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Cambridge University Press eBooks

On Achromatic Interference-Bands

John William Strutt

Published Jul 20, 2009• 0 citations
Publisher

Abstract

Introduction W hen there is interference of light, the width of the resulting bands, measured for example from darkness to darkness, is usually a function of the colour of the light employed. Thus, in the case of Fresnel's well-known interference-experiment, in which light reflected from two slightly inclined mirrors illuminates a screen, the width of the bands is proportional to the wave-length of the light. In order that a considerable number of bands may be visible, it is necessary that the light be highly homogeneous; otherwise it is impossible that the various band-systems can fit one another over the necessary range. If the light could be supposed to be absolutely homogeneous, there would be no limit to the number of observable bands: and, what is especially to be remarked, there would be nothing by which one band could be distinguished from another,—in particular there could be no central band recognizable. When, on the other hand, the light is white, there may be a central band at which all the maxima of brightness coincide; and this band, being white, may be called the achromatic band. But the system of bands is not usually achromatic. Thus, in Fresnel's experiment the centre of symmetry fixes the position of the central achromatic band, but the system is far from achromatic. Theoretically there is not even a single place of darkness, for there is no point where there is complete discordance [opposition] of phase for all kinds of light.

DOI
10.1017/cbo9780511703980.023

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Mathematical Proceedings of the Cambridge Philosophical Society•Mar 1, 1925•2 citations
Introduction W hen there is interference of light, the width of the resulting bands, measured for example from darkness to darkness, is usually a function of the colour of the light employed. Thus, in the case of Fresnel's well-known interference-experiment, in which light reflected from two slightly inclined mirrors illuminates a screen, the width of the bands is proportional to the wave-length of the light. In order that a considerable number of bands may be visible, it is necessary that the light be highly homogeneous; otherwise it is impossible that the various band-systems can fit one another over the necessary range. If the light could be supposed to be absolutely homogeneous, there would be no limit to the number of observable bands: and, what is especially to be remarked, there would be nothing by which one band could be distinguished from another,—in particular there could be no central band recognizable. When, on the other hand, the light is white, there may be a central band at which all the maxima of brightness coincide; and this band, being white, may be called the achromatic band. But the system of bands is not usually achromatic. Thus, in Fresnel's experiment the centre of symmetry fixes the position of the central achromatic band, but the system is far from achromatic. Theoretically there is not even a single place of darkness, for there is no point where there is complete discordance [opposition] of phase for all kinds of light.
1. ~"~.OUY ?and RA'ZLEIG~r :~ have recently] discussed ~9t the question of interference phenomena observed with a source of white light, and have arrived at important results.When the two interfering beams pass through the slit of a spectroscope, the spectrum is seen to be crossed alternately by bright and dark bands, and if high resolving powers are used, these interference effects may be observed, although the difference of path of the two original beams is considerable.This well-known fact has always been taken to prove that the vibrations of the white light are to a certain extent " regular," and efforts have been made to find by experiment the limits of that regularity.The futility of these efforts has been completely demonstrated by Gouy and Rayleigh, who have proved that the bright and dark bands alluded to would appear with sufficient resolving power, even if light consisted of perfectly irregularly distributed instantaneous impulses.These investigations would seem, therefore, to lead to the conclusion that a source of light is completely defined by the distribution of energy in the * Oommun~cated by the Author.
Interference is a classic property of waves. It can be seen most clearly when a coherent wave is split into two partial waves that are then recombined to produce periodic variations in the measured intensity. These variations can be observed directly as a pattern of bright and dark interference fringes on a screen. The classic interferometer set-up is the Young's double-slit experiment: a small light source emitting in a narrow frequency band is placed on one side of the slits, and an interference pattern is observed at the screen on the other side (figure a). The fringes are bright where the partial waves interfere constructively, and dark where the interference is destructive.
The subject of the following Memoir has been already touched on in a communication which I made to the Cambridge Philosophical Society, and which appears in the seventh volume of their Transactions, Art. IX. For the better understanding of what follows, it is desirable to state briefly the contents of that paper. Its object is to estimate the quantity of light which is received on a screen of unlimited dimensions, after passing through a certain aperture, or suffering reflection at two mirrors, as in the case of the interference experiment, so as to exhibit the appearance of bands.
If we turn down our light source from 100 million whatever photons a second to, say, just ten a second, we see the problem, if not the screen, very clearly. These last few photons of light head off, one by one, for the screen, some of them hitting the piece of card but the odd one going through a slit. Now, according to common sense, each should be able to land on the screen unaffected by whether the other slit is there-or not. But none of them, no matter how long we wait, will try to land on the dark areas seen in the interference pattern with lots of light. After all, if an individual photon could behave in this way, it might take a long time but, eventually, the screen would record a picture more like the one-slit experiment with the light diffusing evenly, than the interference one. And the individual photons recognise the contradiction. They continue to behave individually as ‘waves’ all on their own. Points where the light particle could go when just one slit is open become unavailable when the other slit is open. (Incidentally, the same thing, scientists have observed, will