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American Journal of Physics

On the formation of white-light interference fringes

Attila Pál Kovács, Katalin Varjú, K. Osvay, Zsolt Bor

Published Nov 1, 1998• 10 citations
Publisher

Abstract

We describe an experiment in which the white-light interference fringes appearing at the output of a Michelson interferometer are observed through a spectrograph. In this manner the relative positions of monochromatic interference fringes come into sight and it allows a better understanding of the formation of the white-light fringes. A simple model is described for determining the shape of the spectrally resolved white-light interference fringes. An expression for the relationship between the slope of the fringes and the arm length difference of the interferometer is derived and is demonstrated experimentally. In addition, an intuitive explanation based on this experiment is given for the washing out of the white-light fringes.

DOI
10.1119/1.19068

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•Mar 21, 1991•3 citations
We describe an experiment in which the white-light interference fringes appearing at the output of a Michelson interferometer are observed through a spectrograph. In this manner the relative positions of monochromatic interference fringes come into sight and it allows a better understanding of the formation of the white-light fringes. A simple model is described for determining the shape of the spectrally resolved white-light interference fringes. An expression for the relationship between the slope of the fringes and the arm length difference of the interferometer is derived and is demonstrated experimentally. In addition, an intuitive explanation based on this experiment is given for the washing out of the white-light fringes.
The author demonstrates a relationship between the pattern of straight interference fringes formed in Young's experiment and the circular fringes produced at infinity by a Michelson interferometer. The two patterns can both be considered to be produced by the interference of light from two coherent point sources. It is shown that the pattern given by these sources on a large sphere centred midway between them reduces to Young's fringes in the vicinity of zero path difference and to the Michelson pattern in the vicinity of maximum path difference.
Fringes formed in a Michelson interferometer never localize in any plane, in the detector plane and in the localization plane. Instead, the fringes are assumed to localize at infinity. Except for some explanation in Principles of Optics by Born and Wolf (1964 (New York: Macmillan)), the fringe localization phenomena of Michelson's interferometer have never been analysed seriously in any book. Because Michelson's interferometer is one of the important and fundamental optical experiments taught at both undergraduate and graduate levels, it would be appropriate to explain the localization of these fringes. In this paper, we analyse the localization of Michelson interferometer fringes using Fourier optics and temporal coherence, and show that they never localize at any plane even at infinity.
In describing the Michelson interferometer, it is usually stated that in order to observe fringes an extended source must be used. It has to be realized, however, that this requirement applies only to the formation of virtual fringes. Actually two distinct sets of fringes exist; virtual and real. Rarely, if ever, is attention brought to the existence of the latter type. The existence of the real fringes was first noted by the authors using the Sagnac interferometer, which is described in this paper. This little-known interferometer and the Michelson interferometer are both amplitude-splitting types. Real fringes were obtained for both a point source and an extended source while virtual fringes were, of course, only visible for an extended source. Similar sets of real fringes were also observed for the Michelson interferometer using either an extended or a point source. An analysis of the formulation of real fringes is presented.
Abstract The reconciliation of wave-like optical interference phenomena with the particle-like properties of the quantized radiation field has intrigued physicists since the early years of the present century. Two main topics of discussion have been the effect of very low light levels-of the order of one photon at a time in the interferometer-on the interference fringes, and the possibility of determining which of the two optical paths through the interferometer were taken by the photons that produce the fringes. The first experiment with very low light levels was performed by Taylor (1909) at the instigation of J. J. Thomson. He found that Young’s interference fringes persisted when the low light levels were compensated by long photographic exposure times.