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paper, viewed through it, is exhibited as two lines, MN, mn, the amount of separation depending on the thickness of the crystal. The emergent rays, E e, O o, are parallel after they leave the surface, X.

A line drawn through the crystal from one of its obtuse angles to the other is called the axis of the crystal, and if artificial planes be ground and polished, as n m, op, perpendicular to this axis, a b, Fig. 262, rays of light falling upon this axis, or parallel to it, do not undergo double refraction.

Or if new faces, op, n m, Fig. 263, be ground and polished parallel to the axis, a b, a ray falling in the direction dƒ also remains single.

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Fig. 263.

But if the refracting faces are neither at right angles nor parallel

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Fig. 262.

to the axis, double refraction always ensues.

While Iceland spar has only one axis of double refraction, there are other crystals, such as mica, topaz, gypsum, &c., that have two. In crystals that have but one axis there are differences. In some the extraordinary ray is inclined from the axi; in others towards it, when compared with the ordinary ray. The former are called negative crystals, the latter positive.

The explanation which the undulatory theory gives of this phenomenon in crystals having a principal axis is, that the ether existing in the crystal is not equally elastic in every direction. Undulations are therefore propagated unequally, and a division of the ray takes place, those undulations which move quickest having the less index of refraction.

When the two rays emerging from a rhomb of Iceland spar are examined, they are both found to consist of light totally polarized, the one being polarized at right angles to the other. We have, therefore, several different ways in which light can be polarized-by reflection, refraction, absorption, and double refraction.

When a crystal of Iceland spar is ground to a prismatic shape, and then achromatized by a prism of glass, it forms one of the most valuable pieces of polarizing apparatus that we have. Such a prism may be used to very great vantage, instead of the mirror of the apparatus, Fig. 260.

E

If a ray of polarized light is passed through a thin plate of certain crystallized bodies, such as mica or gypsum, and the light then viewed through an achromatic prism, or by reflection from the second mirror of the polarizing machine, brilliant colours are at once developed. Thus, let R A, Fig. 264, be a ray of light incident on the first mirror of the polariscope, A C the resulting polarized ray, and D E F G be a thin plate of gypsum or mica. If, previously to the introduction of this plate, the two mirrors A, and C, be crossed, or at right angles to one another, the eye placed at E will perceive no light; but, on the introduction of the crystal, its surface appears to be covered with brilliant colours, which change their tints according as it is inclined, or as the light passes through thicker or thinner places. On further examination it will be found that there are two lines, D E and F G, which, when either of them is parallel or perpendicular to

Fig. 264.

the plane of polarization, RA C, or A CE, no colours are produced. But if the plate be turned round in its own plane a single colour appears, which becomes most brilliant when either of the lines a b, c d, inclined 45° to the former ones, are brought into the plane of polarization. The former lines are called the neutral, and the latter the depolarizing axes of the film.

This is what takes place so long as we suppose the two mirrors, A C, fixed; but if we make the mirror nearest to the eye revolve while the film is stationary, the phenomena are different. Let the film be of such a thickness as to give a red tint, and be fixed in such a position as to give its maximum coloration, and the eye-mirror to revolve, it will be found that the brilliancy of the colour declines, and it disappears when a revolution of 45° has been accomplished; and now a pale green appears, which increases in brilliancy until 90° are reached, when it is at a maximum. Still continuing the revolution, it becomes paler, and at 135° it has ceased, and a red blush commences, which reaches its maximum at 180°; and the same system of changes is run through in passing from 180° to 360°; so that while the film revolves, only one colour is seen; but as the mirror revolves two appear.

If, instead of using a mirror, we use an achromatic prism, we have two images of the film at the same time, and we find that they exhibit comple

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cut at right angles to the axis is used,
experiment, very brilliant effects are
coloured rings, ar-
ranged symmetrically,
and marked in the
middle by a cross,
which may either be
light or dark-Figs.
266, 267-light if the
second mirror is in the
proper position to re-
flect the light from the
first, and dark if it be
at right angles thereto.

mentary colours that is, colours of such a tint that if they be mixed together they produce white light. This effect is represented in Fig. 265.

That the particular colours which appear, depend on the thickness of the films, is readily established by taking a thin wedge-shaped piece of sulphate of lime, and exposing it in the polariscope. All the different colours are then seen arranged in stripes according to the thickness of the film.

When a slice of an uniaxial crystal instead of the films in the foregoing produced, consisting of a series of

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In crystals having

two axes, a complicated

Fig. 266.

Fig. 267.

system of oval rings, originating round each axis, may be perceived, intersected by a cross. Figs. 268, 269, represent the appearance in a crystal of

nitrate of potash; and in the same way other figures arise with different crystals.

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If transparent non-crystallized bodies are employed in these experiments, no colours whatever are perceived. Thus, a plate of glass, placed in the polariscope, gives rise to no such development; but if the structure of the glass be disturbed, either by warming it or cooling it unequally, or if it be subjected to unequal pressure from screws, then colours are at once developed : Figs. 270, 271. This property may, however, be rendered permanent in glass by heating until it becomes soft, and then cooling it with rapidity. All the phenomena here

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described belong to the division of plane polarization; but there are other modifications which can be impressed on light, giving rise to very remarkable and intricate results; these are designated circular, elliptical, &c., polarization.

Fig. 270.

Fig. 271.

The mechanism of the motions impressed on the ether to produce these results is not difficult to comprehend; for common light, as has been stated, originates in vibrations taking place in every direction transverse to the ray; plane polarized light arises from vibrations in one direction only; and when the ethereal molecules move in circles they originate circularly polarized light, and if in ellipses, elliptical.