happen with any small particle-electrons, whole atoms or even molecules will do just as well.) In experiments, the individual particles of light seem to know about the other slit on the piece of card, indeed what is going on elsewhere in the universe. For, in principle at least, the distance between the slits can be any size, and the same interference effect will apply. (Although if the slits were even a metre apart, the screen might need to be on the moon before the deflected light begins to converge.) Suppose we asked our neighbour if we could borrow their particle detector to check whether the light energy is still travelling in ‘whole photons’, rather than splitting into two and going through both slits and thereby getting in and out of phase with each other. We would find, indeed, that it was still travelling as a whole photon, and that this attempted explanation does not fit with observation. But we would find something else too. The mere act of putting the particle detector next to one slit causes the wavy pattern, the ‘interference’ effect, to disappear!
Abstract Since it was born before its physical achievements, light waves, which have almost no physical properties, are an abstract mathematical concept rather than an objective description. Beguiled by a series of dark and bright streaks, the results of the double-slit test were misjudged as interfering light waves, so this plausible principle implied disastrous flaws. For example, (1) by changing the distance between the device and the screen, the pattern is only scaled synchronously and not reconstructed, and the expected light-wave interference does not occur. (2) Interfering light waves can be subdivided into multiple parts and proliferate greatly. (3) A headless wave of light left outside the screen after the head disappears can still induce much interference. (4) There is no interference effect caused by reflected light waves. (5) The effect of polarization direction on interference is neglected, and the interference condition is incomplete. (6) In the mathematical model, the location where the dark stripe should appear most is actually the spot with the highest brightness. The principle of generating multiple regular dark stripes cannot be found in the mathematical model. (7) Since the quantum property must be expressed in the process of interference, interference will not be triggered if all conditions are not met at the same time, and therefore, the principle of interference will be rejected. (8) Since light comes only from the radiation of the electron transition, it is impossible to generate a light source in a slit that may be a vacuum. (9) In the causality test, to verify the effect of collapse, the photon that has collapsed into a particle should be tested again with a double slit test. (10) Whether the phenomenon of "observed tampering results" obtained by observation has been tampered with. (11) When the phase is shifted π or the signal is reversed, waves become negative waves capable of annihilating themselves, which is typical of antimatter. In this case, matter and antimatter are conjoined. (12) If the general law of waves is followed, not only the targeted light wave passes through the slit. (13) The original version of the double-slit test cannot be reproduced, and the test results are different from those presented by contemporary technology. (14) Waves must obey Fourier's principle, but light waves, quantum waves and matter waves do not. (15) The modulation effect that waves must produce is not present in optical fiber communication. (16) If the light from different slits must interfere with each other, a mask full of slits will cause the lithographer to fail. (17) Since the size is much smaller than the wavelength, the photon is only a sampling of the light wave, but the corresponding physical properties are not presented. (18) The fact that the two stars orbiting each other do not change color only proves that the phenomenon of redshift is impossible but does not support the inference that the speed of light is constant. (19) The Michelson-Morley test process is not open and transparent enough, and pinhole diffraction and mechanical processing using broken lines instead of curves cannot be ruled out. (20) Kepler's law can block Hubble's law and its derivatives, dark matter and dark energy. In conclusion, Newton's particle model was wrong, but neither was the light wave theory.
It is shown that, assuming conservation of energy and momentum in individuai transitions, radiation must be regarded as propagated by linearly directed quanta. Evidence is brought forward in favour of the view that these quanta are spatially localised longitudinally as well as laterally. As these conclusions seem unavoidable, an attempt is made to see if there is any possibility of accounting for interference effects in terms of quants possessing periodic properties. The idea that a single quantum can produce interference effects is untenable. The conception of the phase of a quant is introduced, and it is supposed that atoms may absorb a quant in a given phase provided they are in a “state” corresponding to that phase. Considering radiation emanating from a point, it is shown that a tentative explanation of interference may be obtained if the quants have a constant phase at emission, and if they give atoms at any point an impulse towards the state corresponding to their phase at the point. According as these impulses reinforce or oppose each other, bright or dark parts of a fringe System are obtained. Practically the whole nomenclature and method of the wave theory may be taken over and applied to the quant phase field surrounding an emitting source. Essentially, on this view, an explanation of interference is sought in terms of different quants, and the dark and bright parte of a fringe system are to be explained, not in terms of different numbers of quante arriving at them, but in different phase relations of quante which do arrive. Quante are characterised by a magnetic and electric vector, whose magnitudes and directions define the state of polarisation and the phase. Electron orbite may also be regarded as characterised by two vectors in terms of which it seems as if the “state” may be specified. The relation between transition character and type of radiation emitted is finally considered and it is shown that the evidence so far available renders plausible an explanation of interference of the kind put forward. Much further experimental work, particularly in connection with the Stark and Zeeman effects, is, however, necessary, before sufficient precision can be given to the views put forward to make them satisfying. On the other hand, it seems premature to suppose that only a formal treatment is possible of the physical phenomena involved.