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Transactions of the Royal Society of Edinburgh

XX. On the Theoretical Investigation of the Absolute Intensity of Interfering Light

Philip Kelland

Published Jan 1, 1844• 0 citations
Publisher

Abstract

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.

DOI
10.1017/s0080456800029999

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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.

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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.

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We know that bright fringes on the observation-screen is the Fourier transform of light intensity that passes through diffraction slit (aperture) and we know according to Parseval and Rayleigh Theorems the power or energy of a function before and after Fourier transform is not changed that means the total intensity of light emerging slits is equal to the total intensity of bright fringes on the observation screen, but on the other hand according to destructive and constructive interference of light, some portions of the light passing through the slits destructively interfere to constitute dark fringes which means the total light intensity of fringes should be less than the total intensity passing through the slit. This is a violation of the Fourier transform. On the other hand, this paper is augmented by some very new experiments which show there are no photons in the dark fringes. A diffraction experiment by sticking narrow and small width mirrors on the dark fringes that according to the classical interpretation after destructive interference on the dark fringes should be reflected and could be found by sensors at other directions (specially reflection angle) and another experiment that by making a 1mm hole in the middle of the first dark fringe, we expect that photons can be detected by the light detector after destructive interference (passing through one another) behind the observation plan but no photon is detected. Finally, this paper provides a complete physical model associated with mathematical analysis and formulation that is based on the Schrödinger equation. This model answers to single Photon (electron) double-slit experiment with a high degree of accuracy.

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LXXVII. Further remarks on experiments relative to the interference of light

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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.
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.
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.
Beamsplitting Interference phenomena are certainly among the most exciting phenomena in the whole of physics. In the following we will concentrate mainly on interference of weak fields; i.e. the beams contain, on average, only a few photons. The principle of classical interference is as follows: a light beam is split by an optical element, for example by a semitransparent mirror or a screen with several very small apertures, into two or more partial beams. These beams will take different paths and are then reunited and form interference patterns. The first step, the splitting of the beam into partial beams, plays a decisive role; light beams coming from different sources (or from different spatial areas of the same source) do not interfere with each other! We start our discussion of interference with an analysis of the action of a beamsplitter. To form a realistic idea of this device, let us imagine a semitransparent mirror. (Our considerations apply equally well to a screen with two apertures. We could also generalize to cases of unbalanced mirrors, with reflectivity different from 1/2, or screens with apertures of different size.) The classical wave picture can describe interference phenomena without any great effort: the incoming beam is split into the reflected and the transmitted partial wave, and each of these waves contains half of the energy. The process of splitting becomes conceptually difficult only when we think of the beam as consisting of spatially localized energy packets, or photons.
We know that bright fringes on the observation-screen is the Fourier transform of light intensity that passes through diffraction slit (aperture) and we know according to Parseval and Rayleigh Theorems the power or energy of a function before and after Fourier transform is not changed that means the total intensity of light emerging slits is equal to the total intensity of bright fringes on the observation screen, but on the other hand according to destructive and constructive interference of light, some portions of the light passing through the slits destructively interfere to constitute dark fringes which means the total light intensity of fringes should be less than the total intensity passing through the slit. This is a violation of the Fourier transform. On the other hand, this paper is augmented by some very new experiments which show there are no photons in the dark fringes. A diffraction experiment by sticking narrow and small width mirrors on the dark fringes that according to the classical interpretation after destructive interference on the dark fringes should be reflected and could be found by sensors at other directions (specially reflection angle) and another experiment that by making a 1mm hole in the middle of the first dark fringe, we expect that photons can be detected by the light detector after destructive interference (passing through one another) behind the observation plan but no photon is detected. Finally, this paper provides a complete physical model associated with mathematical analysis and formulation that is based on the Schrödinger equation. This model answers to single Photon (electron) double-slit experiment with a high degree of accuracy.