What is Brewster's law? Derive the formula for Brewster angle.
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Answer:
Brewster's law: The tangent of the polarizing angle is equal to the refractive index of the reflecting medium with respect to the surrounding (1n2). Here n1 is the absolute refractive index of the surrounding and n2 is that of the reflecting medium. The angle θB is called the Brewster angle.
Brewster's angle or angle of polarization is defined as the angle of incidence at which light with a specific polarization is perfectly transmitted without any reflection through a transparent dielectric surface. In other words, the light incident at this angle, when reflects back, is perfectly polarized.
(David) Brewster's law is related to the polarization of light rays. Brewster angle θ
B
is the angle of incidence for a light ray polarized in a certain way p and of a given wavelength, for which there is no reflection of light from the boundary. All the light is perfectly transmitted through the transparent second medium. Brewster angle is also called the polarization angle.
Usually the reflected ray is partially polarized in the electric field. The reflected ray is polarized too. If an Unpolarized light ray is incident on the interface boundary (planar) of medium 1 and medium 2 at this angle θ
B
, the the reflected ray is perfectly polarized.
We prove Brewster's law by a simple qualitative method. Assume light rays are produced by oscillating electrical dipoles. They are absorbed by molecules (oscillating dipoles) at the surface of the boundary. They are then reflected (re-radiated) and retransmitted to pass through by these dipoles. Light rays are polarized in a direction perpendicular to the direction of propagation. Let us say incident rays are p polarized.
We know that the transmitted light rays are polarized in the same direction as the incident light. Dipoles do not radiate any light rays in the direction of the dipole moment. If the angle i and rare such that the angle BOC is 90 deg, then refracted light is in the direction perpendicular to transmitted ray. As transmitted ray is p polarized. The direction of orientation of dipoles (dipole moment) will be in the direction expected reflected ray OB. Since dipoles are also along OB, there will not be any radiation in that direction now.
