# Scientific Memoirs/1/Description of an Apparatus for exhibiting the Phaenomena of the Rectilinear, Elliptic, and Circular Polarization of Light

From the Annalen der Physic und Chemie Second Series, vol. v. p. 596
Article IV.
Description of an Apparatus for exhibiting the Phænomena of the Rectilinear, Elliptic, and Circular Polarization of Light, by H. W. Dove.
From J. C. Poggendorff's Annalen der Physik und Chemie; Berlin, Second Series, vol. v. p. 596.
UPON a common tripod brass telescope-stand with a horizontal and vertical motion, which, from its containing a sliding-tube, may be raised from 16 to 25 inches by means of a tightening-screw $a$ (Plate II. fig. 1.), is placed in a case $h$ a three-sided moveable brass prism $b$ $c$, two feet long, arid divided into Paris inches and lines. This prism carries five sliders $s_{1}$, $s_{2}$, $s_{3}$, $s_{4}$, $s_{5}$, which, by means of tightening-screws, may be fixed at pleasure at any part of the scale. Two of them $s_{2}$, $s_{5}$, the front view of which is separately drawn of the actual size in fig. 2, carry stands terminating above in rings, which by means of a pivot at $r$ (fig. 2.) may be placed horizontally and vertically, so that the apertures of the Nicol's prisms $ll$ revolvable in these rings, with the centre of the convex lens $k$, screwed into the ring of the slider $s_{3}$, (the stand of the convex lens being provided with exactly such a pivot, and in a perpendicular position also to the centre of the condensing-lens $p$ which is carried by the slider $s_{1}$, the focal distance of the condensing-lens being 12 inches and its aperture 3,) lie in a straight line parallel to the rod $b$ $c$, this line being at the same time the optical axis of the instrument. The Nicol's prism of the stand $s_{2}$, which is the nearest to this condensing-lens, may be called the polarizing, and that which is more distant from the stand $s_{5}$, the analysing one.
If parallel light is incident upon the condensing-lens, the polarizing prism must be in its focus, in order to polarize all the incident light; if, on the contrary, the light of a lamp is employed, the polarizing prism must be in the point of convergence of the rays which fall diivergingly upon the condensing-lens. During this process it is of course not the prism but the condensing-lens that is to be moved until the concentrated light of the lamp falls exactly upon the aperture of the prism.
In order to alter at will the planes of polarization of the two prisms, graduated brass plates are placed at the rings of the stands $s_{2}$, $s_{5}$, upon which plates is placed a moving index, which, when intended to be prolonged backwards over the fastening-point, coincides with the longer diagonal of the rhomboidal bases of the Nicol's prism. The graduation ​of the circle is arranged so that, in the vertical position of the stand, the straight line passing through the points 0° and 180° lies horizontally. Fig. 2. exhibits of the actual size a view of these plates, which are not drawn in fig. 1. It is preferable to graduate that side of both plates which is turned toward the eye. The dotted stand in fig. 2. is therefore to be imagined behind the plate, when it belongs to the polarizing prism, and on the contrary- before the plate and the graduation on the back of the plate, when the plate belongs to the analysing prism $d$. It will seldom be requisite to alter the plane of polarization of the incident light; it is most convenient to place it once for all horizontally, that is to say, to place the index of the polarizing prism upon 0° or 180°. In clear weather, when the light reflected by the sky is already more or less polarized, the instrument is to be directed, where this is possible, toward a wall on which the sun shines. If, however, the light reflected by the sky is to be directly employed, and in the greatest possible intensity, this may be most completely performed as follows. The polarizing prism with its plate having been placed horizontally, the analysing one is turned, until the system of rings with the black tufts is obtained in a plate of Iceland spar cut perpendicularly to the axis; within the ring $I$ of the stand $s_{4}$ the polarizing prism $e$ is then placed vertically again, and turned round until the same phænomenon is perceived in the Iceland spar. The index of the polarizing prism $e$ then indicates the direction of the plane of polarization of the incident light, and the rings appear with greater distinctness.
