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FIG. 46.

Fresnel's Rhomb.

T:

A. B. C. D. Fresnel's Rhomb.

1. Fresnel's Method.- Fresnel effected the circular polarization of light by means of a parallelopiped of St. Gobin (crown) glass (fig. 46), whose acute angles, B and C, are about 54°, and consequently whose obtuse ones, A and D, are about 126°. This apparatus is commonly called Fresnel's rhomb. If a ray, a, of plane polarized light be incident perpendicularly on the face, A B, it will suffer two total internal reflections, at an angle of about 54°, one at E, the other at F, and will emerge perpendicularly from the face, DC. If the first plane, B D, of internal reflection, be inclined 45° to the plane of polarization of the incident ray, a, the emergent ray,

a. Incident ray of plane C, will be circularly polarized.

polarized light.

b. Depolarized ray.

ray.

c. Circularly polarized

Let us now endeavour to explain this phenomenon according to the wave hypothesis. So long as reflection is partial, whether performed at the first or second surface of the diaphanous medium, the incident light suffers only a deviation from its plane of polarization, without having its primitive properties altered, whatever may be the azimuth of its plane relatively to that of the plane of reflection.

But when the reflection is total the case is very different. The reflected rays then have, in general, suffered partial depolarization, especially if the plane of reflection is in an azimuth of 45° relatively to the primitive plane of polarization. Now, a ray of light thus modified, or depolarized, as it is termed, may be represented by two rays polarized, the one according to the plane of reflection, the other perpendicularly to it. In other words, the incident-polarized ray (fig. 46, a) is resolved by reflection into two rectangularly plane-polarized rays (b), the planes of which are inclined respectively, the one 45° to the left, the other 45° to the right of the plane of polarization of the incident ray.

But it is obvious that the reflection of these two rectangularly polarized rays must be effected at different depths, and, therefore, under very different circumstances. The ray whose vibrations are performed parallel to the reflecting surface will glide, as it were, on the surface, and be reflected in a stratum of uniform density; whereas the ray, whose vibrations are performed perpendicularly to the reflecting surface, will penetrate to a greater depth, and pass into strata of varying density. The latter ray will, therefore, suffer a greater retardation than the one whose vibrations are performed parallel to the reflecting surface.

Now when, in the case of Fresnel's rhomb, the plane of the first reflecting surface is in an azimuth of 45° to that of the incident ray,

the retardation is equal to th undulation. The same ray is farther retarded another th undulation by the second reflection; and now differs in its phase from that of the other ray 4th of an undulation.

Thus are obtained the conditions necessary for the formation of a ray of circularly-polarized light; namely, two plane rays of equal intensity, polarized in planes perpendicular to each other, and differing in their path 4th of an undulation.

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2. Airy's Method. If a ray of plane polarized light be transmitted through a lamina of either mica or selenite of such a thickness that, for a ray perpendicular to the lamina (that is, the ray polarized in the plane of one of the principal sections of the mica) the ordinary ray shall be retarded, an odd or uneven number of quarter undulations, as th, ths, or ths (according to the convenience of splitting) more than the extraordinary ray (that is, the ray polarized in the plane of the other principal section), the emergent light will be found to be circularly-polarized. In this case the incident light is resolved into two sets of vibrations, at right angles to each other, and one of these is retarded in its phases more than the other.

Between this and Fresnel's method of effecting circular polarization, there is this difference: in Fresnel's rhomb the retardation of the one ray is nearly the same for all colours, that is, for waves of different lengths. But in the case of the lamina of mica or selenite, the retardation is greater for blue rays than for red rays. "This is seen most distinctly on putting several such lamina together [in the same crystalline position], when the light which is reflected from the analyzing plate is coloured, whereas, on putting together several of Fresnel's rhombs, there is no such colour. It is plain that in substituting such a lamina for Fresnel's rhomb, the plane of polarization of that ray which is least retarded, corresponds to the plane of reflection in the rhomb."

3. Dove's Method.-This consists in transmitting plane polarized light through glass to which a certain degree of doubly refracting power has been communicated by pressure, or by rapidly heating or cooling it.

I have already shown that well annealed glass acquires doubly refracting properties when compressed; that unannealed glass possesses similar properties; and also that during the time that glass is rapidly heating or cooling it is likewise a double refractor.

Of the two systems of waves which are thus obtained, one is polarized in a plane parallel to the axis of compression, the other in a plane perpendicular to it.

