In a recent paper (Vigoureux et al. Int. J. Theor. Phys. 47:928, 2007) it has
been suggested that the velocity of light and the expansion of the universe are
two aspects of one single concept connecting space and time in the expanding
universe. It has then be shown that solving Friedmann's equations with that
interpretation (and keeping c = constant) can explain number of unnatural
features of the standard cosmology (for example: the flatness problem, the
problem of the observed uniformity in term of temperature and density of the
cosmological background radiation, the small-scale inhomogeneity problem...)
and leads to reconsider the Hubble diagram of distance moduli and redshifts as
obtained from recent observations of type Ia supernovae without having to need
an accelerating universe. In the present work we examine the problem of the
cosmological constant. We show that our model can exactly generate
(equation of state with ) contrarily to the standard model which cannot generate it exactly. We
also show how it can solve the so-called cosmic coincidence problem
Fresnel coefficients as hyperbolic rotations
We describe the action of a plane interface between two semi-infinite media
in terms of a transfer matrix. We find a remarkably simple factorization of
this matrix, which enables us to express the Fresnel coefficients as a
hyperbolic rotation.Comment: 6 pages, 3 figure
Constructing Fresnel reflection coefficients by ruler and compass
A simple and intuitive geometical method to analyze Fresnel formulas is
presented. It applies to transparent media and is valid for perpendicular and
parallel polarizations. The approach gives a graphical characterization
particularly simple of the critical and Brewster angles. It also provides an
interpretation of the relation between the reflection coefficients for both
basic polarizations as a symmetry in the plane
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