The light diverging from the polarizing prism is at first intercepted by a convex lens indicated by $v$, two inches in diameter, and distant 5/4 inches from the aperture $e$, and which is screwed into the lower end of that part which passes through the plate and is the holder of the prism: it then falls upon the lens three inches distant upon the stand $s_{3}$, and having 1½ inch focal distance. From this point it passes through the crystal of the stand $s_{4}$ in the ring $l$, and which is to be examined in the polarized light, and proceeds into the analysing prism $d$, into whose lower end is screwed a concave lens indicated by $u$, and of four or five inches focal distance. Any inclination to the axis of the instrument may be given at pleasure to the ring $l$, by means of a ball and socket which is represented in fig. 1., or by means of a motion on points (as in the illuminating lenses or mirrors of common microscopes). Since now the crystal in this ring may also revolve in its plane, its optical axes may be altered at will in reference to their position with respect to the plane of polarization of the incident light. If however, for the exhibition of the isochromatic curves, two crystal plates cut parallel to the axis, or two laminte of mica of uniform thickness are to be combined, the process is as follows: two turns of the screw must be given to the ring, which is to be inserted, of which the one that is represented on the larger ​cylinder enters into $l$, but the other, which is on the narrower cylinder, passes through, so that on the side toward $k$ a second crystal is screwed in, whose axis may in this manner be made to assume at pleasure any angle to the axis of the first crystal.
The ring $m$, nearly in the focal distance of <math<k</math>, is intended for the reception of cooled glasses, thin laminae of gypsum, and amethysts. Fastened to a pin, its central point is exactly in the axis of the instrument, when the pin is exactly vertical. Similar rings of wood, provided with straight pins, may be placed in the case of the stand $s_{4}$. Biaxal crystals are fastened to the pins, so that when the ring is turned round the pin, the systems of rings of the two axes pass one after another through the field of view; if therefore the indexes of the two Nicol's prisms stand at 0° and 90°, the black tufts of the systems of rings lie in a horizontal line. The ring $m$ may also serve for the reception of a micrometric arrangement for the systems of rings of the crystals observed in $l$.
In order to change the rectilinear into circular polarization, the arms $f$ and $g$, which revolve round the pegs $n$ and $o$, contain laminae of biaxal mica of such a thickness as to produce a difference of path of exactly a quarter-undulation between the two rays, when the axes of those arms $ff$ and $gg$ (Plate II. fig. 2.) form with the plane of primitive polarization $ee$ angles of 45° and 135°. Instead of the laminae of mica cooled or compressed glasses may be employed, and combined (fig. 5.) in the manner particularly described in the foregoing paper.
If the two thin plates are turned aside, the rectilinearly polarized light is rectilinearly analysed. In order to analyse circularly, the rectilinearly polarized light $f$ is brought forwards. In order to analyse rectilinearly the circularly polarized light, $f$ is to be turned aside, and $g$ placed forward. The two plates must be brought forward, as in fig. 1., when the circular polarized light is to be circularly analysed. The axis of the thin mica plate is indicated upon its frame. If that axis, instead of corresponding with the points 45° and 135°, passes through other points of graduation, we obtain the phænomena of elliptic polarization.If a small pin be fixed in the direction of the axis $gg$, the position of the axis of the lamina of mica may easily be drawn upon the graduation of the stand $s_{2}$.
In order to perform the simple experiments of intensity, it is advantageous to uncover the field of view. This is accomplished by a hollow cylinder one inch in height screwed into the somewhat projecting end of the frame of the lens $k$ up towards $m$. The aperture of the opake diaphragm in the bottom of this cylinder is 1½ line. This well-defined bright circle furnishes a very good object for these experiments. If ​the analysing prism is turned in its frame, we obtain the decrease according to the law of Malus; if one of the laminæ of mica is placed before, on turning the intensity of the light remains unchanged. If, instead of the analysing Nicol's prism an achromatic double-refracting prism in a similar frame is screwed in, the analogous phænomena are obtained for both images.
