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difficult of all the primary forms to determine from its secondary crystals. It is distinguishable from all other forms, when its crystals are single, by the absence of symmetrical planes analogous to those of other prisms; but it very frequently occurs in hemitrope or twin crystals, which must resemble some of the forms of the oblique rhombic prism, and can then be distinguished only by some re-entering angle or other character on the surface of the crystal."

Sulphate of Copper (Cu O. S 03. 5 Aq.) is sometimes cut to show the two sets of rings or lemniscates of this system; but the blue colour of the crystal destroys their brilliancy.

LECTURE IV.

4 CIRCULAR POLARIZATION.

The name of circular or rotatory polarization has been applied to a peculiar modification of light, first observed by Arago in the mineral called Quartz, and whose characteristic and distinctive properties I shall presently point out.

On the wave hypothesis, the term circular or rotatory is peculiarly appropriate, since it is assumed that the ethereal molecules describe circles, in other words that they vibrate or revolve uniformly in circles, and the form of the ethereal wave thereby produced, is that of a spiral or circular helix (that is, to a helix traced round a circular cylinder), of which a corkscrew and a bell-spring are familiar illustrations.

But apart from all hypothetical considerations, the name is an appropriate one. For unlike the rays of common polarized (that is, plane or rectilinearly-polarized) light, those of circularly polarized light have no distinction of sides, or, in other words, they have "no particular relations to certain regions of space," but present similar properties on all sides, and the angles of reflection at which they are restored to plane polarized light, in different azimuths, are all equal, like the radii of a circle described round the ray.

There are two varieties or kinds of circularly polarized light which have been respectively distinguished by the names of dextrogyrate or right-handed, and Icevogyrate or left-handed.

In one of these the vibrations are formed in an opposite direction to those in the other. Unfortunately, however, writers are not agreed on the application of these terms; and thus the polarization, called, by Biot, right-handed, is termed,by Herschel, left-handed, and vice versd. There is, however, no difference as to the facts, but merely as to theirdesignation. If, on turning the analyzing prism or tourmalineyVoOT left to right, the colours descend in Newton's scale, that is, succeed each other in this order—red, orange, yellow, green, blue, indigo, and violet, Biot designates the polarization as right-handed, or +, or ... ;whereas

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if they descend in the scale by turning the analyzer from right

to left, he terms it left-handed, or —, or "^ . Sir John

Herschel, on the other hand, supposes the observer to look in the direction of the ray's motion. Let the reader, he observes, "take a common corkscrew, and holding it with the head towards him, let him use it in the usual manner, as if to penetrate a cork. The head will then turn the same way with the plane of polarization as a ray in its progress from the spectator through a right-handed crystal may be conceived to do. If the thread of the corkscrew were reversed, or what is termed a left-handed thread, then the motion of the head, as the instrument advanced, would represent that of the plane of polarization in a left-handed specimen of rock crystal."

I shall adopt Biot's nomenclature, and designate the polarization right-handed or left-handed, according as we have to turn the analyzing prism to the right or to the left to obtain the colours in the descending order.

In a former lecture I endeavoured to explain the nature of circularly polarized light, according to the wave hypothesis. Powell's machine (see p. 27) gives a very clear notion of the difference between a circular and a plane wave. You may, perhaps, remember that I stated, that a circular wave is composed of two plane waves of equal intensity, polarized at right angles, and differing in their progress one quarter of an undulation. I endeavoured to demonstrate this fact by a machine invented, I believe, by Mr. Wheatstone (see p. 33).

Now, in order that you may comprehend how we effect the circular polarization of light, I must beg of you to keep in mind these statements. Remember, that to convert plane-polarized into circularly-polarized light, two conditions are necessary, namely, 1st, the existence of two systems of luminous waves, of equal intensity, polarized perpendicularly to each other; and, 2dly, a difference in the paths of these two systems of an odd or uneven number of quarter undulations. Now, whenever these two conditions are satisfied, circularly polarized light results. But how are we to satisfy them? By so doubly refracting plane polarized light, that the two resulting waves shall differ in their path an odd quarter undulation.

There are five modes of effecting the circular polarization of light, that is of satisfying the conditions above mentioned; but they all agree in acting on the principle now laid down, namely, that by them plane polarized light is doubly refracted, and two rectangularly polarized waves produced, which differ in their path an odd quarter undulation.

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]. 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, D C. If the first plane, B D, of internal reflection, he inclined 45° to the plane of polarization of the incident ray, a, the emergent ray,

... i..oi.u.ni . ly oTptae c. wi" be circularly polarized. polarized light. Let us now endeavour to explain this phe

*'. Circuhuiy^poiariicd nomenon according to the wave hypothesis. raT- 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, o) is resolved by reflection into two rectangularly plane-polarized rays (6), the planes of which are inclined respectively, the one 45° to the left, the other 46° 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,

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

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 oneof the principal sectionsof the mica) the ordinary ray shall be retarded, an odd or uneven number of quarter undulations, as £th, fths, 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 ihan 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 laminae 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 powerhas 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, trie 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 forconverting 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 135°, and 315°, exhibit a similar effect."

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

Flo. 47.

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If light, rectilinearly polarized in the plane 0° 180°, 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 Ov 180", or 90° 270'; but is circularly polarized when the axis of compression is either 46° 225°, or 135° 315°. At all intermediate azimuths it is ellipticallv polarized.

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