Brewster's Law

Illustration of the polarization of reflected light incident on a media interface at a Brewster angle

Brewster ’s law is the law of optics expressing the relation between the refractive indices of two dielectrics and the angle of incidence of light at which the light reflected from the interface of the dielectrics will be completely polarized in a plane perpendicular to the plane of incidence. In this case, the refracted beam is partially polarized in the plane of incidence, and its polarization reaches its maximum value (but not 100%, since only part of the light polarized perpendicular to the plane of incidence will be reflected from the boundary, and the remaining part will be part of the refracted beam). The angle of incidence at which the reflected beam is completely polarized is called the Brewster angle ^[1] . When falling at a Brewster angle, the reflected and refracted rays are mutually perpendicular.

This optics phenomenon is named for the Scottish physicist David Brewster , who discovered it in 1815 .

The polarizing effect can be understood if we keep in mind the following:

Oscillations of the electric field in an electromagnetic wave always occur perpendicular to the direction of motion.
Interaction with a dielectric occurs in two stages. Initially, the incident wave generates collective oscillations of the dipole moments of the dielectric molecules, then these oscillations in turn generate a reflected and refracted wave.

So, the reflected wave is generated by vibrations of the dipole moments of the molecules of the medium. When the angle between the reflected and refracted waves is 90 degrees, fluctuations in the electric field of the reflected waves in the plane of incidence could be generated only by oscillations of the dipole moments along the refracted beam. Only the longitudinal component of the electric field oscillations of the refracted beam could induce such oscillations. But since it is not in the refracted beam, it cannot be in the reflected beam either.

Brewster's law is written as:

\operatorname {tg} {{\theta }_{Br}}={{n}_{21}},

{\ displaystyle \ operatorname {tg} {{\ theta} _ {Br}} = {{n} _ {21}},}

{\ displaystyle \ operatorname {tg} {{\ theta} _ {Br}} = {{n} _ {21}},}

Where $n_{21}=n_{2}/n_{1}$ ${\ displaystyle n_ {21} = n_ {2} / n_ {1}}$ ${\ displaystyle n_ {21} = n_2 / n_1}$ Is the refractive index of the second medium relative to the first, and ${{\theta }_{Br}}$ ${\ displaystyle {{\ theta} _ {Br}}}$ ${\ displaystyle {{\ theta} _ {Br}}}$ - angle of incidence (Brewster angle).

When light falls on one plate at a Brewster angle, the intensity of the reflected linearly polarized light is very small (for the air-glass interface, about 4% of the intensity of the incident beam). Therefore, in order to increase the intensity of the reflected light (or to polarize the light transmitted into the glass in a plane parallel to the plane of incidence), several fastened plates stacked in the foot - Stoletov's foot are used. It is easy to trace what is happening in the drawing. Let a ray of light fall on the upper part of the foot. A completely polarized beam (about 4% of the initial intensity) will be reflected from the first plate, a completely polarized beam (about 3.75% of the initial intensity) will be reflected from the second plate, and so on. In this case, the beam emerging from the foot from below will be more and more polarized in a plane parallel to the plane of incidence, as the plates are added. The effect of Stoletov's foot on light is clearly shown in one of the films on the polarization of light ^[2] .

Two photos of the lake. Black made by the camera without a polarizing filter and with it. In the right photo, it is rotated so that the reflected light is almost completely filtered out and the glare disappears.

Brewster's law can be derived from Fresnel formulas describing the dependence of the amplitude, phase, and polarization of the reflected and refracted light waves on the corresponding characteristics of the wave incident on the interface of dielectrics.

Content

1 Full refraction
2 notes
3 Literature
4 References

Full refraction

Full refraction is the effect that manifests itself when transverse plane - polarized waves fall on the interface of dissimilar media, and consists in the absence of a reflected wave . The effect can be observed only in the case of a drop in the flux of a vertically polarized wave (the direction of the electromagnetic field vector is in the plane of incidence) at the interface at a Brewster angle. In this case, according to the law of refraction, only horizontally polarized components will be contained in the reflected stream, and since the incident stream did not contain horizontally polarized waves, the reflected stream will be absent. Thus, all the energy of the incident stream will be in the refracted waves.

The concept of total refraction is important for radio communications : most whip antennas emit exactly vertically polarized waves. Thus, if the wave falls on the interface (earth, water or the ionosphere ) at the Brewster angle, there will be no reflected wave, respectively, there will be no communication channel.

Notes

↑ Brewster's Law - an article in the Physical Encyclopedia.
↑ Light polarization (neopr.) (Film strip (digitized video clip)). Studio Lennauchfilm (1981).

Literature

Sivukhin D.V. General course of physics. - M. - T. IV. Optics.
Born M., Wolf E. Fundamentals of Optics. - M .: Science, 1973.

Links

[1] Brewster's Law - an article in the Physical Encyclopedia.

[2] Light polarization (neopr.) (Film strip (digitized video clip)). Studio Lennauchfilm (1981).