Foucault invented in 1857 the polarizer which bears his name, and in the succeeding year devised a method of giving to the speculum of reflecting telescopes the form of a spheroid or a paraboloid of revolution.
This latter process is termed analysation, and an instrument is called a polarizer or an analyser according as it is used for the first or the second of these purposes.
Malus that the interposition of a doubly refracting plate between a polarizer and an analyser regulated for extinction has the effect of partially restoring the light, and he used this property to discover double refraction in cases in which the separation of the two refracted streams was too slight to be directly detected.
Arago in 1811 found that in the case of white light and with moderately thin plates the transmitted light is no longer white but coloured, a variation of brightness but not of tint being produced when the polarizer and analyser being crossed are rotated together, while the rotation of the analyser alone produces a change of colour, which passes through white into the complementary tint.
This explanation is incomplete, as it leaves out of account the action of the polarizer and analyser, and it was with the purpose of removing this defect that Fresnel and Arago undertook the investigations mentioned above and thus supplied what was wanting in Young's explanation.
When the retardation of phase for light of mean period is it or a small multiple of it a crystalline plate placed between a crossed polarizer and analyser exhibits in white light a distinctive greyish violet colour, known as a sensitive tint from the fact that it changes rapidly to blue or red, when the retardation is very slightly increased or diminished.
(Reference should be made to the article Crystallography for illustrations, and for applications of these phenomena to the determination of crystal form.) With an uniaxal plate perpendicular to the optic axis, the curves of constant retardation are concentric circles and the lines of like polarization are the radii: thus with polarizer and analyser regulated for extinction, the pattern consists of a series of bright and dark circles interrupted by a black cross with its arms parallel to the planes of polarization and analysation.
With a crossed polarizer and analyser the rings are interrupted by a dark hyperbolic brush that cuts the plane of the optic axes at right angles, if this plane be at 45° to the planes of polarization and analysation - the so-called diagonal position - and that becomes a rectangular cross with its arms parallel and perpendicular to the plane of the optic axes when this plane coincides with the plane of primitive or final polarization - the normal position.
The isochromatic lines, unless the dispersion be excessive, follow in the main the course of the curves of constant retardation, and the principal lines of like polarization are with a crossed polarizer and analyser dark brushes, that in certain cases are fringed with colour.
The examination of dispersion of the optic axes in biaxal crystals (see Refraction, § Double) may be conveniently made with a plate perpendicular to the acute bisectrix placed in the diagonal position for light of mean period between a crossed polarizer and analyser.
The phenomenon of interference produced by crystalline plates is considerably modified if the light be circularly or elliptically polarized or analysed by the interposition of a quarter-wave between the crystal and the polarizer or analyser.
With a combination of plates in plane-polarized and plane-analysed light the interference pattern with monochromatic light is generally very complicated, the dark curves when polarizer and analyser are crossed being replaced by isolated dark spots or segments of lines.
Thus a bar of glass of sufficient thickness, placed in the diagonal position between a crossed polarizer and analyser and bent in a plane perpendicular to that of vision, exhibits two sets of coloured bands separated by a neutral line, the double refraction being positive on the dilated and negative on the compressed side.
In general a stream of plane-polarized light undergoes no change in traversing a plate of an uniaxal crystal in the direction of its axis, and when the emergent stream is analysed, the light, if originally white, is found to be colourless and to be extinguished when the polarizer and analyser are crossed.
If in the interference experiment with Fresnel's mirrors or biprism the slit be illuminated with white light that has passed through a polarizer and a quartz plate cut perpendicularly to the optic axis, it is found on analysing the light that in addition to the ordinary central set of coloured fringes two lateral systems are seen, one on either side of it.
When the polarizer and analyser are parallel or crossed, the pattern is the same as with inactive plates, with the exception that the brushes do not extend to the centre of the field; but as the analyser is rotated a small cross begins to appear at the centre of the field, while the rings change their form and become nearly squares with rounded corners, when the planes of polarization and analysation are at 45°.
If measurements be required, the plate must have a motion round an axis perpendicular to that of the optical systems, and also about an axis normal to its faces; the polarizer and analyser must also be capable of adjustment.
A web in the focal plane of telescope marks the point in the field at which the bands are to be made to disappear; this is effected by turning the polarizer by means of a rack and pinion worked by an arm from the observer's end of the instrument.
The polarizing prism is fixed at the centre of a circular disk, that has a scale on its circumference, which with a fixed vernier determines the positions of the polarizer, for which the bands disappear at the assigned point of the field.
This combination forms a halfshade polarizer, the sensitiveness of which can be varied by a slight adjustment that can be given to the Nicol.
At one end of the instrument is placed a polarizer and the biquartz, and at the other a Galilean telescope, that must be focused on the edge of biquartz, having in front of its object-glass the compensator and an analyser that is regulated for producing the sensitive tint, when the plates of the compensator have the same thickness.
For examining preparations in polarized light a polarizer D is introduced n the illuminating apparatus below the diaphragm and an analyser E ai.
This small plate can also be laid above the polarizer in the illuminating apparatus or in the eyepiece.