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Journal of Shandong University

Relationship between width of light source and visibility of interference streak

Shiping Wang

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

The visibility of the interference streak on a distant screen will be affected when the light source there has a certain width in a double-slit interference experiment. The visibility of the interference streak on the screen will decline to invisible level. The paper derives the quantitative relation to maximum admitted width of the light source used when unobservable circumstance on the screen appears.

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The visibility of the interference streak on a distant screen will be affected when the light source there has a certain width in a double-slit interference experiment. The visibility of the interference streak on the screen will decline to invisible level. The paper derives the quantitative relation to maximum admitted width of the light source used when unobservable circumstance on the screen appears.
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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.