section_path: Classical optics/Physical optics/Polarisation/Changing polarisation
section_name: Changing polarisation
paragraph_text: Changing polarisation
  
  Media that have different indexes of refraction for different polarisation modes are called birefringent. Well known manifestations of this effect appear in optical wave plates /retarders (linear modes) and in Faraday rotation / optical rotation (circular modes). If the path length in the birefringent medium is sufficient, plane waves will exit the material with a significantly different propagation direction, due to refraction. For example, this is the case with macroscopic crystals of calcite, which present the viewer with two offset, orthogonally polarised images of whatever is viewed through them. It was this effect that provided the first discovery of polarisation, by Erasmus Bartholinus in 1669. In addition, the phase shift, and thus the change in polarisation state, is usually frequency dependent, which, in combination with dichroism, often gives rise to bright colours and rainbow-like effects. In mineralogy, such properties, known as pleochroism, are frequently exploited for the purpose of identifying minerals using polarisation microscopes. Additionally, many plastics that are not normally birefringent will become so when subject to mechanical stress, a phenomenon which is the basis of photoelasticity. Non-birefringent methods, to rotate the linear polarisation of light beams, include the use of prismatic polarisation rotators which use total internal reflection in a prism set designed for efficient collinear transmission.
  
  Media that reduce the amplitude of certain polarisation modes are called dichroic, with devices that block nearly all of the radiation in one mode known as polarising filters or simply " polarisers ". Malus' law, which is named after Étienne-Louis Malus, says that when a perfect polariser is placed in a linear polarised beam of light, the intensity, I, of the light that passes through is given by
  
  I = I 0 cos 2 θ i, {\displaystyle I=I_{0}\cos ^{2}\theta _{\mathrm {i} },} where I is the initial intensity, and θ is the angle between the light's initial polarisation direction and the axis of the polariser.
  
  A beam of unpolarised light can be thought of as containing a uniform mixture of linear polarisations at all possible angles. Since the average value of cos θ is 1/2, the transmission coefficient becomes
  
  I I 0 = 1 2. {\displaystyle {\frac {I}{I_{0}}}={\frac {1}{2}}\,.}
  
  In practice, some light is lost in the polariser and the actual transmission of unpolarised light will be somewhat lower than this, around 38% for Polaroid-type polarisers but considerably higher (>49.9%) for some birefringent prism types.
  
  In addition to birefringence and dichroism in extended media, polarisation effects can also occur at the (reflective) interface between two materials of different refractive index. These effects are treated by the Fresnel equations. Part of the wave is transmitted and part is reflected, with the ratio depending on the angle of incidence and the angle of refraction. In this way, physical optics recovers Brewster's angle. When light reflects from a thin film on a surface, interference between the reflections from the film's surfaces can produce polarisation in the reflected and transmitted light.