116.]

COLOURS OF THIN PLATES.

FIG. 95.

229

to produce any given tint. He thus found that there is a limit to the thickness of all transparent objects, below which they cease to be visible in reflected light, and another limit in thickness above this, beyond which they reflect only white light between these two thicknesses the phenomena which we are now considering take place. The thickness of the film which produces any given colour varies with the nature of the reflecting plate, being in the inverse ratio of its refractive index. At and below the thickness of

78

58

of an inch the film of air exhibits a black spot when viewed by reflection, and above To it reflects white light. In water at of a millionth of an inch a black spot is formed; above Toooooo the reflected light is white. Glass produces the same result at all thicknesses below of a millionth of an inch, and reflects white light at all thicknesses above Too of an inch.

50

To00000

1000

The order of succession of the colours constitutes what is termed Newton's scale. Six or seven series of coloured bands may thus be distinctly traced. These rings when produced by homogeneous light are alternately bright and black; the width of the ring is dependent upon the colour, and is greatest in the least refrangible light. The overlapping of the narrow rings by the broader ones in the mixed light of day, is thus, as in the case of the coloured bands produced by interference, the cause of the brilliant succession of colours.

A similar, but fainter series of colours, may be seen in the light that is transmitted through the film, but the tints are in this case complementary to those of the reflected rays. By increasing the obliquity of the incident rays, the breadth of the rings is increased in both transmitted and reflected light. The tints of the transmitted rays are much paler than those seen by reflection in consequence of the large quantity of white light that is transmitted by the glass; they are produced by the interference of a portion of light twice reflected within the plate, with the beam directly transmitted.

In fig. 96, I R represents a beam of light incident upon the film of glass or soap or some substance of greater refractive index than air, shown in magnified section at FF: part of the light, R Y, is reflected; and part, R s T, transmitted; at s, the second surface of the film, a portion of the light is again partially

230

DOUBLE REFRACTION.

[116.

reflected to u; at u part is transmitted, and interferes with the reflected portion u x, of the beam K U, which falls upon the

F

FIG. 96.

S

K

F

upper surface of the film at the spot where s u emerges. Now, since the lengths of the paths of the rays, IRS U, and K u differ by a fraction of an undulation, owing to the refraction and reflection of the portion RSU within the film, interference between the two rays is the result, and colours are produced in the reflected beam; in addition to this action, a part, u v w, of the beam,

I R, is a second time reflected, and passing out on the lower surface of the film, interferes with the portion of K U, which is directly transmitted, and thus the colours in the transmitted light are occasioned. The dotted line, v z, represents the track which is taken by the portion of the ray, K U V, which undergoes reflection from the internal lower surface of the film.

§ II. DOUBLE REFRACTION-POLARIZATION.

(117) Double Refraction.—The law of refraction (100), which is true for water, for glass, and for other homogeneous uncrystallized media, does not extend to all transparent bodies. In all transparent crystals, excepting those belonging to the regular system, the refracted ray is subdivided into two portions, and hence such bodies are said to possess the property of double refraction.

FIG. 97.

This remarkable action upon light is best exhibited in the transparent crystallized variety of calcic carbonate, known as Iceland spar. Place upon a dot, d, made upon a sheet of white paper, a rhombohedron of Iceland spar, as A B, fig. 97, and look down upon the dot through two of the parallel faces of the rhombohedron, the edges of which, for the sake of simplicity, we will suppose to be all equal; two images, o, e, of the dot will be seen instead of a single one; and if the crystal be turned round upon the paper, keeping the eye steadily fixed, one of the images will appear to rotate round the other, which preserves its fixed position. When the eye is placed above the crystal so that

117.]

DOUBLE REFRACTION.

231

the line between the fixed image and the eye cuts the face of the crystal at right angles, then the line which joins the two images of the dot is, under all circumstances, parallel to the diagonal, A, B, connecting the two obtuse angles of the crystal: around this line the different parts of the crystal are symmetrically arranged. Upon varying the obliquity of the incident ray upon the surface, it is found that the refracted ray which was stationary during the movement of rotation, preserves the constant ratio of the sines, and, as in ordinary cases of refraction, falls always in the plane of the incident ray; whilst in the other ray the ratio of the sines varies at different obliquities of the incident ray; and, excepting in the two positions of the crystal, in which the diagonal joining the obtuse angles is in the plane of incidence, this refracted ray never occurs in this plane. One of the refracted rays follows the usual laws of refraction, and is hence termed the ordinary ray; while the other foilows a different law, and is called the extraordinary ray. There is one remarkable direction in the crystal, in which this double refraction does not take place,—a direction parallel to the line which connects the two obtuse angles of the rhombohedron; this line is called the optic axis of the crystal. To render this obvious, a slice of the mineral may be cut in a direction perpendicular to the optic axis, a, b, fig. 98: it will be found on looking at a minute object perpendicularly through such a plate, that only a single image of it will be seen. When the object is viewed obliquely through the plate, a double image of it will be visible. The separation of the two images increases with the obliquity of the incident light to the optic axis, until it is at right angles to it when it attains its maximum. The point at which the difference between the two rays attains its maximum is selected for determining the index of refraction for the extraordinary ray. In the case of Iceland spar, the extraordinary ray is refracted less than the ordinary ray, the index of the extraordinary ray of yellow light being 1486, that of the ordinary ray 1658; such crystals are termed negative doubly refracting crystals. Instances, however, are not wanting in which the extraordinary ray is more refracted of the two, as in quartz and ice; the index of the extraordinary ray in quartz is 1553, whilst that of the ordinary ray is 1544 (Rudberg, Pogg. Ann. 1828, xiv. 45). Such crystals are said to be positive or attractive.

