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2, 3, 4, &c., these may them being half waves.

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Fig. 250.

represent waves, the alternate lines between It will be perceived that wherever two whole waves or two half waves encounter, they mutually increase each other's effect; but if the intersection takes place at points where the vibrations are in opposite directions, interference, and therefore a total absence of light, results, as is marked in the figure by the large dots.

Wherever, therefore rays of light are arranged so as to encounter one another in opposite phases of vibration, interference takes place. Thus, if we take a convex lens of very long focus, and press it upon a flat glass by means of screws, Fig. 251, at the point of contact, when we inspect the instrument by reflected light, a black spot will be seen, surrounded alternately by light and dark rings. These pass under the name of Newton's coloured rings. When the light is homogeneous the dark rings are black, and the coloured ones of the tint which is employed; but when it is common white light the central black spot is surrounded by a series of colours. When the instrument is inspected by transmitted light, the colours are all complementary, and the central spot is of course white. These rings arise from the interference of the rays reflected from the anterior and posterior boundaries between the two glasses. The colours of soap-bubbles and thin plates of gypsum are referable to the same

Fig. 251.

cause.

By the diffraction of light is meant its deviation from the rectilinear path, as it passes by the edges of bodies or through apertures. It arises from the circumstance that when ethereal, or, indeed, any kind of waves, impinge on a solid body, they give rise to new undulations, originating at the place of impact, and often producing interference. Thus, if a diverging beam of light passes through an aperture, a b, Fig. 252, in a plate of metal, an eye placed beyond will discover a series of light and dark fringes. The cause of these has already been explained in Chapter XXXI., in which it was shown that from the points a and b new systems of undulations arise, which interfere with one another, and also with the original waves.

Fig. 252.

CHAPTER XLII.

OF POLARIZED LIGHT.

Peculiarity of Polarized Light-Illustrated by the Tourmaline-Polarization by Reflection-General Law of Polarization-Positions of no Reflection— Plane of Polarization.

WHEN a ray of common light is allowed to fall on the surface of a piece of glass, it can be equally reflected by the glass upward, downward, or laterally.

If such a ray falls upon a glass plate at an angle of 56°, and is received upon a second similar plate at a similar angle, it will be found to have obtained new properties. In some positions it can be reflected as before; in others it cannot. On examination it is discovered that these positions are at right angles to one another.

Again, if a ray of light be caused to pass through a plate of tourmaline, c d, Fig. 253, in the direction a b, and be received upon a second plate, placed symmetrically with the first, it passes through both without difficulty. But if the second plate be turned a quarter round, as at g h, the light is totally cut off.

Fig. 253.

Considering these results, it therefore appears that we can impress upon a ray of light new properties by certain processes, and that the peculiarity

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consists in giving it different properties on different sides. Such a ray, therefore, is spoken of as a ray of polarized light.*

When light is polarized by reflection, the effect is only completely produced at a certain angle of incidence, which therefore passes under the name of the angle of maximum polarization. It takes place when the reflected ray makes,

* Dr. Pareira, in his "Lectures on the Polarization of Light," delivered before the Pharmaceutical Society of London, contrasts some of the distinguishing characteristics of common and polarized light as follows:

A RAY OF COMMON LIGHT 1. Is capable of reflection at oblique angles of incidence in every position of the reflector.

2. Penetrates a plate of tourmaline (cut parallel to the axis of the crystal) in every position of the plate.

3. Penetrates a bundle of parallel glass plates in every position of the bundle.

4. Suffers double refraction by Iceland spar, in every direction, except that of the axis of the crystal.

A RAY OF POLARIZED LIGHT 1. Is capable of reflection at oblique angles of incidence in certain positions only of the reflector.

2. Penetrates a plate of tourmaline (cut parallel to the axis of the crystal) in certain positions of the plate, but in others is wholly intercepted.

3. Penetrates a bundle of parallel glass plates in certain positions of the bundle.

4. Does not suffer double refraction by Iceland spar in every direction, except that of the axis of the crystal. In certain positions it suffers single refraction only.

A reference to the second column will at once explain the question, "What is polarized light?"-ED.

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with the refracted ray, an angle of 90. Thus, let A B, Fig. 254, be a plate of glass, a b an incident ray, which, at b, is partly reflected along bc, and partly refracted along be, emerging therefrom at e d. Now maximum polar.. ization ensues when e be is a right angle, from which it follows that the polarizing power is connected with the refractive, the law being that the index of refraction is the tangent of the angle of polarization Let A B, Fig. 255, be a plate of glass, on which a ray of light, a b, falls, and after polarization is reflected along bc; at c let it be received on a second plate, C D, similar to the former, and capable of revolving on e b, as it were on an axis. Let us now examine in what positions of this plate the polarized ray, bc, can be reflected, and in what it cannot.

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Fig. 255.

