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Radiotekhnika

Diffraction of light on one and two infinitly narrow slits in a screen

A.V. Bezugliy

Published Sep 18, 2025• 0 citations
Publisher

Abstract

The work addresses the solution of the problems of light diffraction at one and two narrow slits in an opaque screen. The diffraction patterns were analyzed. It was established that their appearance depends on the ratio of the characteristic size of the obstacle to the wavelength of the photon. When this ratio is less than unity, we have a smoothly changing illumination with a maximum at the center of symmetry of the system. If it one is greater than unity, then the pattern has the appearance of light and dark stripes. The numerical value of the specified ratio determines the number of maxima. The obtained results allow us to assume that the reason for the well-known paradox in the interpretation of experiments on the diffraction of light at one and two narrow slits is thе next. The experiments at one slit was carried out for the case when the wavelength was greater than the width of the slit, and at two slits - for the case, when the wavelength is much smaller than the distance between slits.

DOI
10.30837/rt.2025.3.222.21

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The work addresses the solution of the problems of light diffraction at one and two narrow slits in an opaque screen. The diffraction patterns were analyzed. It was established that their appearance depends on the ratio of the characteristic size of the obstacle to the wavelength of the photon. When this ratio is less than unity, we have a smoothly changing illumination with a maximum at the center of symmetry of the system. If it one is greater than unity, then the pattern has the appearance of light and dark stripes. The numerical value of the specified ratio determines the number of maxima. The obtained results allow us to assume that the reason for the well-known paradox in the interpretation of experiments on the diffraction of light at one and two narrow slits is thе next. The experiments at one slit was carried out for the case when the wavelength was greater than the width of the slit, and at two slits - for the case, when the wavelength is much smaller than the distance between slits.
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.
We study electronic multiple-slit diffraction with a quantum mechanical approach. Our theoretical results are in good agreement with classical theoretical calculations and we obtain the following resluts: (1) There are N − 2 secondary maxima and N − 1 minima between the two principle maxima in diffraction pattern. (2) As the slit number N increasing, the diffraction intensity increases and the pattern width becomes narrow. (3) The slit thickness c dose not have any influence on diffraction pattern when slit width a is far greater than the electronic wavelength λ, for example, the ratio of a λ = 10, and at the ratio, the missingorder phenomenon can be observed when d+a a = n (n = 1, 2, 3 . . .), where d is the distance of slit-to-slit. (4) When a is not far greater than λ (the ratio of a λ = 500), the slit thickness c has an effect on diffraction pattern. The missing-order phenomenon can be shown only if the slit thickness c is small enough, and it disappears when the slit thickness c becomes large. In addition, the slit thickness c affects the relative diffraction intensity of the diffraction pattern.
We know that bright fringes on the observation-screen is the Fourier transform of light intensity that passes through diffraction slit (aperture) and we know according to Parseval and Rayleigh Theorems the power or energy of a function before and after Fourier transform is not changed that means the total intensity of light emerging slits is equal to the total intensity of bright fringes on the observation screen, but on the other hand according to destructive and constructive interference of light, some portions of the light passing through the slits destructively interfere to constitute dark fringes which means the total light intensity of fringes should be less than the total intensity passing through the slit. This is a violation of the Fourier transform. On the other hand, this paper is augmented by some very new experiments which show there are no photons in the dark fringes. A diffraction experiment by sticking narrow and small width mirrors on the dark fringes that according to the classical interpretation after destructive interference on the dark fringes should be reflected and could be found by sensors at other directions (specially reflection angle) and another experiment that by making a 1mm hole in the middle of the first dark fringe, we expect that photons can be detected by the light detector after destructive interference (passing through one another) behind the observation plan but no photon is detected. Finally, this paper provides a complete physical model associated with mathematical analysis and formulation that is based on the Schrödinger equation. This model answers to single Photon (electron) double-slit experiment with a high degree of accuracy.
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.