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The London Edinburgh and Dublin Philosophical Magazine and Journal of Science

LXIV. New contributions to interferometry. Part I.—New non-localized interference fringes

Samuel Tolansky

Published Aug 1, 1943• 13 citations
Publisher

Abstract

Summary New non-localized interference fringes, produced with a small source and a Fabry-Perot interferometer, are described. These extend into space in the form of cones, producing sharp rings when allowed to fall upon a screen. The properties of these rings are examined. A striking characteristic is that without lenses sharp rings of great diameter can be produced (diameter of first ring equal to half a metre). Complex patterns are produced with various slit sources. Possible applications of the new fringes are considered.

DOI
10.1080/14786444308521413

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International Journal for Research in Applied Science and Engineering Technology•Nov 7, 2025•0 citations
Summary New non-localized interference fringes, produced with a small source and a Fabry-Perot interferometer, are described. These extend into space in the form of cones, producing sharp rings when allowed to fall upon a screen. The properties of these rings are examined. A striking characteristic is that without lenses sharp rings of great diameter can be produced (diameter of first ring equal to half a metre). Complex patterns are produced with various slit sources. Possible applications of the new fringes are considered.
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.
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.
In 1801, Thomas Young devised what is now known as the Classical Double Slit Experiment. In this experiment, light waves emanating from two separate sources, interfere to form a pattern of alternating bright and dark fringes on a distant screen. By measuring the position of individual fringe centers, the fringe widths and the variation of average light intensity on the screen, it is possible to compute the wavelength of light itself. The original theoretical analysis of the experiment employs a set of geometric assumptions which are collectively referred to here as the Parallel Ray Approximation. Accordingly, any two rays of light arising from either source and convergent on an arbitrary point on the screen, are considered very nearly parallel to each other in the vicinity of the sources. This approximation holds true only when the screen to source distance is very large and the inter-source distance is much larger than the wavelength of light. The predictions that naturally follow are valid only for fringes located near the center of the screen (e.g. the equal spacing of fringes). But for those fringes located further away from the screen center, the precision of these predictions rapidly wanes. Also when the screen to source distance is comparable to the inter-source separation or when the inter-source distance is comparable to the wavelength of light, the original analysis is no longer applicable. In this paper, the theoretical foundations of Young’s experiment are re-formulated using a newly derived analytical equation of a hyperbola, which forms the locus of the points of intersections of two expanding circular wavefronts (with sources located at the respective centers of expansion). The ensuing predictions of the new analysis are compared with those of the old. And finally, it is shown that the latter approach is just a special instance of the former, when the Parallel Ray Approximation can be said to hold true.
The double slit experiment was first conceived of by the English physician-physicist Thomas Young in 1801. It was the first demonstrative proof that light possesses a wave nature. In this experiment, light is made to pass through two very narrow slits that are spaced closely apart and a screen placed on the other side captures a pattern of alternating bright and dark stripes called fringes, formed as a result of the interference of ripples of light emanating from either slit. The relative positions and intensities of the fringes on the screen can be calculated by employing two assumptions that help simplify the geometry of the slit-screen arrangement. Firstly, the screen to slit distance is taken to be larger than the inter-slit distance (far field limit) and secondly, the inter-slit distance is taken to be larger than the wavelength of light. This conventional approach can account for the positions and intensities of the fringes located in the central portion of the screen with a fair degree of precision. It however, fails to account for those fringes located in the peripheral portions of the screen and also, is not applicable to the case wherein the screen to slit distance is made comparable to the inter-slit distance (near field limit). In this paper, the original analysis of Young’s Experiment is reformulated using an analytically derived hyperbola equation, which is formed from the locus of the points of intersections of two uniformly expanding circular wavefronts of light that emanate from either slit source. Additionally, the shape of the screen used to capture the interference pattern is varied (linear, semicircular, semielliptical) and the relative positions of the fringes is calculated for each case. This new approach bears the distinctive advantage that it is applicable in both the far field and the near field scenarios, and since no assumptions are made beyond the Huygens-Fresnel principle, it is therefore, a much more generalized approach. For these reasons, the author suggests that the new analysis ought to be introduced into the Wave Optics chapter of the undergraduate Physics curriculum.
This research was conducted to note the changes in the interference patterns, by different means of reflection. For this, we have used a double slit, different mirrors, and a screen to obtain the image. The hypothesis behind this was that double slit produces a fringe patten on a screen when a coherent light source is passed through it, but what if we put a mirror after the slits and obtain an image on a screen. Not just that, what if we put different kinds of mirrors in between the slit and the screen. We conducted this research in an environment with negligible sources of light except the non-coherent light source, and with negligible vibrations which could affect the image obtained. When this research was conducted with a flat mirror, fringes were roughly the same as predicted by mathematical calculations. But when this research was conducted by a convex mirror, the fringes seemed to be virtual . When this same study was conducted with a concave mirror, the fringes seemed to be either concentrated at a single point, or they seemed to be have enlarged with a virtual image however the ratio of magnified image to the actual image that have been obtained if there was no mirror, remained the same. Whereas in the case of a convex mirror, the image was smaller. This property is useful as it can be used to observe the pattern more precisely by magnifying it and the actual numbers, i.e.- when mirror would not have been used can also be calculated because the magnification is the same.