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arXiv:1606.00254

A Coalition of Single Slit and Double Slit Diffraction

Supantho Rakshit

Published May 30, 2016• 0 citations
arXivHTMLPDF

Abstract

In this paper, we theoretically investigate a particular experimental setup which coalesces the concepts of the double slit and single slit diffraction. In Thomas Young's classic double slit experiment, monochromatic plane light wave impinges on an opaque screen with two parallel, long and narrow slits and the resulting intensity pattern is observed on a screen placed at a great distance placed from the slits. We show, via theoretical calculations that the if another opaque screen with a single long narrow slit is placed at a distance from the two slits, the resulting intensity pattern on the observation screen is nontrivial and interesting.

DOI
10.48550/arxiv.1606.00254

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In this paper, we theoretically investigate a particular experimental setup which coalesces the concepts of the double slit and single slit diffraction. In Thomas Young's classic double slit experiment, monochromatic plane light wave impinges on an opaque screen with two parallel, long and narrow slits and the resulting intensity pattern is observed on a screen placed at a great distance placed from the slits. We show, via theoretical calculations that the if another opaque screen with a single long narrow slit is placed at a distance from the two slits, the resulting intensity pattern on the observation screen is nontrivial and interesting.
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.
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.
Young's double-slit experiment is a classic and fundamentaldemonstration in physics that strongly supports the wave nature of light throughthe phenomenon of interference. The study aims to deeply analyze the formationof diffraction and interference patterns of light that arise due to the pathdifferences between two coherent light sources. The experiment uses a simple yeteffective setup involving a monochromatic light source, two narrow slits placedclose together, and a screen placed at a certain distance to capture the resultinginterference pattern. Several variables are analyzed in the study, including thewavelength of the light used,the distance between two gaps and the distance fromone gap to anotherThe experimental results confirm the occurrence ofconstructive and destructive interference, resulting in the formation of stripesmoving from bright to dark in the layer. These stripes arise due to the phasedifference between overlapping light waves, and their spacing and clarity areaffected by the physical parameters of the setup. The analysis shows that thespacing between the stripes increases with longer wavelengths and decreases withwider slit spacing. In addition, the cohesion of the light source plays an importantrole in producing a clear and stable interference pattern. This experiment not onlyserves as a concrete verification of the theoretical wave principle in physics, butalso has broader implications in modern optical technologies such as diffractiongratings, holography, and quantum mechanics. This experiment is also relevantfor educational purposes because it provides an experiential learning opportunityfor students to understand the behavior of light and wave interactions. Therefore,this study is expected to be a useful reference in supporting the teaching andlearning of wave optics, especially in demonstrating the dual nature of light andits applications in real-world phenomena.