When the polarizing prism $e$ is bent on one side, a double-refracting prism screwed into the ring $l$ gives two mutually perpendicular polarized images of the aperture in the diaphragm, the changes of intensity of which are obtained by turning the analysing prism $u$. If the thin lamina of mica $f$ is placed forwards, the images, when the principal section of the double-refracting prism lies perpendicularly or horizontally, become circular on the right and left, and an arrangement coinciding with the apparatus proposed by Fresnel is obtained, consisting of three rock-crystal prisms, of which two belong to a crystal turned to the right and the single one to that turned to the left. By turning the analysing prism, the intensity of the images remains unchanged. If the analysing prism be also a double-refracting one, on turning it, two images with unchanged intensity (the mica plate lying between) move round the two stationary images with the same property.
If a mica or gypsum plate of a determinate thickness be in the ring $m$, on its turning round the pin to which it is fastened we obtain the phænomena of the so-called coloured polarization between the two Nicol's prisms. The complementary colours appear of great intensity, and give white where they overlap each other, when the analysing Nicol's prism is exchanged for a double-refracting one. Should we wish to combine two double-refracting prisms as above, the mica plate $f$ must be exchanged for a thicker one. When the aperture of the diaphragm is diminished the images separate from each other. If a plate of Iceland spar, cut perpendicularly to the axis, is screwed upon the universal setting of the Nicol's analysing prism, the corresponding modifications of the system of rings in the separated and circularly polarized vacant spaces are obtained, when the double-refracting prism is in $l$; if on the contrary there is in the ring $l$ a second plate of Iceland spar likewise cut perpendicularly to the axis, it is easy by turning this ring to cause the centres of the second and first plates to coincide. In this manner we may imitate the phænomena (as described in the preceding paper) of certain twin-crystals of Iceland spar by interposing a mica plate of definite thickness in $f$. If $f$ lies at the side, by turning the ring $l$ the isochromatic curves originating from the combination of two plates of which the centres do not coincide are obtained. In a similar ​manner the plates of different crystallized bodies are combined, in order to examine the positive or negative character of their axes.
If, instead of white, either homogeneous or dichromatic light is to be made incident, small rings of wood one inch in diameter, with coloured glasses, must be fastened before the aperture of the polarizing prism $e$. When the concentrated light of a lamp giving white light falls upon dichromatic glasses, they exhibit with biaxal crystals different optical axes for the various colours, and with uniaxal crystals they yield beautiful changes of differently coloured rings. Blue glasses, which separately transmitted the extremes of the spectrum, exhibit (in arragonite, for instance,) the inner curve divided into two particoloured vacant spaces and corresponding changes within each ring; on the contrary, the two inner lings in the Iceland spar are exhibited of a deep red surrounded by violet rings gradually passing more and more into each other, during which, lighted by a flame of spirits of wine coloured by chloride of strontium, the three inner rings are violet, to which three red ones then succeed, and so forth. Through a ruby glass we now obtain only a very homogeneous red, then dark rings, in the red field of view.A flame of spirits of wine coloured yellow with common salt, or nitrate of soda, yields the most beautiful phænomenon. The dark rings and the junction-curves of the different systems of rings of twin-crystals of arragonite then appear in the linear and circular light with the utmost distinctness. For blue and violet it is best to employ the colours of the spectrum. The condensing-lens is then removed, in order that the light may fall directly upon the aperture of the polarizing prism.
