Abstract The textbook description of multiple slit interference employs a standard path difference formula that was originally calculated for the purpose of analyzing Young’s double slit experiment. It was arrived at on the basis of a pair of assumptions that help simplify the geometry of the slit-barrier-screen arrangement and the ensuing formalism needed to estimate the positions of interference fringes on the detection screen. According to the conventional approach, convergent rays of light that emanate from different slits can be treated as effectively parallel in the far field limit. Such a parallel ray approximation-based analysis was shown by Thomas (2019; 2020) to be redundant, paradoxical and limited in accuracy. In this paper, the task of reformulation that began previously with the elementary two-slit experiment is now extended to encompass the N-slit scenario, diffraction at a single-slit and the formation of circular fringes. In order to derive one of the key results (the generalized hyperbola theorem for N-point sources), a novel computational technique called analytical induction is introduced. The procedure involves a synthesis of concepts from Cartesian geometry and discrete mathematics, namely coordinate transformation by Euclidean translation and a method of proof called the principle of mathematical induction, respectively. The final goal attained are two distribution functions that succinctly and precisely describe the variation of intensity of interference fringes on the distant screen, when it is oriented parallel and perpendicular relative to the line joining the sources. A comparison is drawn between the predictions of the conventional and the new analyses by means of numerical-graphical simulation with MATLAB. The theoretical methods and results presented herein may have a significant bearing in areas of applied optics like interferometry and diffraction crystallography. On the pedagogic front, it is suggested that the current geometrical program being visually more intuitive, be incorporated into the standard curriculum of an advanced undergraduate/graduate level course in physical optics, to complement the conventional approach.
Abstract The textbook description of multiple slit interference employs a standard path difference formula that was originally calculated for the purpose of analyzing Young’s double slit experiment. It was arrived at on the basis of a pair of assumptions that help simplify the geometry of the slit-barrier-screen arrangement and the ensuing formalism needed to estimate the positions of interference fringes on the detection screen. According to the conventional approach, convergent rays of light that emanate from different slits can be treated as effectively parallel in the far field limit. Such a parallel ray approximation-based analysis was shown by Thomas (2019; 2020) to be redundant, paradoxical and limited in accuracy. In this paper, the task of reformulation that began previously with the elementary two-slit experiment is now extended to encompass the N-slit scenario, diffraction at a single-slit and the formation of circular fringes. In order to derive one of the key results (the generalized hyperbola theorem for N-point sources), a novel computational technique called analytical induction is introduced. The procedure involves a synthesis of concepts from Cartesian geometry and discrete mathematics, namely coordinate transformation by Euclidean translation and a method of proof called the principle of mathematical induction, respectively. The final goal attained are two distribution functions that succinctly and precisely describe the variation of intensity of interference fringes on the distant screen, when it is oriented parallel and perpendicular relative to the line joining the sources. A comparison is drawn between the predictions of the conventional and the new analyses by means of numerical-graphical simulation with MATLAB. The theoretical methods and results presented herein may have a significant bearing in areas of applied optics like interferometry and diffraction crystallography. On the pedagogic front, it is suggested that the current geometrical program being visually more intuitive, be incorporated into the standard curriculum of an advanced undergraduate/graduate level course in physical optics, to complement the conventional approach.
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.
Abstract The double slit experiment was the first demonstrative proof of the wave nature of light. It was expounded by the English physician-physicist Thomas Young in 1801 and it soon helped lay to rest the then raging Newton–Huygens debate on whether light consisted of a fast-moving stream of particles or a train of progressive waves in the ether medium. In the experiment, light is made to pass through two very narrow slits spaced closely apart. A screen placed on the other side captures a pattern of alternating bright and dark bands called fringes which are formed as a result of the phenomenon of interference. In prior work by the same author, it was shown that the conventional analysis of Young’s experiment that is used in many introductory physics textbooks, suffers from a number of limitations in regards to its ability to accurately predict the positions of these fringes on the distant screen. This was owing to the adoption of some needless and paradoxical assumptions to help simplify the geometry of the slit barrier-screen arrangement. In the new analysis however, all such approximations were discarded and a hyperbola theorem was forwarded which was then suitably applied to determine the exact fringe positions on screens of varied shapes (linear, semi-circular, semi-elliptical). This paper further builds on that work by laying down the mathematical framework necessary for counting fringes and then comparing their distributions on differently shaped screens, using MATLAB software package for numerical–graphical simulation. In addition, a pair of equivalent laws of proportionality are predicted that govern the distribution of fringes independent of the shape of the detection screen employed.
