The Fresnel–Arago laws are three laws which summarise some of the more important properties of
interference
Interference is the act of interfering, invading, or poaching. Interference may also refer to:
Communications
* Interference (communication), anything which alters, modifies, or disrupts a message
* Adjacent-channel interference, caused by extr ...
between light of different states of
polarization.
Augustin-Jean Fresnel
Augustin-Jean Fresnel (10 May 1788 – 14 July 1827) was a French civil engineer and physicist whose research in optics led to the almost unanimous acceptance of the wave theory of light, excluding any remnant of Newton's corpuscular th ...
and
François Arago, both discovered the laws, which bear their name.
The laws are as follows:
# Two
orthogonal,
coherent
Coherence, coherency, or coherent may refer to the following:
Physics
* Coherence (physics), an ideal property of waves that enables stationary (i.e. temporally and spatially constant) interference
* Coherence (units of measurement), a deri ...
linearly
polarized waves cannot interfere.
# Two parallel coherent linearly polarized waves will interfere in the same way as
natural light
Natural Light, sometimes Natty Light, is an American reduced-calorie light lager brewed by Anheuser-Busch since its introduction on July 31, 1977. Its ingredients are listed as water, barley malt, cereal grains, yeast, and hops. One serving c ...
.
# The two constituent orthogonal linearly polarized states of natural light cannot interfere to form a readily observable interference pattern, even if rotated into alignment (because they are incoherent).
One may understand this more clearly when considering two waves, given by the form
and
, where the boldface indicates that the relevant quantity is a
vector
Vector most often refers to:
*Euclidean vector, a quantity with a magnitude and a direction
*Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism
Vector may also refer to:
Mathematic ...
, interfering. We know that the
intensity of light goes as the electric field squared (in fact,
, where the angled brackets denote a time average), and so we just add the fields before squaring them. Extensive algebra
[Optics, Hecht, 4th edition, pp. 386-7] yields an interference term in the intensity of the resultant wave, namely:
, where
represents the
phase difference
In physics and mathematics, the phase of a periodic function F of some real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is denoted \phi(t) and expressed in such a scale that it v ...
arising from a combined
path length and initial phase-angle difference.
Now it can be seen that if
is perpendicular to
(as in the case of the first Fresnel–Arago law),
and there is no interference. On the other hand, if
is parallel to
(as in the case of the second Fresnel–Arago law), the interference term produces a variation in the light intensity corresponding to
. Finally, if natural light is decomposed into orthogonal linear polarizations (as in the third Fresnel–Arago law), these states are incoherent, meaning that the phase difference
will be fluctuating so quickly and randomly that after time-averaging we have
, so again
and there is no interference (even if
is rotated so that it is parallel to
).
References
Interference
Polarization (waves)
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