The apparatus shown in Plate II. fig. 3. serves to analyse the light by reflexion, and is screwed into the pillar $s_{5}$ instead of the analysing prism. The screw at $u$ holds a concave lens of an equal focal distance. The unbordered mirror inclined at the angle of polarization is 7/4 inch long and 5/4 inch wide. A line is drawn over the three parts of the hinge $q$ on the left side of fig. 1. If the parts of this line form one straight line, the rod $bc$ is inclined towards a horizontal mirror at the angle of polarization. If $k$ and $v$ are placed aside, the light polarized by reflexion may be analysed either linearly by the prism, by the mirror in $u$, or circularly by means of $f$. But in order to examine larger cooled glasses in circularly polarized incident light, I employ a larger lamina of mica than that in $g$, which may be called $g_{\prime }$, and which fixed to the screw of the condensing-lens $p$ is screwed directly upon a wooden ring of 2 inches internal diameter. The axis of this mica lies like that of the thin plate in $g$, which is turned aside. The concave lens in $u$ is taken out, and the stand supporting the cooled glasses is brought to the distance most suitable to the eye. By holding the glasses in the hand, the various phænomena of the linear and circular light may be observed without alteration of the apparatus. If the glass be held ​between the condensing-lens and the minor, $f$ and $g$, being placed for- wards, there is seen a cooled cube upon the mirror darkened by the analysing prism, fig. 6.; and consequently when the cube is turned 45°, fig. 7, the same phsenomena are observed as if both the mica plates had been removed. Between the two mica-plates, whose axes cross each other at right angles, appears fig. 8, and indeed unchanged when the tube is turned in its ring. Fig. 9. is the complementary figure to it, which is obtained by turning the analysing prism to 90°, without changing the position of the mica plates, lf $f$ is bent backwards, there appears the modification of the linear figure, which produces circularly polarized incident light linearly analysed.
Of this as well as of that modification produced by circular analysis of the linear light which follows when the cube is close to the condensing-lens, it is easy to form an idea, by imagining the linear figure divided into four equal quadrants by two perpendicular lines, and the even quadrants removed from the central point about 1/4 interval, and the odd ones approaching to within the same distance; or vice versâ, these removed, whilst those are made to approach. To polarize lamp-light by reflexion, the better way is to fix upon the condensing-lens (itself capable of revolving,) a mirror inclined at the fixed angle of polarization. If, by means of the polarizing prism, the instrument has before been placed upon the lamp, after the prism is turned aside and the mirror is fixed, that instrument, without changing its inclination, is turned round its perpendicular stand, until the system of rings is seen anew in the Iceland spar within the ring. Instead of employing Nicol's prisms, the light may be polarized by absorption in tourmaline plates, or by successive refractions through a series of glass plates. These are screwed into the stands in similar frames.
In order to obtain the deviation of the plane of polarization by refraction, the refracting bodies are introduced into the stand $s_{3}$. The deviation by reflexion may be conveniently observed by turning the rod at an angle toward a definite point. As, however, this (experiment is easily made in another manner, I thought it unnecessary to complicate the apparatus for it. In the same manner the apparatus may be changed into a polarizing microscope, with a still larger field of view, by the addition of some lenses and stands. But as this will be desirable in very few experiments, besides that the construction of such an apparatus by means of single rings fitting one another is easy, I omitted them in this instrument.
When a glass warming or cooling is to be examined in the polarized light, the prismatic rod is so inserted into the frame h that one of its faces which have hitherto formed the sides, is brought into a horizontal position below. All the stands are then at the side of the horizontal rod turned to 120", which presents no obstacle to the heating by ​an interposed lamp. If instead of looking into the prism $u$ we look into $e$, on a slight change of the distance of the lens we obtain precisely the same phænomena. Thus an inverted order may also be given to all the stands with respect to the condensing-lens.
The superior advantages of the apparatus just described appear to me to be as follows:
1. The intensity of its light, which is so great that the flame of spirit of wine, 12 feet distant and coloured yellow by common salt, exhibits the system of rings of Iceland spar with great distinctness in an undarkened room.
