Sine wave

“ As far as I know, the image may be composed of two sine waves of similar, but not quite identical, frequency added together. Maybe I just don't know what you mean by "spread". There can be media in which lower-frequency waves propagate faster than higher-frequency waves, so is this figure caption asserting something about light (that lower-frequency light travels more slowly? or what?) or is it asserting something that's true of all waves with a mathematical form similar to what's shown? I've changed the wording in the earlier part of the figure caption. ”

“ When light is analysed by a prism or grating into a spectrum, the course of each ray is deflected—refracted or diffracted—by an amount corresponding to its frequency of vibration or wave-length.
Motion of the medium, so long as it is steady, affects neither frequency nor wave-length, and accordingly is without influence on the result. ”

“ Whenever we can produce interference in this manner between two sets of sound-rays, or light-rays, or rays of any other kind, we have the strongest possible proof that we are concerned with a wave-motion; because in no other way that we can understand is it possible that a destruction of sound by sound can take place by, so to speak, superimposing two sound-rays, or a destruction of light by bringing together two rays of light. ”

“ From the fact that all Hertz waves travel with the same speed as light, and from our ability to imitate, as you have seen, the well-known optical phenomena with Hertz radiation of short wave-length, the great induction has been made that all æther waves have the same essential nature, and that invisible actinic rays, light rays, dark-heat rays, and Hertz rays are all of them æther waves of various wave-lengths and amplitudes. ”

“ The emission theory died hard and the early advocates of the undulatory theory of light were forced to work up with a completeness, probably without parallel in the history of science, the evidence, necessarily indirect, that in optics we have to do with a wave-motion. The standpoint of optical theory may be deemed conclusive, possibly final, so far as the general proposition is concerned that it is the science of a wave-motion. ”

“ Thus resonance might occur, and the consequent vibrations of the electrons would start a series of secondary waves.
If, however, we assume resonance, it is difficult to see why there is a range of wave-lengths produced and another range of wave-lengths which may produce them. We should have expected one definite wave-length or a few definite ones producing one or a few definite wave-lengths in the glow, while if a whole range of waves will produce the effect it is difficult to see why all bodies do not exhibit the phenomenon. ”

“ Let us suppose that we are looking at a coloured object—let us say, a red railway signal-lamp; from the lamp to our eye there flows a continuous line of luminous undulations; these undulations enter the eye and become depicted on the retina. For every wave that passes through the pupil, there is a separate and corresponding vibration of the optic nerve, and the number of these vibrations that take place in the course of a second can be easily calculated if we know the velocity of light and the breadth of the waves. We have before found that light travels at the rate of 185,000 miles per second ”

“ The action of a convex or converging lens upon light may be better understood by studying Fig. 379 in which light is passing from S to F. The successive positions and shape of the advancing light waves are indicated by lines drawn across the beam. The light being retarded more in the thicker part of the lens, the light waves on leaving the lens have a concave front. Since light waves tend to move at right angles to the front of the wave, the light is brought to a focus. ”

“ Returning to a simple lens of considerable diameter, as shown in Diagram 6, and still assuming it to have spheroidal surfaces so that the emerging wave-fronts shall be spherical, and considering the light-waves to be originated by a single vibrating molecule situated at an infinite distance, we come to a peculiar phenomenon, also a result of the excessive minuteness of the light-waves, and the consequent tendency of light to move in straight rays. ”

“ In ordinary light the vibrations are in all directions perpendicular to the line along winch the light travels, that is, the vibrations at any point are in a plane perpendicular to this line. Now any vibration in a plane may be expressed as the sum of two component vibrations, one component in one direction and the other in a perpendicular direction. If we divide up the vibrations all along the wave in this way we shall have two waves, one of which has its vibrations all in one direction and the other in a perpendicular direction. ”

“ But now by the equivalent of a magnetic force along the lines of the hooks, let a different angular222 turning of the frames be produced; the medium will possess a specific angular momentum in every part. If a wave of transverse vibrations which are parallel to one direction (that is, if the wave be plane-polarised) enter the medium in the direction of the axes of the frames, the direction of vibration will be turned as the wave proceeds, that is, the plane of polarisation will be turned round. ”

“ If we can send out a spherical wave front, and have it lengthen rapidly as it proceeds, we will have a wave front that is, at all points, different. Any entering wave would, sooner or later, meet a wave that was half a phase out, no matter what the motion was, nor what the frequency, as long as it lies within the comparatively narrow molecular wave band. ”

“ Translated into ordinary English the phrase signifies, with accuracy and comprehensive completeness, the full details of "a disturbance periodic both in space and time." Anything thus doubly periodic is a wave; and all waves—whether in air as sound waves, or in ether as light waves, or on the surface of water as ocean waves—can be comprehended in the definition.
What properties are essential to a medium capable of transmitting wave-motion? Roughly we may say two: elasticity and inertia. Elasticity in some form, or some equivalent of it,—in order to be able to store up energy and effect recoil ”

“ A train of plane waves traveling in the direction of the arrows encounters a convex lens. The velocity is less in glass, and since the lens is thickest at the center, the retardation is greatest there, gradually diminishing toward the edge. The effect is to change the form of the wave front from a plane to a spherical shell, FIG. 19which advances toward the focus at O, and produces at this point a maximum of light, which is the image of the point whence the waves started. ”

“ Every colour in the spectrum has a different wave-length, and it is owing to this difference in wave-length that we are able to separate them by refraction, or diffraction, and to isolate them. Light, or indeed any radiation, is caused by a rhythmic oscillation of the impalpable medium which we, for want of a better term, call ether, and the distance between two of these waves which are in the same phase is called the wave-length of the particular radiation. The extent of the oscillation is called the amplitude, which when squared is in effect a measure of the intensity of the radiation. ”

