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College Physics

Estimation of the position of diffraction object in the interference and diffraction experiments

Hong Li

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

The formulae used to estimate the position of the diffraction object in the interference and diffraction experiments are derived through two approaches:analyzing the space coherence property of the source and consider- ing the edge diffraction property of the practical source.The double slits interference experiment and the circle o- paque diffraction experiment are analyzed as two examples.

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The formulae used to estimate the position of the diffraction object in the interference and diffraction experiments are derived through two approaches:analyzing the space coherence property of the source and consider- ing the edge diffraction property of the practical source.The double slits interference experiment and the circle o- paque diffraction experiment are analyzed as two examples.
The problem of an approximate description of the wave field of many sources is considered. It is shown that, if the problem is considered more comprehensively, the description of the interference and diffraction experiments can be given within the framework of a single scheme. It is shown that the character of wave amplification in these two classical experiments is different. In the case of an interference experiment, the field amplification is fixed at a point, while in the case of a diffraction experiment the field amplification is fixed in the observation direction. The problem of determining the intensity maximum of a diffraction grating in the Fresnel pattern is studied under the condition that the maximum is satisfied in the Fraunhofer pattern. A condition under which a diffraction grating behaves like a lens is obtained.
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.
Diffraction patterns of electrons are believed to resemble those of electromagnetic waves (EMW). I performed a series of experiments invoked to show that the periodicity of peaks in the diffraction diagram of electrons is concerned with the periodicity of the arrangement of scattering centers in the diffraction grating in combination with the supposed character of the spatial structure of the electron as a system of regularly spaced concentric shells of elasticity. I started from the experiment on the diffraction of electrons and EMWs at the sharp edge of the opaque half-plane. This simple scattering configuration enabled me to discriminate between the re-radiation mechanism of the wave diffraction and ricochet scattering of electrons on the edge of the half-plane. Then I made experiments with scattering on composite objects proceeding step by step from a single straight edge to a couple of edges (one slit) and then to four edges (two slits). Thus I succeeded in interpretation of the double-slit diffraction (four straight edges) in terms of the scattering on a single edge. I managed also to observe the electron's trajectory. Equipping the slit's edge with a semiconductor sensors I registered the passing of the electron through the slit detecting simultaneously a weaker signal at another slit. This technique appeared not to destroy or disturb the "interference" pattern. Closing one slit by inserting therein a transparent for EMWs piece of dielectric I have found that the scattering pattern beneath this slit vanishes while the scattering pattern under the open slit remains as before when both slits were open. This experiment indicates that the electron "interferes" with its electromagnetic component passed via the slit plugged by the transparent for it dielectric.
Interference and diffraction of light are the nature performance of wave character,which is the result of superposition of waves.The essential difference between interference and diffraction phenomena is that interference comes from the superposition by the two or limited interfering beams of light,and diffraction is from the superposition by an infinite beam.From the perspective of optical path difference,corresponding to the same optical path difference,the minimum conditions of single-slit diffraction becomes the maxima conditions of double-slit interference.The reason is that the slot width is so small that can be considered as a single light source under the double-slit case,and the interference in the same slit can be ignored;while the single-slit diffraction minimum conditions are exactly correspond to the interference in the same slit.
The theoretical results for the diffraction of electrons by a disk and a pair of rectangular slits is derived from the Schrödinger equation using results from time-dependent perturbation theory in both the strong and weak scattering limits. The double-slit ‘‘thought’’ experiment is often used in introductions to quantum mechanics as a demonstration that electrons have wave-like properties. It seems desirable to include a derivation of the result both as an interesting example and also as reassurance that the diffraction of ‘‘matter waves’’ leads to the same results as the diffraction of electromagnetic waves by the same obstacle.
Abstract In Chapter 21, we turn to interference and diffraction. We start by describing the interference pattern in Young’s classic two-slit experiment, whose analysis is subsequently generalised to determine the interference pattern behind a multi-slit grating. The diffraction pattern for a single slit is then estimated using Huygens’ principle, and this is combined with the interference pattern for a multi-slit grating to get the entire wave pattern generated by a diffraction grating. Next, we turn to the diffraction of electrons. This starts with a brief introduction to quantum mechanics, focussed on Schrodinger’s wave equation, de Broglie waves, and the collapse of the wavefunction following measurements. Finally, we use these elementary quantum concepts to describe the diffraction of electrons.