This work presents a structural reexamination of Young’s double-slit experiment by identifying a missing stage in its standard formulation and restoring it within a finite, geometry-based framework. The conventional treatment assumes continuous propagation, neutral boundaries, and observation on a single fixed screen, reducing the experiment to a geometric division of a continuous entity. Using exact geometry, interference is described by the condition , which defines a family of hyperbolas in space. From the triangle inequality, the number of interference fringes for monochromatic light is shown to be finite and exactly determined. The commonly observed linear fringe pattern arises from the far-field approximation and represents only a partial cross-section of this global structure. A central result of this work is the identification of the in-slit stage as a necessary part of the experiment. The slit is treated as a finite region in which particles interact with boundary-defined electromagnetic environments, leading to directional redistribution prior to propagation. This interpretation is supported by an asymmetric single-slit experiment using different materials, which produces a reversible asymmetric pattern inconsistent with a purely geometric model. The framework is extended to limiting and classical cases, including tiny apertures and diffraction phenomena such as the Poisson spot, where symmetry and lack of comparison may conceal boundary-dependent effects. The suppression of interference in which-way detection experiments is interpreted as a modification of the electromagnetic environment within the slit. These results show that interference in Young’s experiment is a finite, spatial, and timing phenomenon that cannot be fully described by post-slit geometry alone. Restoring the in-slit interaction provides a complete factual description and introduces material-dependent effects absent from standard treatments.
In Young's Double Slit Experiment (YDE) and improved versions, waves causing interference travel different distances.As speed of light is constant, waves require different time spans to reach the point of interference.Thereby, if the waves are generated simultaneously at the slits/source, they cannot meet on the screen anywhere outside the mid-line.Formation of fringes is commonly interpreted as interference caused by the meeting (super-positioning) of two waves generated simultaneously.The reality is that fringes are formed by interference of waves generated at different times.However, unless impacted by other phenomena, two waves generated at different times converging to form fringes, as this paper shows, will mandatorily come in same phase to the interference point, producing constructive interference.Interference observed, however, is not only constructive.The effect on the phase of waves while bending (diffraction) is also to be considered.Consequently, it addresses three phenomena causing phase shifts: (1)different starting times,(2)bending at slits, and (3)distances traveled (In contrast, the first two are overlooked by the conventional approach).(Dirac and Feynman Path Integral methods on quantum particles have different approaches).The paper reveals the widespread misconception in the analysis of YDE and would impact the wave/particle and other YDE interpretations.
Young’s double-slit experiment was first demonstrated with light and was later extended to electrons and other particles. These experiments share a common geometry: something approaches the slits, passes through them, and produces an interference pattern afterward. However, monochromatic water waves, electrons, and photons are physically different, and their interactions with a real slit need not be the same. Most discussions of the double-slit experiment focus on the interference pattern collected on a screen after the slits. Some descriptions also consider what happens before the slits, including the role of an eraser or observer and the splitting of an electron or photon to interfere with itself. Much less attention is given to what happens while an electron or photon is passing through a real slit. A real slit has thickness and is made of matter. Its surfaces contain atoms, electrons, and nuclei and therefore provide an electromagnetic environment through which an electron or photon passes. An electron or photon enters the slit, travels between its surfaces, and leaves it. This raises a missing question: can an electron or photon interact with this electromagnetic environment while passing through the slit, and can such an interaction affect its motion, particularly its exiting direction? We examine experimental evidence together with geometrical and accumulated-count evidence, including the observed spacing of interference maxima, the nonlinear geometry of constant-path-difference loci, the finite number and different possible counts of interference fringes, and the accumulation of individual detection events. Figures derived from the corresponding experimental and geometrical constructions are used to make these distinctions explicit. These results motivate a global description of Young’s double-slit experiment in three physically connected regions: pre-slit, in-slit, and post-slit. We call this the global trilogy of Young’s double-slit experiment. The global trilogy places the physical slit and its electromagnetic environment explicitly between the familiar pre-slit and post-slit descriptions and provides a framework for investigating the complete process from source, through the slit, to interference and detection.