CHAPTER XLIV.

NATURAL OPTICAL PHENOMENA.

The Rainbow-Conditions of its Appearance-Formation of the Inner Bow -Formation of the Outer Bow-The Bows are Circular Arcs-Astronomical Refraction-Elevation of Objects-The Twilight-Reflection from the Air-Mirages and Spectral Apparitions, and Unusual Refraction. THE rainbow, the most beautiful of meteorological phenomena, consists of one or more circular arcs of prismatic colours, seen when the back of the observer is turned to the sun, and rain is falling between him and a cloud,

which serves as a screen on which the bow is depicted. When two arches are visible, the inner one is the more brilliant, and the order of its colours is the same in which they appear in the prismatic spectrum-the red fringing its outer boundary, and the violet being within. This is called the primary bow. The secondary bow, which is the outer one, is fainter, and the colours are in the inverted order. When the sun's altitude above the horizon exceeds 42° the inner bow is not seen, and when it is more than 54° the outer is invisible. If the sun is in the horizon, both bows are semicircles, and according as his altitude is greater, a less and less portion of the semicircle is visible; but from the top of a mountain bows that are larger than a semicircle may be seen.

BLUE
CREEN

These prismatic colours arise from reflection and refraction of light by the drops of rain, which are of a spherical figure. In the primary bow there is one reflection and two refractions; in the secondary there are two reflections and two refractions. Thus, let S, Fig. 272, be a ray of light incident on a rain drop, a. On account of its obliquity to the surface of the drop, it will be refracted into a new path, and at the back of the drop it will undergo reflection, and returning to the anterior face and escaping, it will be again refracted, giving rise to violet and red, and the intermediate prismatic colours between, constituting a complete spectrum; and as the drops of rain are innumerable, the observer will see innumerable spectra arranged together so as to form a circular are.

Fig. 273.

I", where it is a second

Fig. 272.

PED

The secondary rainbow arises from two refractions and two reflections of the rays. Thus, let the ray, S, Fig. 273, enter at the bottom of the drop; it passes in the direction towards I' after having undergone refraction at the front; from I' it moves to

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time reflected, and then emerges in front, undergoing refraction and dispersion again. the same reason as in the other case, prismatic spectra are seen arranged together in a circular arc, and form a bow.

In Fig. 274, let O be the spectator, and O P a line drawn from his eye to the centre of the bows. The rays of the sun, S S, falling on the drops, A B C, will produce the inner bow, and falling on D E F, the outer bow, the former by one, and the latter by two reflections. The drop A reflects the red, B the yellow, and C the blue rays to the eye; and in the case of the outer bow, F the red, E the yellow, and D the blue. And as the colour perceived is entirely dependent on the angle under which

Fig. 274.

the ray enters the eye, as in the case of the interior bow, the blue entering at the angle CO P, the yellow at the larger angle B O P, and the red and the largest A O P, we see the cause why the bows are circular ares; for out of the innumerable drops of rain which compose the shower, those only can reflect to the eye a red colour which make the same angle, A O P, that A does with the line O P, and these must necessarily be arranged in a circle of which the centre is P. And the same reasoning applies for the yellow, the blue, or any other ray as well as the red, and also for the outer as well as for the inner bow.

Another interesting natural phenomenon connected with the refraction of light is what is called "astronomical refraction," arising from the action of the atmosphere on the rays of light. It is this which so powerfully disturbs the positions of the heavenly bodies, making them appear higher above the horizon than they really are, and changes the circular form of the sun and moon to an oval shape. It also aids in giving rise to the twilight.

R*

Fig. 275.

Let O, Fig. 275, be the position of an observer on the earth, Z will be his zenith, and let R be any star, the rays from which come, of course, in straight lines, such as RE. Now, when such a ray impinges on the atmosphere at s, it is refracted, and deviates from its rectilinear course. At first this refraction is feeble; but the atmosphere continually increases in density as we descend in it, and therefore the deviation of the ray from its original path, R E, becomes continually greater. It follows a curvilinear line, and finally enters the eye of the observer at O. This may perhaps be more clearly understood by supposing the concentric circles a a, b b, c c, represented in the figure, to stand for concentric shells of air of the same density, the ray at its entry on the first becomes refracted, and pursues a new course to the second. Here the same thing again takes place, and so with the third and other ones successively. But these abrupt changes do not occur in the atmosphere, which does not change its density from stratum to stratum abruptly, but gradually and continually. The result ing path of the ray is, therefore, not a broken line, but a continuous curve. Now, it is a law of vision that the mind judges of the position of an object as being in the direction in which the ray by which it is seen enters the eye. Consequently the star, R, which emits the ray we have under consideration, will be seen in the direction O r-that being the direction in which the ray entered the eye-and therefore the effect of astronomical refraction is to elevate a star or other object above the horizon to a higher apparent position than that which it actually occupies. Astronomical refraction is greater according as the object is nearer the horizon, becoming less as the altitude increases, and ceasing in the zenith. An object seen in the zenith is, therefore, in its true position.

On these principles the figure of the sun and moon, when in the horizon, changes to an oval shape; for the lower edge being more acted upon than the upper, is therefore relatively lifted up, and those objects made less in their vertical dimensions than in their horizontal. Even when an object is below the horizon, it may be so much elevated as to be brought into view; for just in the same way that a star, R, is elevated to r, so may one beneath

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