FIG. 98.

It has already been stated (113) that the velocity of light in bodies is inversely proportional to their refractive indices, con

232

DOUBLE REFRACTION-POLARIZATION OF LIGHT.

[117.

sequently in negative crystals the ordinary ray which is the more refracted passes through the crystal with a lower velocity than the extraordinary ray: in the case of Iceland spar, the velocities of the ordinary and extraordinary rays are as 1486 to 1658. In positive crystals, in which the extraordinary ray is more refracted than the ordinary, the latter traverses the crystal with the greater velocity: in quartz, the velocities of the ordinary and extraordinary rays are in the proportion of 1553 to 1'544.

Both rays, if they emerge from a surface parallel to the one at which the incident ray entered, are parallel to each other; but if the surface be inclined, both rays proceed with increasing divergence, each exhibiting the colours of the prismatic spectrum. In all cases, the thicker the crystal the greater is the separation of the two images.

(118) Influence of Crystalline form on Double Refraction.Crystallized substances may be divided into two classes, according to their action upon light; and their optical properties are intimately related to their crystalline form. Thus we have

1. Singly refracting crystals:-These all belong to the regular system.

2. Doubly refracting crystals:-These may be further divided into two sub-classes. a. The first sub-class, like Iceland spar, presents only one optic axis in which no double refraction occurs, and it includes all crystals of the rhombohedral and pyramidal systems; such crystals are termed uniaxal. b. The second, of which aragonite and nitre are examples, comprises all crystals of the three remaining systems,-namely, the prismatic, the oblique, and the doubly oblique systems; they have two optic axes, which, however, do not coincide with any of the crystalline axes. Such crystals are said to be biaxal.

In biaxal crystals, both the doubly refracted rays obey extraordinary laws of refraction.

(119) Polarization.-Light that has been transmitted through a doubly refracting prism, has undergone a remarkable modification. If received upon a second crystal of Iceland spar of equal thickness, placed in a position similar to that of the first (fig. 99, 1), both rays pass through it unchanged, except that they are separated further from each other in proportion to the thickness of the crystal, but the extraordinary ray will still be refracted extraordinarily, and the ordinary ray ordinarily; the principal sections*

*In uniaxal crystals a principal section is, in optical language, a plane containing the optic axis and the transmitted ray.

119.]

POLARIZATION BY DOUBLY REFRACTING CRYSTALS.

233

of the two crystals are parallel. On causing the second plate to describe a quarter of a revolution, as shown at 2, still but two

1.

FIG. 99.

2.

3.

images will be seen; but now, the ordinary ray is refracted extraordinarily, the extraordinary ray is refracted ordinarily. When the second crystal describes another quarter of a revolution as at 3, only one image is visible, the rays separated by the first are reunited by the second; in all other intermediate positions, each ray is doubly refracted, and four images become visible: the intensity of the images taken together is constant, one pair fading as the other increases in brightness, and vice versa. Each ray, therefore, on emerging from a crystal of calcareous spar, has acquired new properties: it is no longer subject to further subdivision by a second crystal when placed in particular positions. The rays in fact appear to have acquired sides, and to have new relations to certain planes within the crystal; such rays are said to be polarized.

I

FIG. 100.

2

Tourmaline is a doubly refracting prismatic crystal, which, when cut parallel to the axis and sufficiently thick, transmits the extraordinary ray alone, and absorbs the ordinary ray. If a plate of this mineral cut from a brown or green specimen, parallel to the axis of the prism, a a, (fig. 100, 1), be placed between the eye and a lighted candle, a considerable portion of light will traverse the plate, and the amount of light will be in no way affected on turning the plate round in its own plane; but if light which has been thus transmitted through one

plate of this mineral, be allowed to fall upon a second similar plate, it will traverse this without interruption only when the axes of the two plates are parallel (fig. 100, 1); but it will be completely interrupted where the plates overlap, when the second