Malusgesetz

Malusgesetz, known in English as Malus’s law, is a principle in optics that describes how the intensity of linearly polarized light changes as it passes through a linear polarizer whose transmission axis is at some angle relative to the light’s polarization direction. For an ideal, monochromatic beam of linearly polarized light, if the angle between the incident polarization and the polarizer’s axis is theta, the transmitted intensity is Iout = Iin cos^2(theta). The angle is measured in radians or degrees, and the relation holds for a single polarization state and an ideal polarizer.

Historically, the law was discovered by Étienne-Louis Malus in 1809 during experiments on the polarization of light and the effects of reflection. Malus’s observations supported the wave theory of light and laid groundwork for quantitative analysis of polarization, later integrated with the broader understanding of anisotropic optical filters.

In classical terms, Malus’s law applies directly to polarized light. If the incident beam is unpolarized, a first polarizer yields a transmitted intensity of Iout = Iin/2, and subsequent polarizers follow Malus’s law with respect to their relative orientations. In quantum terms, a single photon with a polarization state has a probability cos^2(theta) of passing through a polarizer oriented at angle theta to its polarization; repeated trials reproduce the cos^2 dependence on average.

Applications of Malus’s law include the calibration of polarizers, polarization analysis in imaging and spectroscopy, liquid crystal displays, and various optical measurement techniques. Real-world factors such as non-ideal polarizers, broadband or partially polarized light, and depolarization can cause deviations from the ideal cos^2 behavior. See also Malus’s law in polarization.