We have seen that the value of K, as obtained from a comparison of the values of the electro-static units with the corresponding electromagnetic ones, was equal to the velocity of light, so that this formula of Maxwell's shows that electrical waves will travel with the velocity of light. When electrical waves are passing through a dielectric, then, at any point we shall have an electrical displacement produced which will be in a direction at right angles to the direction of motion of the waves. The displacement will occur first in one direction, reach a maximum value, gradually decrease to zero, and then become negative, and so on. Thus the electrical displacement will play the same part in electrical waves as does the displacement in a vertical direction of the water particles in a water wave. As we have seen, the displacement within a dielectric is accompanied by a stress which opposes the displacement, and this stress plays the same part as the action of gravity in the case of water waves. A B FIG. 547. Suppose we consider a cylindrical portion, AB (Fig. 547), of a medium through which electrical waves are passing, the direction in which the waves are moving being at right angles to the axis of the cylinder and as shown by the arrow. As the waves pass, the electrical displacements in the cylinder AB will take place parallel to the axis, that is, at right angles to the direction of motion of the waves. The sense of the displacement will be alternately in the direction AB and in the direction BA. Now a displacement in the direction AB will produce the same magnetic field as a current in the cylinder from A to B, and will therefore produce a system of magnetic lines of force which will be a series of circles having their centres on AB and lying in planes at right angles to AB. Hence the wave of electro-static displacement will be accompanied by a wave of magnetic force, for when the displacement changes sign the direction of the magnetic force will also change sign. From considerations similar to those adopted in § 273, when considering Huyghens's construction for the wave-front, it will be evident that the only portion of the line of force due to the cylinder AB that will produce a magnetic field will be that portion which is perpendicular to the direction of motion of the wave, that is, the portion in the wave-front. For if we imagine a second cylinder in the dielectric alongside AB, then, if these are both in the wave-front, the displacement currents in them will be in the same phase, and hence the lines of magnetic force in the space between them will be in the opposite direction, and will therefore interfere with one another. Hence every electrical wave will be accompanied by a magnetic wave, the directions of the electrical displacement and the magnetic force being at right angles, but both being in the wave-front. Since it is impossible to obtain one wave without the other, we shall often speak of the one only when discussing the phenomena of electro-magnetic waves; it must be remembered that the other always exists. A somewhat more concrete picture of the condition of a dielectric through which electric waves are passing may be formed by considering the motion of Faraday tubes. Along each Faraday tube there exists an electrical displacement, and hence, when a tube moves through a dielectric, the portion of the dielectric which at any given instant is included within the tube is the seat of an electrical displacement. The displacement takes place in the direction of the length of the tube and towards the positive end.1 Thus if we have a series of tubes, such as those shown in Fig. 548, moving FIG. 548. in the direction of the arrow, the displacement produced at any point within the dielectric will be upwards when any of the tubes which have their positive ends upwards are passing the point, and downwards whenever one of the tubes having its negative end upwards are passing. In this manner of picturing the passage of electrical waves, the accompanying magnetic field is that which we have already seen occurs whenever we have motion of Faraday tubes, the direction of the magnetic field being at right angles both to the length of the tubes and to the direction of their motion, that is, at right angles to the plane of the paper. Since each Faraday tube is the seat of a certain amount of energy stored up in the form of electrical strain, this energy will be carried forward by the motion of the tubes, and so we have here a picture of how the energy corresponding to the waves travels. Each tube behaves very much like a stretched rod of india-rubber, for such a rod would possess energy owing to its strained condition, and would be made to do work while regaining its unstrained condition. There is, however, this important difference, that in the case of the rubber the portion of matter which is in the state of strain is carried forward. In the electrical case it is otherwise, for the strain in the ether is handed on from one portion to the next, and at present the mechanism by which this handing on is performed, as well as the nature of the electrical strain 1 Of course, by the term direction of the displacement, we refer to the direction of the displacement of positive electricity. There will be a displacement of negative electricity in the opposite direction, but as the displacement of positive electricity in one direction is equivalent to the displacement of negative electricity in the opposite direction, we need only speak of the displacement of the positive electricity. itself, is unknown, and till these are known we are unable to answer the question, “What is electricity?" Since the motion of the energy takes place at right angles to the tubes of force, that is, to the direction of the electro-static field, and also at right angles to the magnetic field, we have here a confirmation of Poynting's theory on this subject (§ 569). 