{"id":146380,"date":"2024-03-21T14:06:45","date_gmt":"2024-03-21T14:06:45","guid":{"rendered":"https:\/\/www.electricity-magnetism.org\/equation-interferometre-michelson-explication-usage\/"},"modified":"2024-03-29T19:32:56","modified_gmt":"2024-03-29T19:32:56","slug":"equation-interferometre-michelson-explication-usage","status":"publish","type":"post","link":"https:\/\/www.electricity-magnetism.org\/fr\/equation-interferometre-michelson-explication-usage\/","title":{"rendered":"\u00c9quation Interf\u00e9rom\u00e8tre Michelson | Explication &#038; Usage"},"content":{"rendered":"<p class=\"sidekick\">D\u00e9couvrez l&rsquo;interf\u00e9rom\u00e8tre de Michelson, un instrument cl\u00e9 en physique pour mesurer les distances pr\u00e9cises et \u00e9tudier la lumi\u00e8re.<\/p>\n<h2>L&rsquo;Interf\u00e9rom\u00e8tre de Michelson : Vue d&rsquo;ensemble<\/h2>\n<p>L&rsquo;interf\u00e9rom\u00e8tre de Michelson est un instrument optique invent\u00e9 par le physicien am\u00e9ricain Albert A. Michelson vers la fin du 19e si\u00e8cle. Cet appareil permet d&rsquo;observer des interf\u00e9rences lumineuses et peut donc \u00eatre utilis\u00e9 pour mesurer avec pr\u00e9cision de tr\u00e8s petites distances ou pour d\u00e9terminer la coh\u00e9rence spatiale de sources de lumi\u00e8re. En physique, l&rsquo;interf\u00e9rence fait r\u00e9f\u00e9rence au ph\u00e9nom\u00e8ne o\u00f9 deux ondes superpos\u00e9es donnent lieu \u00e0 un nouveau mod\u00e8le d&rsquo;onde r\u00e9sultant de leur combinaison.<\/p>\n<h2>Composition et Fonctionnement<\/h2>\n<p>L&rsquo;interf\u00e9rom\u00e8tre de Michelson consiste en deux miroirs perpendiculaires l&rsquo;un \u00e0 l&rsquo;autre et un s\u00e9parateur de faisceau, \u00e9galement connu sous le nom de diviseur de faisceau. Lorsque de la lumi\u00e8re arrive sur le diviseur de faisceau, elle est s\u00e9par\u00e9e en deux rayons. Chacun de ces rayons est r\u00e9fl\u00e9chi par un miroir et retourne ensuite vers le diviseur de faisceau o\u00f9 ils se recombinent. L&rsquo;interf\u00e9rence entre les deux faisceaux r\u00e9fl\u00e9chis cr\u00e9e un motif d&rsquo;interf\u00e9rence qui peut \u00eatre observ\u00e9 ou analys\u00e9.<\/p>\n<h2>L&rsquo;\u00c9quation de l&rsquo;Interf\u00e9rom\u00e9trie Michelson<\/h2>\n<p>La formulation de l&rsquo;interf\u00e9rence repose sur le principe que lorsque deux ondes se combinent, l&rsquo;intensit\u00e9 lumineuse (I) observable n&rsquo;est pas simplement la somme des intensit\u00e9s des ondes individuelles, mais d\u00e9pend de la diff\u00e9rence de phase (\\(\\Delta \\phi\\)) entre elles, qui \u00e0 son tour d\u00e9pend de la diff\u00e9rence de chemin optique travers\u00e9e par les deux faisceaux.<\/p>\n<p>La diff\u00e9rence de chemin optique (\\(\\Delta d\\)) est li\u00e9e \u00e0 la diff\u00e9rence de longueur de chemin (\\(\\Delta L\\)) entre les deux bras de l&rsquo;interf\u00e9rom\u00e8tre et l&rsquo;indice de r\u00e9fraction (n) du milieu \u00e0 travers lequel la lumi\u00e8re se propage conform\u00e9ment \u00e0 l&rsquo;\u00e9quation suivante:<\/p>\n<p>\\[<br \/>\n\\Delta d = n \\Delta L<br \/>\n\\]<\/p>\n<p>L&rsquo;\u00e9quation d&rsquo;intensit\u00e9 d&rsquo;interf\u00e9rence peut s&rsquo;\u00e9crire comme :<\/p>\n<p>\\[<br \/>\nI = I_0 \\cos^2\\left(\\frac{\\pi \\Delta d}{\\lambda}\\right)<br \/>\n\\]<\/p>\n<p>o\u00f9 \\(I_0\\) est l&rsquo;intensit\u00e9 maximale de la lumi\u00e8re lorsque les deux ondes sont en phase, et \\(\\lambda\\) est la longueur d&rsquo;onde de la lumi\u00e8re utilis\u00e9e.