Polarisation of Light.
Common light moves in two planes at right angles to each other, while polarised light moves in one plane only. Common light may be turned into polarised light either by transmission or reflection; in the first instance, one of the planes of common light is got rid of by reflection; in the other, by absorption. Huyghens was one of the first physicists to notice that a ray of light has not the same properties in every part of its circumference, and he compared it to a magnet or a collection of magnets; and supposed that the minute particles of which it was said to be composed had different poles, which, when acted on in certain ways, arranged themselves in particular positions; and thence the term polarisation, a term having neither reference to cause nor effect. It is to Malus, however, who, in 1808, discovered polarisation by reflection, that we are indebted for the series of splendid phenomena which have since that period been developed; phenomena of such surpassing beauty as to exceed most ordinary objects presented to the eye under the microscope.
Certainly no more misleading name could well have been found to describe the causation, in one particular direction, of small displacements in the medium, through which the light waves are made to pass.
The effect of “polarising” light is simply to alter the directions of the vibrations of light, and allow of certain waves to pass which are vibrating in one direction only, vertical, horizontal, or oblique, as the case may be. The most efficient agent discovered for the polarisation of light is that of Iceland spar, cut and mounted as a “Nicol” prism.
By cutting crystals of Iceland spar into two parts, at a particular angle, and cementing them together again in the reverse way, Nicol succeeded in showing that one of the two polarising pencils could be totally deflected to one side, while the other is directly transmitted through the Nicol prism, and thereby the beam of light becomes at once “polarised” in one plane only. No apparent difference can be seen in the prism on holding it up to the light, except it be in a very slight loss of brightness; but if another similarly heated crystal be held before, and made to revolve around, a quarter of the circle just where the two cross each other, total darkness results. This phenomenon alternately recurs at every quadrature of the circle. A pair of Nicol prisms, when appropriately mounted, constitute “a polarising apparatus” for the microscope, one being fitted into the sub-stage, and the other either immediately above the objective or eye-piece, where it can be easily rotated, the object to be examined being placed on the stage of the microscope, that is, between the polarising and analysing prisms.
Polariscope Objects.
Tuffen West, del. Edmund Evans.
Plate VIII.
The significance of polarised light centres in the fact that it affords a wider insight into the structure of crystals, minerals, and a number of other substances, and which could not otherwise be obtained without its aid. Its usefulness is multifold, as even glass itself, when not properly annealed, exhibits points of fracture, by a display of Newton’s rings. The knowledge thus acquired is turned to account by glass manufacturers.
Double refraction.—When an incident ray of light is refracted into a crystal of any other than the cubic system, or into compressed or unannealed glass, it gives rise to two refracted rays which take different paths; this phenomenon is termed double refraction. Attention was called to this in 1670, by Bartolin, who first observed it in Iceland spar; and the laws for this substance were accurately determined by Huyghens.
Iceland spar or calc spar is a form of crystallized carbonate of lime. It is composed of fifty-six parts of lime and forty-four parts of carbonic acid, and is usually found in rhombohedral forms of crystallization.
To observe the phenomenon of double refraction, a rhomb of Iceland spar may be laid on a page of a printed book, when all the letters seen through it will appear double; the depth of the blackness of the letters is seen to be considerably less than that of the originals, except where the two images overlap.
In order to state the laws of the phenomena with precision, it is necessary to attend to the crystalline form of Iceland spar, which has equal obtuse angles. If a line be drawn through one of these corners, making equal angles with the three edges which meet there, it, or any line parallel to it, is called the axis of the crystal; the axis being, properly speaking, not a definite line but a definite direction.
The angles of the crystals are the same in all specimens. If the crystal is of such proportions that these three edges spoken of are equal, as in the smaller crystal ([Fig. 176]), the axis is the direction of one of its diagonals, as represented.
Any plane containing (or parallel to) the axis is called the principal plane of the crystal.
In the next diagram, [Fig. 177], the line appears double, as a b and c d, or the dot, as e and f. Or allow a ray of light, g h, to fall thus on the crystal, it will in its passage through be separated into two rays, h f, h e; and on coming to the opposite surface of the crystal, will pass out at e f in the direction of i k, parallel to g h. The plane l m n o is designated the principal section of the crystal, and the line drawn from the solid angle l to the angle o is where the axis of the crystal will be found; this is its optic axis. Now when a ray of light passes along this axis, it is undivided, and there is only one image; but in all other directions there are two images.