Now, if the degree of doubly refracting power thus communicated to glass be just sufficient to effect the retardation of one of the systems of waves of an undulation, we obtain a structure fitted for converting plane-polarized into circularly-polarized light. "If a square or circular plate of glass," says Dove, “ be com

pressed so that the axis of compression forms an angle of 45° or 135° with the plane of primitive polarization, the light passing through the centre of the glass at a certain degree of the pressure will be circularly polarized. During a complete revolution of the plate in its plane round the perpendicular incident ray as an axis of revolution, the light is polarized four times rectilinearly and four times circularly: rectilinearly when the compressing screw acts on the points 0°, 90°, 180°, 270°, that is to say, when the axis of compression is perpendicular to the plane of primitive polarization, or lies within it; and on the contrary, it is polarized circularly when that point of action corresponds to the points of division, 45°, 135°, 225°, 315°, whilst 45°, and 225°, as also 135o, and 315°, exhibit a similar effect."

These statements may be rendered more intelligible by the following diagram :

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If light, rectilinearly polarized in the plane Oo 180o, or in that of 90° 270°, be incident on a circular disk of compressed glass (fig. 47, A, B, C, D), the emergent light is rectilinearly polarized when the axis of compression is either O° 180°, or 90° 2709; but is circularly polarized when the axis of compression is either 45° 225°, or 135° 315°. At all intermediate azimuths it is elliptically polarized.

The degree of compression to which the glass is to be subjected, to produce these effects, is such that when the compressed glass is placed in the polariscope, with the tourmalines crossed, a black cross is seen with bloud-white vacant spaces in the corners. Unannealed glass, possessing the same degree of doubly refracting power, acts in a similar manner to compressed glass. Annealed glass, while either rapidly heating or cooling, likewise gives rise to similar effects at the time when its doubly refracting power is just equal to that of the compressed glass above described. 4. Quartz. I now proceed to notice the remarkable optical properties of the substance denominated Quartz.

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This term, the etymological origin of which is not clearly made out, is applied to some of the crystalline forms of silica. The transparent variety, called rock or mountain crystal, is the kind used for optical purposes. Very perfect transparent crystals are found near Bristol and in Cornwall, and are called Bristol or Cornish diamonds. The opticians cut some of the most limpid and large crystals, which usually come from the Brazils, for making lenses for spectacles and eye-glasses, and which they denominate pebbles.

FIG. 48.

Ordinary Crystal of
Quartz.

FIG. 49.

Quartz belongs to the rhombohedric system. Its most common form is the six-sided prism, terminated by six-sided pyramids (fig. 48). Its fracture is conchoidal.

Now, as quartz belongs to the same system of crystals to which Iceland spar belongs, it might be expected that when we place a plate of it, cut perpendicularly to its principal or prismatic axis (fig. 49 a a), in the polariscope, we should observe the cross and a system of circular rings, as in the case of Iceland spar and other crystals of the rhombohedric system. But this is not the case. We do, indeed, observe a system of rings, but the centre of the cross is wanting (fig. 50). Instead of the cross within the inner ring we observe an uniform tint, the colour of which changes when the analyzer is revolved; and, in succession, Different modes of slit- all the colours of the spectrum are brought ting quartz for optical into view. But the order of succession (supaa. Plates transverse posing the direction or revolution of the anashowing (in the polari- lyzer to remain the same) varies in different scope) the system of cir- crystals. Thus, suppose we turn the analyzer bb. Plates cut obliquely right-handed, that is, as we screw up, the to the axis, for showing colours succeed each other, either in this red, orange, yellow, green, blue, inbly refracting prisms. digo, violet, red again, and so on; or in the

purposes:

C

to the prismatic axis, for

cular rings (fig. 50).

the straight bands.

cc. Wedges for making order

Wollaston's quartz dou

FIG. 50.

following order-red, violet, indigo, blue, green, yellow, orange, red again, and so on. So that to obtain the same order of succes. sion, the analyser must be turned in the one case right-handed, or as we screw up, in the other left-handed, or as we unscrew. This will be rendered more obvious by the following diagrams:

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Right-handed.

FIG. 52.

Left-handed.

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In each of these diagrams the arrow shows the direction in which the analyzer is to be rotated, in order to obtain the spectral tints in the descending order. In one complete revolution of the analyzer each of the colours of the spectrum occurs twice. In other words, all the colours are seen in one semi-revolution of the analyzer.

Hence those specimens of quartz which present the colours in the descending order by a right-handed rotation of the analyzer, are denominated dextrogyrate, or right-handed quartz; while those which present them by a left-handed rotation are called lævogyrate, or left-handed quartz.

FIG. 53.

Between these two varieties there has been discovered by Sir John Herschel another difference. In that form of quartz, termed by Haüy plagiedral (from λáytos oblique, and edpa a base), it has been found that when the unsymmetrical or plagiedral faces (fig. 53 x) lean to the right, the polarization is righthanded, and vice versa, when they lean to the left the polarization is left-handed. So that the cause, whatever it may be, which determines the optical phenomena is also connected with the production of the plagiedral faces.

Plagiedral Quartz.

If, instead of using white light in our experiments, we employ homogeneous light, we find that the plane of polarization of the

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