who Whence if be the angle through which the plane of polarization is rotated, measured towards the right hand of a person is looking along the ray Substituting the values of V,,V, from (38) we obtain approxi 1 which is the expression for Biot's law. The sign of p is positive or negative, according as the medium is right-handed or lefthanded. If the wave were travelling in the opposite direction, the sign of t would have to be reversed in (37); this would not make any alteration in the form of (39), but since in this case z would be negative, the rotation would be in the opposite direction. This agrees with experiment. 275. We must now consider the theory of quartz. Taking the axis of the crystal as the axis of z, we must put whence writing = Px Py Pi P2 = 0; = n/Px = a2, n/p2 = c3, q=p1/n, and recollecting that A-B=-n, the equations of motion become Since everything is symmetrical with respect to the axis, we may without loss of generality suppose, that the axis of y is parallel to the wave-front; we may therefore put where u = A1S, v = A „S, w= Substituting in (40) we obtain A&S, (V2 — a2n3) A1 + a2lnA ̧ − (2ıπ/VT) qa3n3A, = 0, 1 THEORY OF QUARTZ. 281 whence eliminating A1, A2, A3, and putting for the angle which the direction of propagation makes with the axis of the crystal, we obtain ( V2 — a2) ( V 2 — a2 cos2 0 — c2 sin2 ) =(4π/V13) q2a cos 0 (V2 - c2 sin2 ) ......(41). This equation is a biquadratic for determining V2, but since q is a small quantity, we may put U for V in the right-hand side ; and we thus obtain a quadratic equation for determining the two values of V2. = It follows from (41), that when the direction of propagation is perpendicular to the axis, so that π, quartz behaves in the same way as Iceland spar. When the direction of propagation is parallel to the axis, so that = 0, the first two of (40) are of the same form as (36); consequently there are two waves, which travel through the crystal with different velocities, and are circularly polarized in opposite directions. For directions which are slightly inclined to the axis, the two waves are elliptically polarized in opposite directions; but owing to the smallness of q, it follows that the right-hand side of (41) diminishes rapidly as increases, so that when is not small, the elliptic polarization becomes insensible, and the two waves are sensibly plane polarized. CHAPTER XVI. MISCELLANEOUS EXPERIMENTAL PHENOMENA. 276. THE present chapter is descriptive and not mathematical; and its object is to give an account of a variety of experimental phenomena. The subjects of which it treats are, Dispersion, Spectrum Analysis, Absorption, Colours of Natural Bodies, Dichromatism, Anomalous Dispersion, Selective Reflection, Fluorescence, Calorescence, and Phosphorescence. We shall give an account of the principal experimental results connected with these phenomena, so far as they relate to the Theory of Light; and in the next chapter, we shall enquire how far they may be explained by theoretical considerations. Dispersion. 277. When sunlight, proceeding from a horizontal slit, is refracted by a prism whose vertex is downwards, and the emergent light is received upon a screen, it is found that the image of the slit, instead of consisting of a narrow line of white light, presents the appearance of a coloured band, which is called the solar spectrum. The order of succession of the colours is violet, indigo, blue, green, yellow, orange, red; the red end of the band being lowest, and the violet highest. This experiment shows, that light of different colours possesses different degrees of refrangibility, violet being the most refrangible, and red the least. All transparent bodies, which are capable of resolving light into its constituent colours, are called dispersive media; and the phenomenon of resolution is called dispersion. 278. Observations of eclipses have shown, that the velocity of light of all colours is the same in vacuo. We have also proved by more than one theory, that the index of refraction of light, which passes from a vacuum into a transparent medium, is equal to the ratio of the velocity of light in vacuo, to the velocity of light in the transparent medium; hence the velocity of light in a dispersive medium is a function of the period, and is greater for red light than for violet. Now, subject to an exception, which will be explained in § 329, it follows from the fundamental principles of Dynamics, that the period of light of any particular colour is an invariable quantity, which is independent of the physical constitution of the medium through which the light is passing; hence the wave-length of light of any particular colour, depends upon the constitution of the medium, and is smaller in glass than in vacuo. It can also be proved experimentally, that the wave-length of violet light in vacuo is less than the wave-length of red, and that the wave-lengths of different colours increase continuously in going down the spectrum from violet to red; whence the period of violet light is less than that of red, and the periods increase continuously in going down the spectrum. 279. That the colour of light depends upon the period, is a fact of fundamental importance in Physical Optics; and when we consider some of the dynamical theories which have been proposed to explain dispersion, we shall see that there are strong grounds for thinking, that the qualities of transparency and opacity do not depend so much upon the particular substance of which the medium consists, as upon the period of the ethereal waves. 280. A table of the principal wave-lengths and periods is given on p. 284, but at present it will be only necessary to notice, that the frequency (or number of vibrations per second) of the extreme red waves is about 395 x 102, and the frequency of the extreme violet is about 763 x 1012. Accordingly the interval between the extreme red and violet is slightly less than 2, and the sensitiveness of the eye is therefore confined to less than an octave; on the other hand the sensitiveness of the ear to sound extends to about eleven octaves. Spectrum Analysis. 281. Dispersion was discovered by Newton' in 1675; but in 1802 Wollaston observed, that if sunlight is allowed to pass through a very narrow slit, the spectrum is not continuous, but is crossed by a number of fine dark lines. The investigation of these dark lines was subsequently taken up by Frauenhofer in 1814, who observed 576 of them, and they are now universally known by his name. Frauenhofer selected certain of the principal lines as land-marks, which he denoted by the letters A, a, B, C, D, E, b, F, G, H, I, and which we shall proceed to consider. 282. A is a line in the extreme red portion of the spectrum; a is a group of lines, and B and C are well defined lines also in the red; D is a double line in the orange, which consists of two lines very close together; E lies in the yellow end of the green; b is a group of lines in the green; F is a line in the blue end of green; G lies in the indigo; H in the violet; and I is the extreme end of the spectrum. The wave-lengths of these lines were first measured by Frauenhofer, subsequently by Ångström, and more recently by Rowland, Bells and others in America, and some of the values obtained are given in the following table in tenthmetres. A tenth-metre is 10-10 of a metre. Frauenhofer's examination of these dark lines is one of the most important scientific events of the present century. It has laid the 1 Opticks, Book I. Part I. 2 Phil. Trans. 1802, p. 378. 3 Denkschriften der Münchener Akad. 1814. Recherches sur le Spectre Solaire, Spectre Normal du Soleil, p. 25. Upsala, 1868. 5 Phil. Mag. (5) vol. xxv. p. 368. |