Brewster's Law

Brewster's law

[¦brü·stərz ¦lȯ]
The law that the index of refraction for a material is equal to the tangent of the polarizing angle for the material.

Brewster’s Law


a law that expresses the connection of the index of refraction of a dielectric with an angle of incidence of light or radio waves such that the radiation reflected from the surface of the dielectric is completely polarized. The law was established by D. Brewster in 1815. According to Brewster’s law, natural, nonpolarized light falling on the surface of a dielectric at an angle φ for which the condition tan φ= n is fulfilled (where n is the index of refraction) is completely polarized upon reflection. The angle φ is called the Brewster angle. The angle between the reflected and refracted beams in this case is 90° (see Figure 1).

The elementary physical explanation of Brewster’s law is as follows: the electrical field Ei of the incident light wave [its components are (Ep)i in the plane of incidence and (Es)1 perpendicular to it] causes electron oscillations in the dielectric whose direction coincides with that of the electrical vector of the refracted wave Erefr. These oscillations excite on

Figure 1. Brewster’s law

the section’s surface a reflected wave Er, which propagates in the first medium. However, the oscillating electron does not radiate in the direction of its own oscillations. Thus, in the reflected light wave the oscillations of the electrical field (Es)r) take place only in a plane perpendicular to the plane of incidence.

Brewster’s law is of an approximate nature: experiments show deviations from the law to a greater or lesser degree, caused by the structural peculiarities of the dielectric’s surface.

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