“ I will conclude by showing how to measure the length of light waves by means of the interferometer. By turning FIG. 53the head attached to the screw, one of the interferometer mirrors (namely C, Fig. 39) can be moved very slowly. This motion will produce a corresponding displacement of the interference fringes. Count the number of interference fringes which pass a fixed point while the mirror moves a given distance. Then divide double the distance by the number of fringes which have passed, and we have the length of the wave. ”

“ Optics has nevertheless certain distinctly speculative features. Wave-motion demands a medium. The enormous velocity of light excludes known forms of matter; the transmission of radiation in vacuo and through outer space from the most remote regions of the universe, and at the same time through solids such as glass demands that this medium shall have properties very different from that of any substance with which chemistry has made us acquainted. ”

“ Now Fig. 2 also represents a parallel beam of light travelling from a moving source, and entering a telescope or the eye of an observer. The beam lies along A B C D, but this is not the direction of vision. The direction of vision, to a stationary observer, is determined not by the locus of successive waves, but by the path of each wave. A ray may be defined as the path of a labelled disturbance. ”

“ And as the inclination is increased the part of the light transmitted will diminish, until, when the second Nicol is in a position to transmit only vertical vibrations (i. e., when it has turned through a right angle) , the light will vanish. Such is an explanation of this fundamental experiment in polarization on the principle of what is called the Wave Theory of Light ”

“ At first, we consider a light bundle of plane waves, that propagates in the aether, after it went through an additional opening in a non-transparent screen which is connected to Earth. For a moment we neglect the motion of Earth. Let:
l, m, n the direction constants of the wave normal, q a constant, f, g, h the direction constants of the dielectric displacement, a the "amplitude" of the latter. Consequently, the light motion can be represented by the equations
with the condition We can easily see, that these values satisfy all equations of motion. ”

“ Suppose that each key when struck caused some kind of electric radiator to emit an æther wave whose wave-length reckoned in microns or thousandths of a millimetre, is indicated by the number on the key. Of all this great gamut of æther waves only the notes of one octave, viz. the third from the treble end, the wave-lengths of which lie between 0·4μ and 0·8μ, affect the retina of the human eye as light. ”

“ After the emerging waves have run to a focus, they diverge again from this focus as a new center, with spherical fronts, and in exactly the opposite direction to that from which they arrived, just as if the light emerging from all parts of the lens was propagated through and beyond the focus in straight lines; hence the marginal portion of the converging and diverging wave-fronts on each side of the focus will form two cones, turned in diametrically opposite directions, their common apex being the common center of the spherical wave-fronts, viz., the focus of the lens. ”

“ In a similar manner many phenomena of interference of rays of light admit of the measurement of the wave lengths. Fringes of interference arise from rays of light which cross each other at a small angle, and an excessively minute difference in the lengths of the waves makes a very perceptible difference in the position of the point at which two rays will interfere and produce darkness. ”

“ COMPARISON OF THE MICROSCOPE AND TELESCOPE WITH THE INTERFEROMETER
One of the principal objections which have been urged against the wave theory of light is the fact that light appears to travel in straight lines, whereas sound, which is known to be a wave motion, does not cast a shadow; in other words, the sound waves are capable of bending around an obstacle in the path of the waves. ”

“ These ruby rods were the heart of the power system, converting the random wave fronts of noncoherent light received from the mirror into a tremendous beam of coherent infrared energy which could be bundled in such a pattern as to reach Earth's surface in a focal point adjustable from here to be something between twenty-two feet in diameter to approximately one mile in diameter. ”

“ Again, the perfectly free passage of light or the waves of aether through a piece of glass, or a wave of obscure heat through a block of rock-salt, also of the magnetic disturbance through all matter, would by itself prove the extremely open structure of matter. ”

“ The physical effect we call light, and that which we have up to the present moment merely called electric radiation, are really identical in nature, and both consist in waves propagated through the space-filling æther, the only difference between them is in wave-length and wave-amplitude. ”

“ In the case of circularly-polarized light, the magnitude of this vector remains always the same, but its direction rotates round the direction of the ray so as to complete a revolution in the periodic time of the wave. The uncertainty which exists as to whether this vector is in the plane of polarization or perpendicular to it, does not extend to our knowledge of the direction in which it rotates in right-handed and in left-handed circularly-polarized light respectively. ”

“ The oldest valid and conclusive requisition of an ethereous medium depends on the wave theory of light, one of the founders of which was the Royal Institution Professor of Natural Philosophy at the beginning of last century, Dr. Thomas Young.
No ordinary matter is capable of transmitting the undulations or tremors that we call light. The speed at which they go, the kind of undulation, and the facility with which they go through vacuum, forbid this. ”

“ It was this fact that Professor Hertz discovered, and the waves are sometimes called the Hertzian waves. Light is one variety of wave motion, and heat another. The ether must be distinguished from the air, for science means by it a medium which exists everywhere and is to be regarded as permeating all space and all matter. The ether exists in a vacuum, for, although all the air may have been withdrawn, an object placed in a vacuum can still be seen from outside, and hence the wave motions of light are traveling through a space devoid of air. ”

“ In the next series the wave starts outside of the field of the lens, and enters a hemispherical mirror. We know that a concave mirror has the power of bringing light to a focus at a point situated half-way between the surface of the mirror and its center of curvature. If the light comes from a very distant point, and the mirror is parabolic in form, the rays are brought accurately to a focus; which means that the reflected wave is a converging sphere,—a condition the opposite of that in which spherical waves start in the focus of such a mirror. ”