Fig. 176.—Axis of Crystals of Iceland Spar.
Fig. 177.—A Rhomb showing the passage of Rays of Light.
Mr. Nicol, of Edinburgh first succeeded in making a rhomb of Iceland spar into a single-image prism. His method of splitting up the crystal into two equal parts was as follows:—
A rhomb of Iceland spar of one-fourth of an inch in length, and about four-eighths of an inch in breadth and thickness, is divided into two equal portions in a plane, passing through the acute lateral angle, and nearly touching the obtuse side angle. The sectional plane of each of these halves must be carefully polished, and the two portions cemented firmly together with Canada balsam, so as to form a rhomb similar to that before division; by this management the ordinary and extraordinary rays are so separated that only one is transmitted: the cause of this great divergence of the rays is considered to be owing to the action of the Canada balsam, the refractive index of which (1·549) is that between the ordinary (1·6543) and the extraordinary (1·4833) refraction of calcareous spar, and which will change the direction of both rays in an opposite manner before they enter the posterior half of the combination. The direction of rays passing through such a prism is indicated by the arrow, [Fig. 178].
Fig. 178.
Polarised light cannot be distinguished from common light, as already said, by the naked eye; and for all experimental purposes in polarisation, two pieces of apparatus must be employed, one to produce polarisation, and the other to show or an analyse it. The former is called the polariser, the latter the analyser; and every apparatus that serves for one of these purposes will also serve for the other.
Fig. 179.—Polariser.
Fig. 179a.—Analyser.
Polarising Apparatus for Students’ Microscope.
In all cases there are two positions, differing by 180°, which give a minimum of light, and the two positions intermediate between these give a maximum of light. The extent of the changes thus observed is a measure of the completeness of the polarisation of light.
The two prisms mounted as shown in Figs. 179 and 179a constitute the apparatus adapted to the microscope. The polariser slips into place below the stage, and the analyser, with the prism fixed in a tube, is screwed in above the objective.
The definition is considered by some experimenters as somewhat better if the analyser be used above the eye-piece, and is certainly more easily rotated.
Fig. 180.—Prism mounted as an Eye-piece.
Method of employing the Polarising Prism ([Fig. 179]).—After having adapted it to slide into a groove on the under-surface of the stage, where it is secured and kept in place by the small milled-head screw, the other prism [Fig. 179]a) is screwed on above the object-glass, and thus passes directly into the body of the microscope. The light from the mirror having been reflected through them the axes of the two prisms must be made to coincide; this is done by regulating the milled-head screw until, by revolving the polarising prism, the field of view is entirely darkened twice during its revolution. If very minute salts or crystals are submitted for examination then it will be found preferable to place the analyser above the eye-piece, as in [Fig. 180]. Thus the polariscope is seen to consist of two parts; one for polarising, the other for analysing or testing the light. There is no essential difference between the two parts, except what convenience or economy may lead us to adopt; and either part, therefore, may be used as polariser or analyser; but whichever is used as the polariser, the other becomes the analyser.
Fig. 181.—More Modern Polariser and Analyser.
Opticians have their own methods of adapting the polariser and analyser to their several microscopes. Watson’s special form of apparatus is represented in [Fig. 181], the polariser being adapted to the sub-stage, and the analyser to screw into the objective.
Tourmaline.—A semi-transparent mineral, of a neutral or bluish tint, called tourmaline, when cut into thin slices (about 1⁄20-inch thick) with their faces parallel to their axes exhibit the same phenomena as the Nicol prism. The only objection to which is that the transmitted polarised beam is more or less coloured. The tourmaline to be preferred stops the most light when its axis is at right-angles to that of the polariser, and yet admits the most when in the same plane. Make choice of a tourmaline as perfect as possible; size is of less importance when intended for use with the microscope.
Transmission of rays through tourmaline is only one of several ways in which light can be polarised. When a beam of light is reflected from a polished surface of glass, wood, ivory, leather, or any other non-metallic substance, at an angle of 50° to 60° with the normal, it is more or less polarised, and in like manner a reflector composed of any of these substances may be employed as an analyser. In so using it, it should be rotated about an axis parallel to the incident rays which are to be tested, and the observation consists in noting whether this rotation produces changes in the amount of reflected light.
For every reflected substance there is a particular angle of incidence, which gives a maximum of polarisation in reflected light. It is called the polarising angle for the substance, and its tangent is always equal to the index of refraction of the substance; or, what amounts to the same thing, it is that particular angle of incidence which is the complement of the angle of refraction, so that the refracted rays are at right angles. This important law was discovered experimentally by Sir David Brewster.