Experiment at once shows that when the plane of reflection of the first mirror coincides with the plane of reflection of the second, the polarized ray

undergoes reflection; but if they are at right angles to one another, it is no longer reflected. To make this clear, let a b, Fig. 256, be the first mirror, and cd the second, so arranged as to present their edges, as seen depicted on this page. Again, let e f be the first, and g h the second, now turned half-way round, but still presenting its edge; in both those positions, the planes of incidence and reflection of both the mirrors coinciding, the ray polarized by a bor e f will be reflected. But if, as in ik, the second mirror, l, is turned so as to present its face, or, as in m n, it is turned at o, so as to present its back, in these cases, the planes of incidence and reflection of the two mirrors being at right angles, the polarized ray can no longer be reflected. We have, therefore, two positions in which reflection is possible, and two in which it is impossible, and these are at right angles to one another. By the plane of polarization we mean the plane in which the ray can be completely reflected from the second mirror.

Fig. 256.

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When a ray of light falls on the surface of a transparent medium, it is divided into two portions, as has already been said, one of these being reflected, and the other refracted. On examination, both these rays are found to be polarized: but they are polarized in opposite ways, or, rather, the plane of polarization of the refracted is at right angles to the plane of polarization of the reflected ray.

Polarization by Refraction-Application of the Undulatory Theory-The Polariscope.

When it is required to polarize light by refraction, a pile of several plates

of thin glass is used, for polarization from a single surface is incomplete.

nomena.

On the undulatory theory we can give a very clear account of all these pheCommon light originates in vibratory movements taking place in the ether; but it differs from the vibrations in the air which constitute sound in this essential particular-that while in the waves of sound the movements of the vibrating particles lie in the course of the ray, in the case of light they are transverse to it. This may be made plain by considering the wavelike motions into which a cord may be thrown by shaking it at one end, the movement being in the up-and-down, or in the lateral direction, while the wave runs straight onward. The ethereal particles, therefore, vibrate transversely to the course of the ray. But then there are an infinite number of directions in which these transverse vibrations may be made: a cord may be shaken vertically or laterally, or in an infinite number of intermediate angular positions, all of which are transverse to its length.

d

Common light, therefore, arises in ethereal vibrations taking place in every possible direction transverse to the path of the ray; but in polarized light the vibrations are all in one plane. Thus, in the case of tourmaline, when a ray passes through it all vibrations are taking place in one direction, and therefore the ray can pass through a second plate placed symmetrically with the first; but if the second be turned a quarter

round the vibrations

can no longer pass in

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the same way as a Fig. 257.
sheet of paper, cd, Fig. 257, may be slipped
through a grating, a b, while its plane
coincides with the length of the bars; but
can no longer go through when it is turned
as at ef, a quarter round.

Again, in the case of polarization by reflection, let AB, Fig. 258, be the mirror on which a ray of common light, ab, falls Dat the proper angle of polarization, and is reflected in a polarized condition along b c. CD will be the plane in which the ethereal particles vibrate after reflection, and the curve line drawn on it may represent the intensities of their vibrations.

Fig. 258.

So, too, in Fig. 259, we have an illustration of polarization by refraction. Let A B be a bundle of glass plates, a b the incident, and cd the polarized

B

Fig. 259.

ray; the plane C D at right angles to the plates is the plane of polarization, and the curve drawn on it represents the intensities with which the polarized particles move.

In every instance the plane of polarization is perpendicular to the planes of reflexion and refraction.

The polariscope is an instrument for exhibiting the properties of polarized light. There are many different forms of it: Fig. 260 represents one of them. It consists of a mirror of black glass, a, which can be set at

any suitable angle to the brass tube, A B, by means of a graduated arc, e; it can also be rotated on the axis of the tube, B A, and the amount of that rotation read off on the graduated circle, b. At the other end of the tube there is a second mirror of black glass, d, which, like a, can be arranged at any required angle, and likewise turn round on the axis of the brass tube, A B, the amount of its rotation being ascertained by the divided circle, c. Sometimes, instead of this mirror of black glass, a bundle of glass plates in a suitable frame is used. The instrument is supported on a pillar, C.

C

A

The fundamental property of light polarized by reflection may be exhibited by this instrument as follows:-Set its two mirrors, a and d, Fig. 260. so as to receive the light which falls on them at an angle of 56°. Then, when the first, a, makes its reflection in a vertical plane, the light can be reflected by d, also in a vertical plane, upward or downward. But if d be turned round 90°, so as to attempt to reflect the ray to the right or left in a horizontal plane, it will be found to be impossible, the light becoming extinct and in intermediate positions. As the mirror revolves the light is of intermediate intensity.

CHAPTER XLIII.

ON DOUBLE REFRACTION AND THE PRODUCTION OF COLOURS IN
POLARIZED LIGHT.

Double Refraction of Iceland Spar-Axis of the Crystals-Crystal with two Axes-Production of Colours in Polarized Light-Complementary Colours produced-Colours depend on the Thickness of the Film-Symmetrical Rings and Crosses-Colours produced by Heat and Pressure— Circular and Elliptical Polarization.

By double refraction we mean a property possessed by certain crystals, such as Iceland spar, of dividing an incident ray into two emergent ones.

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Let

Rr, Fig. 261, be a ray of light falling on a rhomboid of Iceland spar, ABCX, in the point r; it will be divided during its passage through the crystals into two rays, r E, r O, the latter of which follows the ordinary law of refraction, and therefore takes the name of the ordinary ray; the former follows a different law, and is spoken of as the extraordinary ray.

Objects through such a crystal appear double. A line, M N, on a piece

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