573. Connection between Refractive Index and Specific Inductive Capacity. If v is the velocity of electro-magnetic waves in air, then, according to Maxwell's theory, we have v= Kμ, where μ and K are the permeability and specific inductive capacity of air. Similarly, if is the velocity in a medium for which the permeability and specific inductive capacity are μ' and K', then v' = √K'|p'. Now in the case of all transparent bodies μ is very nearly unity, so that in this case we have v′]v= √K"]K. But the ratio of the velocity of light in air to the velocity in a given medium is called the refractive index of the medium, while the ratio KK is the specific inductive capacity of the medium taken with reference to air. Thus if n is the refractive index, and K the specific inductive capacity, both taken with reference to air, we have n = √K. That is, the refractive index is equal to the square root of the specific inductive capacity. When we attempt to test the accuracy of this conclusion by experiment, we are met with the difficulty that since the refractive index changes with the wave-length, that is, the velocity changes with the wave-length of the light, the question arises, what wave-length are we to employ? It is evident that the correct wave-length will be that which corresponds to experiments made when determining K. Now measurements made of the specific inductive capacity by means of the ordinary methods with condensers, are made with alternating currents to avoid the effect of absorption, but the alternations have a frequency of, at most, a few thousands per second. Hence the refractive index which has to be used in testing Maxwell's formula is that which corresponds to a very small frequency, that is, to a very long wave-length; in fact, the wave-length of a light wave of which the frequency is a thousand would be 3× 107 cm. Now measurements of refractive index can only be made for comparatively short wave-lengths, and it is only by exterpolation. that we can calculate what the refractive index would be for very great wave-lengths, and most of the differences in the annexed table are probably due to this cause, for we have no evidence that the laws of the change of refractive index with wave-length derived from the small range of wave-lengths over which we are able to make experiments will hold over very much greater ranges. * These values of the square of the refractive index are for D-light. It will be seen that in general the agreement is satisfactory. In some cases, such as water and alcohol, however, the values obtained for the specific inductive capacity are very much greater than Maxwell's theory would indicate. In the case of water, it has been found that the refractive index for electrical waves having a frequency of about 50 x 106 is 89. Hence for waves of this frequency the square of the refractive index, 79.2, is equal to the specific inductive capacity. 574. Transmission of Light and Conductivity.--Electrical waves can only be transmitted through a medium in which an electrical displacement calls forth an elastic resistance, for otherwise a vibratory motion is impossible. In a conductor of electricity, however, electrical displacement can take place, and no force will be called into play tending to oppose the displacement. Electrical waves cannot, therefore, be transmitted through a conducting medium, and since light waves are also electromagnetic waves, they also will not be transmitted through a conducting medium. Maxwell's theory thus explains why the metals are, without exception, opaque to light. Insulators or dielectrics, on the other hand, since they can transmit electrical waves, will also transmit light. It does not follow that if a body will not transmit light that it must be a conductor, for a medium may be opaque because its structure is not homogeneous. Thus glass in a block is transparent, but pounded glass is opaque, the opacity being due to the scattering of the light by the small particles of glass, since there will be a certain amount of reflection at every surface. 575. The Faraday Effect.-In 1845 Faraday discovered that when a beam of plane polarised light (§ 400) is passed through a magnetic field in the direction of the lines of force, the plane of polarisation of the light is rotated owing to its passage through the field. Thus if the light from the source L (Fig. 549) is passed through a polarising Nicol, P, then through a tube T containing water, or better, carbon bisulphide, and finally through an analysing Nicol A, then, on rotating this analyser so that its principal plane is perpendicular to that of the polarising Nicol, no light will be transmitted. If, however, a current is passed through a coil c which surrounds the tube T, C T so as to produce a magnetic field with the lines of force L parallel to the direction in ✡ which the light is travelling, the light will be found to pass through the analyser A. By turning the analyser it is, however, possible to again cut off all the light. This experiment, therefore, shows not only that the plane of polarisation of the light has been rotated, but also, since by rotating the analyser it is possible to cut off all the light, that the beam must remain plane polarised. If the direction of the current is reversed, the direction of the rotation is also reversed. FIG. 549. There is an important difference between the rotation of the plane of polarisation thus produced by matter when placed in a magnetic field and that produced when a ray of light is transmitted through a plate of an alotropic body such as quartz (§ 411). Suppose a ray of plane polarised light is transmitted through a tube containing water, T (Fig. 549), in the same direction as that in which the lines of force of the field proceed. Then, looking in the direction in which the lines of force run, the plane of polarisation will be rotated in the clockwise direction. If the direction of the light is reversed, the rotation will still take place in the clockwise direction, as seen by an observer looking along the direction of the lines of force, but will appear in the opposite direction to an observer looking in the direction in which the light is travelling. Hence, if the ray of light, after having once passed through the tube of water in the magnetic field, is reflected back along its course, it will be again rotated in the same direction, as far as the coil is concerned, as during its first passage, and the plane of polarisation will therefore be turned through twice the angle through which it was turned owing to the single passage. In the case, however, of a ray of plane polarised light transmitted through a plate of quartz, Q (Fig. 550), in a direction parallel to the axis of the crystal, the rotation will take place in one direction when the light passes one way, but will take place in the opposite direction, as far as the crystal is concerned, if the direction of the light is reversed. Hence, if a ray of plane polarised light is transmitted through such a plate of quartz, and is then reflected so as to again traverse the crystal in the reverse direction, བརྙ་འ་འུ་རིགས་ ་་ FIG. 550. |