2. The easy change of the linear into circular and elliptic polarization.
3. Its rendering unnecessary a particular arrangement for illumination.
4. The extent of the field of view.
5. The purity of the colours, which are produced by colourless crystals only.
6. The cheapness of the instrument, since it serves equally as a model of an open telescope and as a microscope (the condensing-lens is the object-glass of the telescope; the stands $s_{2}$, $s_{3}$, $s_{5}$ form the eyeglass, $s_{4}$ becomes the stand for the microscopic objects).
7. The easy execution of all single changes in the various experiments above described.
The mechanician Hirschmann, of this place [Berlin], whose Nicol's prisms are in the hands of many natural philosophers, has already executed this apparatus according to my instructions in several sets made to order. Its price, if it is to be used both as an open telescope and microscope, is 60 rix-dollars.
Postscript.
Fig. 4. Plate II. represents a small apparatus consisting of a single piece of glass, which exhibits united the modifications of the light by reflexion. The mutually parallel surfaces ad and bc are perpendicular to the parallel surfaces ac and bd; but, on the contrary, ab is inclined at 45° towards ad, and cd towards bd. The light therefore, falling perpendicularly upon ad, will after being reflected by ab and cd proceed from bd. The prismatic arcs bounding the vacant space of total and partial reflexion, therefore, intersect each other, as in the annexed figure. In the vacant space m, the light, after two reflexions, is un-polarized; in the vacant spaces o and n it is polarized perpendicularly; ​and in the vacant space $p$, on the contrary, the partially polarized incident light is changed in the direction of the second reflexion. The light of the vacant space m differs from that in a Fresnel's parallelopiped by having the planes of the two reflexions perpendicular to each other, instead of coinciding as they do when that is used.
The phænomena of cooled glasses in circular light have not yet been described particularly, and those of compressed glasses not at all; we shall therefore add a few words respecting them.
In circular analysis solid cooled cylinders have the same properties as Iceland spar plates. In linear analysis they exhibit the system of rings without the cross displaced in the quadrants. The same may be said of the rings of colours of hollow cylinders, which are concentric with the inner black ring, and abruptly separated. The cross in three-sided plates consists of four black points (with two plates placed upon each other it consists of four triangles), which, united by bright gray shades, form a Y. In six- and eight-sided plates the black central spot becomes a six- and eight-sided star, while the colours of the angles are arranging themselves into a very regular inclosure particularly when by turning the analysing prism the centre becomes white: figs. 8. and 9. represent the figures of cooled cubes. The isochromatic lines of rectangularly crossed parallelopipedal plates remain, with regard to their form, identical with those in the linear light, which appear when the plane of polarization bisects the right angle between the plates. All the figures remain unchanged when the glasses are turned in their plane at the time of circular polarization and analysis. The irregularities of the figures produced by unequal cooling appear in the circular light, particularly with thin plates, and often even with those which appear regular in the linear light ; nevertheless, I have also observed precisely the reverse, and that indeed with a six-sided plate.
A cylinder compressed by brass wire wound round it had the same properties as a cooled one. Square and circular plates diametrically compressed by a screw, exhibit between the rings originating at the compressing points of the screw a coloured junction without a cross. If the axis of compression lies in the plane of polarization of the rectilinearly polarized incident light, the figure is also here displaced in the quadrants, when the light becomes circularly analysed.
* ↑ Although the same phænomena may be obtained by the determinate inclination of a thin plate of uniaxal mica, yet the employment of the biaxal mica appears tome much more convenient.
* ↑ In order to obtain the four mutually involved spirals of a rock-crystal plate turned right and left, I combine aright-handed plate ground plano-concave with a left-handed crystal ground with parallel faces.
* ↑ In order not to diminish this, the arm $f$ must move to and fro, close by $u$. The cylindrical setting of the polarizing prism must not be higher than half an inch.
* ↑ This application of Weber's method of compressing glass to the phænomena of polarization was shown to me by Prof. Mitscherlich. (Compare Poggenclorff's Annalen, vol. xx. p. 1.)