But 10 represents the velocity of the corpuscle in air, while RO represents its velocity in water. Hence Velocity in water and since the refractive index from air to water is greater than unity, it follows that, according to the emission theory, the velocity of light must be greater in water than in air. In the second theory, called the undulatory or wave theory of light, a luminous body is supposed to set up vibrations in an all-pervading ether, and these vibrations are supposed to travel through the ether, and when they enter the eye excite the sense of vision. During the passage of the light from the source to the eye, the energy emitted by the source, and which we recognise when it is given up to the retina as light, must be stored up in the ether. On the older undulatory theory, it was supposed that light-waves consisted of a transverse vibratory movement of the ether itself, but a difficulty was introduced by the fact that, if we suppose that the motion is propagated by the successive parts of the ether setting each other in motion by mutually attracting forces, these forces would be inclined to the direction in which the wave was travelling, and hence they would have a component in the direction of the wave normal, and this component would tend to set up longitudinal waves, in addition to the transverse waves which are required to explain optical phenomena. We have no evidence, however, of the existence of such longitudinal waves in the ether. In the later form of the undulatory theory, called the electromagnetic theory of light, the supposition is made that the vibrations consist not in the change in position of the ether particles, but in a periodic alteration in the electrical and magnetic condition of the ether during the passage of the light. This supposition does not lead to the same difficulty as to the formation of longitudinal waves as does the older theory, and hence possesses a marked advantage. Since both forms of the theory suppose the existence of a transverse vibration set up in the medium, and only differ as to the nature of the entity the displacement of which constitutes the vibration, the explanations which we shall make in the succeeding sections, since they do not involve the nature of the waves, will apply to either form of the theory. We shall also sometimes talk of the displacement of an ether particle during the vibration, but this must be taken as a short and convenient method of stating the displacement of the electric and magnetic condition of the ether at the point under consideration. We now pass on to consider what assumptions as to the relative velocity of light in air and in water have to be made on the undulatory theory to account for the refraction of light when it passes from air to water. Let AB (Fig. 340) be the line of separation between air and water. Let PP' represent a wave-front in the air, then if va is the velocity of distance, we describe a circle, and then from O draw a tangent OR, OR will represent the wave-front in water at the instant when the point P' on the wave-front PP' reaches o (see § 273). If ON and PN' are normals to AB, we have = αμπυ sin NOP Now in the triangle PP’O the angle at P' is a right angle, hence the two angles P'PO and P'OP are together equal to a right angle. But the angles P'ON and P'OP are also together equal to a right angle. Hence the angle P'ON is equal to the angle P'PO. In the same way, the angle N'PR is equal to the angle POR. So that Or the velocity of light in air is to that in water in the ratio of the refractive index from air to water. It will thus be seen that according to the undulatory theory light travels slower in water than in air, while according to the emission theory it travels more quickly in water. Thus a measurement of the velocity of light in air and in water would form a crucial experiment to test the validity of the rival theories. This crucial experiment was performed by Foucault, who placed a tube filled with water and closed by glass ends between the fixed mirror C and the rotating mirror B, and thus was able to measure the velocity of light in water, and found it to be less than in air. This experiment, although it does not in any way prove the truth of the undulatory theory, yet shows that the emission theory, at any rate, cannot be true. CHAPTER VI DISPERSION 367. Dispersion.