Tourmaline, like Iceland spar, is a negative uniaxial crystal; and its use as a polariser depends on the property which it possesses of absorbing the ordinary much more rapidly than the extraordinary ray, so that a thickness which is tolerably transparent to the latter is almost completely opaque to the former. Its pale cobalt blue colour enhances the beauty of certain crystal and mineral substances, but like Iceland spar, the paler and more perfect crystals are becoming scarce.
Selenite is another mineral of value in polarisation experiments. It is a native crystalline hydrated sulphate of lime. A beautiful fibrous variety called satin-gypsum is found in Derbyshire. The form of the crystal most frequently met with is that of an oblique rectangular prism, with ten rhomboidal faces, two of which are much larger than the rest. It is usually split up into thin laminæ parallel to their lateral faces; each film should have a thickness of from one-twentieth to one-sixtieth of an inch. In the two rectangular directions these films allow perpendicular rays of polarised light to traverse them unchanged, termed their neutral axes. In two other directions, however, which form respectively angles of 45° with the neutral axes, these films have the property of double refraction, a direction known as the depolarising axis.
Fig. 182.—Darker’s Selenite Films and Stage.
The thickness of the film of selenite determines the particular tint. If, therefore, we use a film of irregular thickness, different colours are presented by the different thicknesses. These facts admit of very curious and beautiful illustration, when used under the object placed on the stage of the microscope. The films employed should be mounted between two glasses for protection. Some persons employ a large film, mounted in this way between the plates of glass, with a raised edge, to act as a stage for supporting the object, it is then called the “selenite stage.” The best film for the microscope is that which gives blue, and its complementary colour yellow. The late Mr. Darker constructed a selenite stage for the purpose ([Fig. 182]). With this a mixture of colours will be brought about, by superimposing three films, one on the other. By slight variations in their positions, produced by means of an endless-screw motion, all the colours of the spectrum can be shown. When objects are thus exhibited, it should be borne in mind that all negative tints, as they are termed, are diminished, and all positive tints increased; the effect of which is to mask the true character of the phenomena.
For a certain thickness of selenite the ellipse will become a circle, and we have thus what is called circularly-polarised light, which is characterised by the property that rotation of the analyser produces no change of intensity. Circularly-polarised light is not, however, identical with ordinary light; for the interposition of an additional thickness of selenite converts it into elliptically (or in a particular case into plane) polarised light.
It is necessary, for the exhibition of colour in our experiments, that the plate of selenite should be very thin, otherwise the retardation of one component vibration as compared with the other will be greater by several complete periods for violet than for red, so that the ellipses will be identical for several different colours, and the total non-suppressed light will be sensibly white in all positions of the analyser.
Two thick plates may, however, be so combined as to produce the effect of one thin plate. For example, two selenite plates of nearly equal thickness may be laid one upon the other, so that the direction of greatest elasticity in the one shall be parallel to that of least elasticity in the other. The resultant effect in this case will be that due to the difference of their thicknesses. Two plates so laid are said to be crossed.
Fig. 183.—Red is represented by perpendicular lines; Green by oblique.
The following experiments will well serve to illustrate some of the more striking phenomena of double refraction, and will also be a useful introduction to its practical application. Take a plate of brass ([Fig. 183]) three inches by one, perforated with a series of holes from about one-sixteenth to one-fourth of an inch in diameter; the size of the smallest should be in accordance with the power of the objective, and the separating power of the double refraction.
Experiment 1.—Place the brass plate so that the smallest hole shall be in the centre of the stage of the microscope; employ a low power (1½ or 2 inches) objective, and adjust the focus as for the ordinary microscopic object; place the double image prism over the eye-piece, and two distinct images will be seen; by revolving the prism, the images will describe a circle, the circumference of which will cut the centre of the field of view; one of which is the ordinary, the other the extraordinary ray. By moving the slide from left to right the larger orifices will appear in the field, the images seen will not be completely separated, but will overlap, as represented in the figure.
Experiment 2.—Insert the Nicol’s prism into its place under the stage, still retaining the double image prism over the eye-piece; then, by examining the object, there will appear in some positions two images, in others only one image; it will be seen, that at 90° this ray will be cut off, and that which was first observed will become visible; at 180°, or one-half the circle, an alternate change will take place; at 270°, another change; and at 360°, the completion of the circle, the first image will reappear.
