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.
The analyser can be rotated, the angle being read by a divided circle F.
A spectroscope may be compared to a mechanical harmonic analyser which when fed with an irregular function of one variable represented by a curve supplies us with the sine curves into which the original function may be resolved.
This analogy is useful because the application of Fourier's analysis to the optical theory of spectroscopes has been doubted, and it may be urged in answer to the objections raised that the instrument acts in all respects like a mechanical analyser,' the applicability of which has never been called into question.
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.
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.
When, however, a plate of quartz is used in this experiment, the light is coloured and is in no case cut off by the analyser, the tint, however, changing as the analyser is rotated.
Righi has, however, pointed out that this experiment may be explained by the fact that the function of the quartz plate and analyser is to eliminate the constituents of the composite stream of white light that mask the interference actually occurring at the positions of the lateral systems of fringes, and that any other method of removing them is equally effective.
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°.
Planes of the plate: the plane of polarization is determined by turning the analyser until the bands, ordinarily seen, disappear,.
The field is divided into two parts that for most positions of the analyser have different intensities, and the setting is effected by turning the analyser until both halves are equally dark.
The more usual half-shade analyser is available for light of only one frequency, as it depends upon the action of a half-wave plate, in traversing which the plane of polarization is turned until it makes the same angle with the principal section as at first but on the opposite side: half the field is covered with the plate, to which is attached a Nicol's prism with its principal section inclined at a small angle to that of the plate.
One method consists in finding directly the elliptic constants of the vibration by means of a quarterwave plate and an analyser; but the more usual plan is to measure the relative retardation of two rectangular components of the stream by a Babinet's compensator.
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.
The light is finally received in a Galilean telescope, containing an analyser and carried at the centre of a circular plate, that is graduated on its rim and can be turned in front of a vernier by means of a rack and pinion.
If then a stream of polarized white light traverse the biquartz, it is possible by an analyser to cut off the mean yellow light from each half of the field, and the whole will then have the sensitive tint; but a small change in the plane of analysation will give the one half a red and the other half a blue tone.
A rotation of the plane of polarization is not, however, measured by an adjustment of the analyser, but by annulling the rotation with a compensator.
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.
Very often the analyser is placed in the tube, a little above the objective: it is then generally in a case G, which can be put into the tube.
The placing of the analyser near the objective has the advantage that the field of view is not restricted, as is the case if the analyser .is used above the eyepiece.
Below the analyser G a plate H of selenite or mica may be put in the course of the rays.
Thomson's tide gauge, tidal harmonic analyser and tide predicter are famous, and among his work in the interest of navigation must be mentioned his tables for the simplification of Sumner's method for determining the position of a ship at sea.