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Law of Malus in Polarization with Graph



What is Malus's Law in Polarization

When two pieces of Polaroid are placed in succession along the path of a light wave, the intensity of light received behind the two Polaroids is described by Malus’ Law. The law expresses light intensity, I, as a function of the angle θ which is the angle between the directions of polarization of the two filters. The law can be expressed as follows:

I = Imax cos2θ

where, Imax is the light intensity between the two sheets of Polaroid.

In 1808 Malus from his experiment found that if polarized light, obtained by reflection from a plain glass surface, falls on another reflecting surface at polarizing angle, intensity of reflected light from the lattersurface is directly proportional to the cosine of angle between the two reflecting surfaces (say λ). When the two surfaces are parallel, the intensity is maximum (say Io). Similarly when the surfaces are normal to each other, the intensity is a minimum. Malus found that the output is directly proportional to the irradiance (that is, intensity) of incident light that is Malus Law express as

I = Io cos2θ

malus law polarization

Where, I is the intensity obtained after transmission through analyzer, I0 is the intensity of polarized light obtained through polarizer and θ is the angle between the optic axes of polarizer and analyzer.

Figure demonstrates Malus law using two polaroids for any orientation θ between polarizer and analyzer axes. Figure demonstrates the minimum or zero transmission case for θ = 90º. Similarly transmission will be maximum for θ = 0º. Through direct vision, these positions of maximum and minimum intensity are most readily detectable. The orientation of polarized light can be read using a photo detector.

Polariser and Analyser working in Malus Law Apparatus

polarizer analyzer in malus law

Figure shows polarization of natural light propagating along the x-direction. The analyzer and the polarizer are identical Polaroids, differing only in their orientation. If the electric field vector passing through the polarizer has maximum amplitude Eo, then Eo cosθ is simply the component of electric field that transmits through the analyzer. It means that electric field vector of light passed by the polarizer is oscillates in a plane that makes an angle θ relative to the optic axis of polarizer.