Brewster's angle
From Free net encyclopedia
Image:Brewsters-angle.png Brewster's angle (also known as the polarization angle) is an optical phenomenon named after the Scottish Physicist, Sir David Brewster (1781–1868).
When light moves between two media of differing refractive index, light which is p-polarized with respect to the interface will not be reflected from the interface at one particular incident angle, known as Brewster's angle, θB.
A physical mechanism for this follows from the manner in which the dipoles in the media respond to p-polarized light. The direction of polarization is always perpendicular to the direction the light is travelling in. The electric dipoles in the media oscillate in the direction of the polarization of the transmitted (refracted) light. The oscillating dipoles radiate, which creates the reflected light. However, dipoles do not radiate any energy in the direction they oscillate along. Consequently, if the direction of the refracted light is perpendicular to the direction in which the light is predicted to be specularly reflected, the dipoles will not create any reflected light. Since, by definition, the s-polarization is parallel to the interface, the corresponding oscillating dipoles will always be able to radiate in the specular-reflection direction. This is why there is no Brewster's angle for s-polarized light.
With simple trigonometry this condition can be expressed as:
- <math> \theta_1 + \theta_2 = 90^\circ,</math>
where θ1 is the angle of incidence and θ2 is the angle of refraction.
Using Snell's law,
- <math>n_1 \sin \left( \theta_1 \right) =n_2 \sin \left( \theta_2 \right),</math>
we can calculate the incident angle θ1=θB at which no light is reflected:
- <math>n_1 \sin \left( \theta_B \right) =n_2 \sin \left( 90 - \theta_B \right)=n_2 \cos \left( \theta_B \right).</math>
Rearranging, we get:
- <math>\theta_B = \arctan \left( \frac{n_2}{n_1} \right), </math>
where n1 and n2 are the refractive indices of the two media. This equation is known as Brewster's law.
Note that, since all p-polarized light is refracted, any light reflected from the interface at this angle must be s-polarized. A glass plate or a stack of plates placed at Brewster's angle in a light beam can thus be used as a polarizer.
For a glass medium (n2≈1.5) in air (n1≈1), Brewster's angle for visible light is approximately 56° to the normal. Since the refractive index for a given medium changes depending on the wavelength of light, Brewster's angle will also vary with wavelength.
The phenomenon of light being polarized by reflection from a surface at a particular angle was first observed by Etienne-Louis Malus in 1808. He attempted to relate the polarizing angle to the refractive index of the material, but was frustrated by the inconsistent quality of glasses available at that time. In 1815, Brewster experimented with higher-quality materials and showed that this angle was a function of the refractive index, defining Brewster's law.