-The phenomenon of refraction is not in reality as simple as we have hitherto considered it to be, for if a narrow parallel pencil of white light, such as sunlight, is allowed to pass obliquely from one medium to another, it is found that in the second medium the white light is split up into light of several colours, a phenomenon which is referred to as dispersion. Thus if a beam of parallel rays of white light, such as is obtained by reflecting sunlight through a narrow slit, is introduced into a dark room and meets a screen DE at F, forming a white patch of light, then on interposing a prism ABC (Fig. 341) in the path of the beam with its refracting edge parallel to the slit, the light will be refracted towards the base of A the prism, but the patch on the screen is no longer the same size as before, nor is it white. The patch is drawn out in the direction RV, in which the light is deviated, and exhibits all the colours of the rainbow. These colours pass imperceptibly the one into the next, but starting with red nearest the original undeviated patch F, the colours pass through orange, yellow, green, blue, indigo, to violet, which is the most deviated. These colours constitute what is called a spectrum. B FIG. 341. Thus white light has been split up by the prism into light of a number of different colours, these coloured lights being deviated to a different amount by the prism, so that the refractive index between two media, on which the deviation depends, is different for light of different colours; and since the violet rays are more deviated than the red, the refractive index for violet light is greater than for red light. That white light is really formed by the superposition of light of all the colours of the spectrum can be shown by receiving the colours of the spectrum on a number of separate mirrors, and reflecting the light from them to the same point, when it will be found that white light will be reproduced. In the form of the experiment described above, the different colours overlap on the screen to a certain extent; and in order to obtain a spectrum where no overlapping takes place, or a pure spectrum, as it is called, we may adopt the arrangement shown in Fig. 342. Light from a source L, such as the electric arc, passes through a narrow slit in a screen S, and then falls on a con ated towards the base of the prism, and a spectrum will be formed on a screen placed at D. If we suppose that the slit is illuminated by violet light only, then an image of the slit will be produced at v, while if red light is used the image will be at R. Hence the spectrum VR is composed of a series of images of the slit formed by differently coloured light. If the slit is very narrow, one image will overlap very little on the adjacent images, and a pure spectrum will be obtained. As the slit is widened the images will overlap more and more, till with a very wide slit we shall get a white patch in the centre of the spectrum where all the images overlap, with a red edge at one end and a violet edge at the other. Another method of obtaining a pure spectrum is shown in Fig. 343. Parallel light, which may be obtained by means of a collimator, being R B FIG. 343. incident on the prism, a lens L is placed after the prism, and this lens brings the rays of the different colours to real foci between R and V, where a pure spectrum may be received on a screen or viewed with an eye-piece. This arrangement will also allow of the recomposition of the different colours of the spectrum to form white, for if the screen be placed at AB the red and violet rays, as shown by the figure, and therefore also the rays of the other colours, will be uniformly spread over the patch Ar Under these circumstances a white patch will appear on the screen. If, however, a small obstacle be placed at V, so as to cut off the violet, the patch at AB will appear coloured a greenish-gold colour, produced by the mixture of the remaining colours. In the same way, by cutting off the red rays by an obstacle placed at R, the patch will appear a greenish blue. When the slit of the spectrometer shown in Fig. 327 is illuminated with white light, a pure spectrum is formed at the principal focus of the lens F in the manner considered above, and can be observed with the eye-piece. The spectrometer, when used to observe spectra, is sometimes called a spectroscope. By using light of different colours, the refractive index of a substance for light of these colours can be obtained by any of the methods given in §§ 344, 346. 368. Fraunhofer's Lines. When the slit of a spectroscope is illuminated by sunlight, it is found that the spectrum is traversed by an enormous number of dark lines parallel to the length of the slit. These dark lines are called Fraunhofer's lines, and are due, as we shall see later, to the light of the colours which are thus missing from the solar spectrum being absorbed in the sun's or the earth's atmosphere. These lines form a very convenient means of specifying any particular colour in the spectrum, and hence the more prominent of them are indicated by the letters A, B, C, D, &c. Their relative position in the spectrum are shown in Fig 344. The lines A, B, and C are in the red, D in the orange-yellow, E in the green, F in the greenish-blue, G in the indigo, and H in the violet part of the spectrum. Hence when we refer to light of any particular colour as, say, D light, we mean light of the colour which corresponds to the dark line D in the orange-yellow of the solar spectrum. 369. Refractive Index for Light of Different Colours Dispersive Power.-In the following table the refractive index of some substances are given for the light corresponding to Fraunhofer's lines : : |