Editing Optics (section)

=====Changing polarisation=====
Media that have different indexes of refraction for different polarisation modes are called ''[[birefringence|birefringent]]''.{{sfnp|Young|Freedman|2020|p=1124}} Well known manifestations of this effect appear in optical [[wave plate]]s/retarders (linear modes) and in [[Faraday rotation]]/[[optical rotation]] (circular modes).{{sfnp|Hecht|2017|pp=367,373}} 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]].{{sfnmp |1a1=Hecht|1y=2017|1p=372 |2a1=Young|2a2=Freedman|2y=2020|2pp=1124–1125}} Non-birefringent methods, to rotate the linear polarisation of light beams, include the use of prismatic [[polarisation rotator]]s which use total internal reflection in a prism set designed for efficient collinear transmission.<ref>{{cite book |author=F.J. Duarte |author-link=F. J. Duarte |title=Tunable Laser Optics |edition=2nd |publisher=CRC |year=2015 |location=New York |pages=117–120 |isbn=978-1-4822-4529-5 |url=http://www.tunablelaseroptics.com |url-status=live |archive-url=https://web.archive.org/web/20150402145942/https://www.tunablelaseroptics.com/ |archive-date=2015-04-02 }}</ref>

[[File:Malus law.svg|class=skin-invert-image|right|thumb|upright=1.6|A polariser changing the orientation of linearly polarised light. In this picture, {{math|1= ''θ''{{sub|1}} – ''θ''{{sub|0}} = ''θ''{{sub|i}}}}.]]

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 "[[polariser]]s". 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, {{mvar|I}}, of the light that passes through is given by

<math display="block"> I = I_0 \cos^2 \theta_\mathrm{i} ,</math>
where {{math|''I''{{sub|0}}}} is the initial intensity, and {{math|''θ''{{sub|i}}}} is the angle between the light's initial polarisation direction and the axis of the polariser.{{sfnmp |1a1=Hecht|1y=2017|1p=338 |2a1=Young|2a2=Freedman|2y=2020|2pp=1119–1121}}

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 {{math|cos{{sup|2}} ''θ''}} is 1/2, the transmission coefficient becomes

<math display="block"> \frac {I}{I_0} = \frac {1}{2}\,.</math>

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.{{sfnp|Hecht|2017|pp=339–342}}

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]].{{sfnp|Hecht|2017|pp=355–358}} When light reflects from a [[Thin-film optics|thin film]] on a surface, interference between the reflections from the film's surfaces can produce polarisation in the reflected and transmitted light.