The polarization of light
§ 1 The natural and polarized light
The emission of a photon of light is due to the transition of an
electron from the excited state to the ground. The electromagnetic
waves emitted by this transition is transverse, that is a vector and are mutually perpendicular and perpendicular to the direction of propagation. Oscillations of the vector пare in the same plane. Light, in which vector oscillates in one direction is called a plane-polarized light (or electromagnetic wave). Called polarized light, in which the direction of oscillation of the vector
are ordered in some way.
is electromagnetic radiation of the total set of atoms. Atoms emit
light waves independently of each other, so the light wave emitted by
the body as a whole, is characterized by all sorts of vibrations of the
light vector .equally. Light with all kinds of equally probable orientations vectoris natural. Light, which has a preferred direction of oscillation of the vector and small amplitude oscillations of the vector in the other direction is a partially polarized. In plane polarized light plane that varies vector ,called the plane of polarization, plane, which varies vector ,called the plane of oscillation.
Vector is a light
vector, because the action of light on the matter of primary importance
is the electric component of the wave field acting on the electrons in
the atoms of the substance.
A distinction is also elliptically polarized light: the propagation of electrically polarized light vector describes an ellipse, and circularly polarized light
(a special case of elliptically polarized light) - a vector describes a
circle (compare with the addition of perpendicular oscillations are
possible: straight line, an ellipse and a circle).
The degree of polarization is the quantity
where Imax and Imin - maximum and minimum components of the light intensity corresponding to two mutually perpendicular components of the vector (ie, Ех and Еу - components). For the plane of polarized light Еу = Е, Ех = 0, so P = 1. For natural light Еу = Ех = Е and Р = 0. For partially polarized light Еу = Е, Ех = (0...1)Еу, hence 0 < P <1.
If the vector
into elliptically polarized light is rotated when the light propagates
in a clockwise direction, the polarization is called right - against
the left. In elliptically polarized light vibrations completely
ordered. For elliptically polarized light concept of the degree of
polarization is not applicable, so that P = 1 always.
§ 2 The analysis of polarized light by reflection and refraction.
Brewster's law. Malus law
Most simply polarized light can be obtained from natural light by reflection of light waves from the boundary between two dielectrics.
light is incident on the boundary between two dielectrics (eg,
air-to-glass), then part of it is reflected and part is refracted and
propagates in the second medium.
At an angle of incidence equal to the Brewster angle іBr:
1. reflected from the boundary between two dielectric beam is
completely polarized in the plane perpendicular to the plane of
incidence, 2. the degree of polarization of the refracted beam reaches a
maximum value less than unity, 3. refracted ray is partially
polarized in the plane of incidence, 4. the angle between the reflected
and refracted rays is equal to 90°; 4. Brewster angle is equal to the
tangent of the relative refractive index
the refractive index of the second medium with respect to the first.
The angle of incidence (reflection) - the angle between the incident
(reflected) ray and the normal to the surface. The plane of incidence -
the plane through the incident ray and the normal to the surface.
The degree of polarization of the refracted light can be significantly
enhanced by repeated refraction of the condition of the light on the
boundary between at the Brewster angle. If the glass (n =
1,53) the degree of polarization of the refracted beam is ≈ 15%, after
refraction at 8-10 overlapping glass plates, the light will be
released almost completely polarized - ream Stoletov.
Polarized light can be obtained from a natural with polarizers -
anisotropic crystals transmit light in only one direction (Iceland spar,
Polarizer, which is analyzed in the plane of polarized light, is called by the analyzer.
If on analyzer is an incident plane polarized light amplitude Е0 and intensity I0 (), the plane of polarization is at an angle φ
with the plane of the analyzer, the incident electromagnetic
oscillation can be decomposed into two vibrations, with amplitudes and ,
parallel and perpendicular to the plane of the analyzer.
Pass through the analyzer component parallel to the plane of the analyzer, it is a constituent
the perpendicular component will be delayed by the analyzer. Then the
intensity of the light transmitted through the analyzer is ():
The law of Malus
The intensity of the light transmitted through the polarizer, is
directly proportional to the product of the intensity of the incident
plane polarized light I0 and to the square of the cosine of the angle between the plane of the incident light and the plane of the polarizer.
If on polarizer falls natural light, the intensity of light emerging from the polarizer is half Inat I0, and then from the analyzer exit
All crystals, except for cubic crystals -isotropic crystals, are
anisotropic, that is, the properties of crystals depend on the
direction. The phenomenon of double refraction was first discovered in
1667 Bartalinom a crystal of Iceland spar (a form of СаСО3).
The phenomenon of of birefringence is: a beam of light falling on an
anisotropic crystal, it is split into two beams: ordinary and
extraordinary, propagating at different speeds в различных направлениях.
Anisotropic crystals are divided into uniaxial and biaxial.
uniaxial crystals in the same direction, called the optical axis,
along which the distribution is no distinction between ordinary and
extraordinary rays. Any line parallel to the direction of the optical
axis will also be the optical axis. Any plane passing through the
optical axis and the incident beam, called the principal or main
section of the crystal planes.
Distinction between ordinary and extraordinary rays:
- ordinary ray obeys the laws of refraction extraordinary - no;
is polarized perpendicular to the principal plane, the plane of
polarization of the extraordinary ray is perpendicular to the plane
polarized ordinary ray;
Besides the optical axis of the ordinary and extraordinary rays are distributed in different directions. The refractive index n0
ordinary ray is constant in all directions, therefore, the phase
velocity of the ordinary ray is constant in all directions. The
refractive index of the extraordinary ray ne (vph.e.) depends on the direction.
Speed ??difference between v0 and ve
for all directions except the direction of the optical axis, causes
the phenomenon of double refraction in uniaxial crystals. In biaxial
crystals, there are two directions along which there is no double
The concept of
the ordinary and extraordinary rays takes place until the rays
propagate in the crystal, when the output of the crystal these concepts
have no meaning, that is, the rays differ only in the plane of
The nature of the birefringence due to the fact that the ordinary and extraordinary rays have different speeds, as well as ,for the ordinary and extraordinary rays will have different refractive indices n0 and nе, and since then we can say that the root cause of birefringence is the anisotropy of the dielectric constant of the crystal. Crystals in which vе < v0 ( nе > n0)) called positive and who vе > v0 (nе < n0) are called negative.