
The Faraday effect is the rotation of the plane of polarization of light in a material under a magnetic field.In 1845, Michael Faraday sought a connection between light and magnetism and discovered that heavy glass placed in a strong magnetic field changes the polarization of transmitted light. This became the first proof of the unity of electromagnetism. Essentially, the magnetic field makes the medium anisotropic for light — as if light were forced to go up a spiral staircase where one turn is steeper than the other.
Discovered by Michael Faraday in 1845 after years of trying to detect the influence of magnetism on light. Experimenting with samples of heavy flint glass (lead glass) placed between the poles of a powerful electromagnet, he noticed the rotation of the plane of polarization. This phenomenon, along with the discovery of electromagnetic induction, formed the basis of the concept of the unified nature of electricity, magnetism, and light, later developed by James Clerk Maxwell.
Used in optical isolators (valves) to prevent back-reflections in laser systems, circulators, and modulators. In astrophysics, measurement of Faraday rotation from pulsars and radio sources is used to map magnetic fields in the interstellar and intergalactic medium. Limits of applicability: limited by medium transparency and saturation in strong fields; applicable from radio to ultraviolet radiation.
Allows building optical isolators in lasers and measuring magnetic fields in the interstellar medium.
Faraday had been trying to find the effect for several years unsuccessfully until he took super-transparent lead glass from a chandelier. It turned out that ordinary glass gave too weak a rotation.
| Δθ | variable | Rotation angle of polarization plane — polarization rotation angle radian |
| λ | variable | Wavelength of light — wavelength metre |
| RM | constant | Rotation measure, proportional to integrated electron density times magnetic field along the line of sight — rotation measure = varies (e.g., 0.812 rad m^-2 for typical radian per metre squared |
| n_e | variable | electron number density — electron number density per cubic metre |
| B_parallel | variable | magnetic field component along line of sight — magnetic flux density tesla |
| dl | variable | infinitesimal path element along line of sight metre |
| e | constant | elementary charge — elementary charge = 1.602176634e-19 coulomb |
| m_e | constant | electron rest mass — electron mass = 9.1093837015e-31 kilogram |
| c | constant | speed of light in vacuum — speed of light = 299792458 metre per second |
| ∫ | operator | summation over the line of sight — integral operator |
| p_m | variable | observed polarization degree — polarization degree |
| p_0 | variable | intrinsic polarization degree (without Faraday effects) — polarization degree |
| σ_RM | variable | dispersion of rotation measure along the line of sight — rotation measure dispersion radian per square metre |
| λ | variable | wavelength of radiation — wavelength metre |
| exp | operator | exponential function — exponential |
| RM | variable | Rotation measure — rotation measure radian per metre squared |
| n_e | variable | Electron number density — number density per metre cubed |
| B_parallel | variable | Magnetic field component along line of sight — magnetic field tesla |
| s | variable | Path length along line of sight — length metre |
| L | variable | Total path length through plasma — length metre |
| e | constant | Charge of a single electron — elementary charge = 1.602176634e-19 coulomb |
| m_e | constant | Rest mass of an electron — electron mass = 9.1093837015e-31 kilogram |
| c | constant | Speed of light in vacuum — speed of light = 299792458 metre per second |
| ∫ | operator | Integration along the line of sight — integral operator |



