Before proceeding to make the next experiment, the position of the Nicol’s prism should be adjusted, and its angles brought parallel with the square of the stage. The true relative position of the selenite should also be determined by noticing the natural flaws in the film, which should run parallel with each other, and be adjusted at an angle of about 46° with the square bars of the stage.
Experiment 3.—If we now take the plate of selenite thus prepared, and place it under the piece of brass on the stage, we shall see, instead of the alternate black and white images, two coloured images composed of the constituents of white light, which will alternately change by revolving the eye-piece at every quarter of the circle; then, by passing along the brass, the images will overlap; and at the point at which they do so, white light will be produced. If, by accident, the prism be placed at an angle of 45° from the square part of the stage, no particular colour will be perceived, and it will then illustrate the phenomena of the neutral axis of the selenite, because when placed in the relative position no depolarisation takes place. The phenomena of polarised light may be further illustrated by the addition of a second double image prism, and a film of selenite adapted between the two. The systems of coloured rings in crystals cut perpendicularly to the principal axis of the crystal are best seen by employing the lowest object-glass.
Biaxial Crystals.—To show perfectly the beautiful series of rings and brushes which biaxial crystals exhibit, it becomes necessary to convert the microscope, for the time being, into (so to speak) a wide-angled telescope.
Huyghenian Eye-piece.
Inner draw-tube.
Objective in draw-tube.
Analysing Prism.
Objective.
Specimen under Examination.
Sub-stage Condenser.
Polarising Prism, fixed in sub-stage below.
Fig. 184.—Diagrammatic arrangement of the Polarising Microscope.
In Sub-stage: P, polarising prism; C, sub-stage condenser on stage; M, mineral or crystal. On nose-piece: O1, objective, 4⁄10-inch; A, analysing prism.
In Draw-tube: O2, 2 or 3 inch Objective; H, Huyghenian eye-piece.
For the purpose, screw on a low-power objective to the end of the draw-tube ([Fig. 184]).[31] As the light requires to be passed through the crystals at a considerable angle, a wide-angled condenser should be employed, but it need not be achromatic. The objective most suitable is a 4⁄10-inch, of ·64 numerical aperture, but a ¼-inch of ·71 numerical aperture, or a 1⁄3-inch of ·65 numerical aperture, will answer the purpose equally well. As the whole of the back lens of the objective should be visible through the analysing Nicol prism, the back lens of the objective must not be too large; thus a ½-inch of ·65 numerical aperture will not be so effective. The analysing prism may be placed either where it is in the drawing, below the stage, or above the eye-piece. It works equally well above the objective, the position it ordinarily occupies in the microscope.
For the draw-tube a 2-inch objective and a B Huyghenian eye-piece answers very well. Before screwing the objective on to the end of the draw-tube centre the light in the usual manner, the Nicol’s being turned so as to give a light field, then screw the objective on to the end of the aperture, and put the crystal on the stage, rack down the body so that the objective on the nose-piece nearly touches the crystal, then focus with the draw-tube only. The sub-stage condenser should be racked up close to the underside of the crystal.
Opticians, however, have more recently furnished a special form of microscope (The Petrological Microscope, [Fig. 79], p. 112), for the use of those students who may desire to prosecute so fascinating a study, and determine the optic axial angles of crystals.
Fuess[32] lately introduced a new form of microscope for polarising and viewing biaxial crystals, which he believes to be needed, as in the ordinary microscope the opening of the polariser is scarcely a third of that of the condenser; moreover, it is not absolutely necessary that the polariser and analyser should be Nicol’s prisms. This fact was discovered by myself many years ago. Fuess utilises a bundle of thin glass plates, as in the older Nuremberg polariscope. The frame holding plates can be readily adjusted at the proper polarising angle, the analyser being the ordinary small Nicol, screwed above the objective. The illuminator is an Abbe’s triple condenser, of numerical aperture 1·40, which can be adjusted in the ordinary way. The front lens of this should have a diameter of 11·12 mm. and the lower lens of 30 mm. This increase in the condenser fully compensates for the loss of light by the bundle of glass plates, and also enables thick sections of crystals to be examined in convergent polarised light. The ocular used should have a large field; the A Huyghenian answers best. A suggestion to return to the original Nuremberg polariser is very opportune, as Iceland spar is becoming scarce.
Mr. A. Mickel accidentally discovered that an opalescent mirror can be converted into an excellent and inexpensive substitute for the Nicol-prism polariser.