The Faraday Effect - Theory
In 1845, Michael Faraday in his laboratory at the Royal Institute, discovered the magneto-optic effect. He observed after trying many subjects as media, that polarized light traveling through a substance which is exposed to a strong magnetic field will have its plane of polarization rotated. This effect was later named after him: The Faraday Effect.
From Cosmos 2.0, 'The Electric Boy', Michael Faraday applies current to an electromagnet applying the magneto-optic effect on a piece of flint glass, which in turn changes the angle of the plane of polarization of a light beam. 
The importance of this discovery is that it demonstrated for the first time a relation between light and electricity and magnetism. The amount of rotation of the plane of polarization depends on three things: the magneto-optical properties of the material that the light traverses, the length of the path of travel through the material, and the strength of the magnetic field.
In addition, the magneto-optical properties of a substance are dependent on the wavelength of the light and the temperature of the substance. A single value can be attributed to the magneto-optical properties of a material at a given temperature acting upon a specific wavelength of light.
- Under what circumstances might the temperature of a substance NOT remain constant?
- What difficulties would this present in trying to assign numerical values to the magneto-optical properties of a substance? Or in measuring the angle of rotation?
The magneto-optical properties of a substance at a given temperature and interacting with a given wavelength of light is called the Verdet constant.
In mathematical terms, the angle of rotation is equal to the product of the Verdet constant, the length of the material, and the strength of the magnetic field. 
This can be expressed as:
Δ = VℓB
|Δ||radians (rad)||the angle of rotation of polarized light|
|V||radians per Tesla meter (rad)/(T)(m)||the magneto-optical property of the substance for a given wavelength of light and temperature is named after the French physicist Émile Verdet.|
|ℓ||meters (m)||the length of the substance|
|B||Tesla (T)||the strength of the magnetic field parallel to the direction of light travel|
Visually, Faraday Rotation can be conceptualized below. Incoming light at a single wavelength enters from the left. Imagine that it is polarized nearly vertically (zero degrees). It enters a substance that is ℓ meters in length and with a Verdet constant of V. Along the direction of travel the magnetic field strength is B Teslas.
The resulting rotation of the polarization angle is Δ:
Conceptual diagram of a beam of polarized monochromatic light. If it passes through a substance with a known Verdet constant, length and applied magnetic field strength, the rotation of its angle of polarization can be calculated. 
- How would you approach calculating the angle of rotation for light traveling through different layers of several substances (assuming everything else was constant)? Consider, for example, a stack of glass plates with different optical properties.
- What happens to a light beam that travels through a substance with blended wavelengths?
- Suppose that you have a lab apparatus with known physical parameters of Δ, V, ℓ, B. If you doubled the magnetic field strength, what would happen to the angle of rotation?
- By what measure would you have to increase the field strength in order for the angle of rotation
to come full circle?
(That is, an angle measuring Δ + 2π radians) ?
- Can you think of a procedure you could employ that would determine if the angle of rotation was simple, or a multiple addition of 2π ?
Besides the historical significance of Michael Faraday's discovery, the study of the Faraday Effect allows for many interesting investigations. Here are just a few:
- Physicists in Palestine and Iraq have discovered that certain kinds of premium virgin olive oil have characteristically high Verdet values. They have developed methods to measure the Verdet constants of samples of olive oil to determine their place of origin, shelf life, storage conditions and authenticity. 
- Astronomers at the European Southern Observatory have used the Faraday Effect to determine the magnetic field strength near the vicinity of super massive black holes in other galaxies. 
- Consider that some materials are opaque to light in the visible spectrum. Can you think of any applications involving non-visible light, such as x-rays?
 Druyan, A., Sagan, C., & Soter, S. (2014). The electric boy. In Cosmos: A spacetime odyssey.
 Suchat, S., Viriyavathana, P., Jaideaw, P., Haisirikul, N., Kerdsang, W., & Petcharavut, S. (2011). Progress in electromagnetics research symposium proceedings. In Measurement of the verdet constant in different mediums by using ellipsometry technique (pp. 803-806). Suzhou, China.
 Adapted from an illustration on wikipedia.org, http://en.wikipedia.org/wiki/Faraday_effect#/media/File:Faraday-effect.svg
 Abu-Taha, M. I., Halasa, M. A., & Abu-Samreh, M. M. (2013). On the usage of the faraday effect as an authentication technique for vegetable oils. Journal of Modern Physics, 04(02), 230-235. doi:10.4236/jmp.2013.42032
 Shakir, A. A., AL-Mudhafa, R. D., & Al-Dergazly, A. A. (2013). Verdet constant measurement of olive oil for magnetic field sensor. International Journal of Advances in Electrical and Electronics Engineering, 2(3), 362-368. Retrieved from http://www.sestindia.org/volume-ijaeee/.
 ALMA Reveals Intense Magnetic Field Close to Supermassive Black Hole. (2015, April 16). eso1515. Retrieved from http://www.eso.org/public/news/eso1515/