<\/p>\n<h2>Applications de l&rsquo;Interf\u00e9rom\u00e8tre de Michelson<\/h2>\n<p>L&rsquo;interf\u00e9rom\u00e8tre de Michelson a plusieurs applications induisant :<\/p>\n<ul>\n<li><strong>M\u00e9trologie<\/strong> : Il est utilis\u00e9 pour mesurer avec pr\u00e9cision des distances tr\u00e8s petites, comme le diam\u00e8tre d&rsquo;une mol\u00e9cule ou les changements de longueur caus\u00e9s par la dilatation thermique.<\/li>\n<li><strong>Tests de mat\u00e9riaux<\/strong> : Les diff\u00e9rences dans les indices de r\u00e9fraction caus\u00e9es par de petites variations de densit\u00e9 ou de composition peuvent \u00eatre \u00e9tudi\u00e9es gr\u00e2ce \u00e0 l&rsquo;interf\u00e9rom\u00e9trie Michelson.<\/li>\n<li><strong>Astronomie<\/strong> : Il aide \u00e0 mesurer le diam\u00e8tre apparent des \u00e9toiles et \u00e0 analyser leur structure et leur composition en observant les variations dans les motifs d&rsquo;interf\u00e9rence.<\/li>\n<li><strong>Physique fondamentale<\/strong> : Il a \u00e9t\u00e9 utilis\u00e9 historiquement dans l&rsquo;exp\u00e9rience de Michelson-Morley pour \u00e9tudier l&rsquo;existence de l&rsquo;\u00e9ther, un suppos\u00e9 m\u00e9dium pour la propagation de la lumi\u00e8re. Ce fut une exp\u00e9rience cruciale qui a contribu\u00e9 \u00e0 l&rsquo;av\u00e8nement de la th\u00e9orie de la relativit\u00e9 restreinte d&rsquo;Einstein.<\/li>\n<li><strong>D\u00e9tection des ondes gravitationnelles<\/strong> : Les versions modernes de l&rsquo;interf\u00e9rom\u00e8tre, comme celles utilis\u00e9es dans les d\u00e9tecteurs LIGO\/VIRGO, sont con\u00e7ues pour d\u00e9tecter les infimes modifications de distance provoqu\u00e9es par le passage des ondes gravitationnelles.<\/li>\n<\/ul>\n<h2>Conclusion<\/h2>\n<p>L&rsquo;interf\u00e9rom\u00e8tre de Michelson est un exemple remarquable d&rsquo;une simple id\u00e9e de physique transform\u00e9e en un outil puissant avec une pl\u00e9thore d&rsquo;applications pratiques. En utilisant le concept d&rsquo;interf\u00e9rence lumineuse, cet instrument nous permet de sonder l&rsquo;univers \u00e0 une \u00e9chelle allant des sub-particules jusqu&rsquo;aux vastes \u00e9tendues de l&rsquo;espace-temps, t\u00e9moignant de la beaut\u00e9 et de l&rsquo;efficacit\u00e9 des principes fondamentaux de la physique.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>D\u00e9couvrez l&rsquo;interf\u00e9rom\u00e8tre de Michelson, un instrument cl\u00e9 en physique pour mesurer les distances pr\u00e9cises et \u00e9tudier la lumi\u00e8re.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_generate-full-width-content":"","footnotes":""},"categories":[48],"tags":[49],"class_list":["post-146380","post","type-post","status-publish","format-standard","hentry","category-equations","tag-equations","generate-columns","tablet-grid-50","mobile-grid-100","grid-parent","grid-50"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u00c9quation Interf\u00e9rom\u00e8tre Michelson | Explication &amp; 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