# Archimedes to Hawking: Laws of Science and the Great Minds behind Them

By Clifford A. Pickover | Go to book overview

BREWSTER’S LAW OF LIGHT
POLARIZATION

Scotland, 1815. The amount of the polarization of light reflected from a transparent surface is a maximum when the reflected ray is at right angles to the refracted ray.

CROSS REFERENCE: SNELL’S LAW AND WILLIAM LAWRENCE BRAGG.

In 1815, the first commercial cheese factory was founded in
Switzerland. Napoleon abdicated and Louis XVIII returned to
Paris. Brazil declared itself a kingdom “equal” to Portugal.

A light wave consists of an electric field and a magnetic field that oscillate perpendicular to each other and to the direction of travel. Usually, the electric vector of light vibrates in all directions. However, it is possible to restrict the vibrations of the electric field by plane-polarizing the light beam. For example, one may pass the light through oriented dichroic crystals in a plastic film so that the electric field in one direction is almost completely absorbed, while a large fraction of the electric field in a direction perpendicular to the absorbed component is transmitted. (More generally, “dichroic” often refers to a material in which light in different polarization states experiences a varying absorption as it travels through the material.)

Another approach for obtaining plane-polarized light is via the reflection of light from a surface between two media such as air and glass. The component of the electric field parallel to the surface is most strongly reflected. At one particular angle of incidence on the surface, called the Brewster angle, the reflected beam consists entirely of light whose electric vector is parallel to the surface—and the reflected and refracted beams are at right angles. The Brewster angle can be found by

where n1 and n2 are the refractive indices of the two media. This equation is one way to express Brewster’s Law. (See “Snell’s Law of Refraction” in part I for an explanation of refraction, which is exemplified by the bending of light when it passes from one material into another.)

For the example of shining light from air onto glass, n2 is approximately equal to 1.5 for glass, and n1 is approximately equal to 1 for air. We find that Brewster’s angle for visible light is approximately 56° to the normal of the glass surface, where the term “normal” refers to an imaginary line perpendicular to the surface. Because the refractive index for a given

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