Generalized form of vectorial laws of reflection and refraction and application to meta material

Generalized form of vectorial laws of reflection and refraction and application to meta material | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Generalized form of vectorial laws of reflection and refraction and application to meta material Anchal Debnath, Debajyoti Bhattacharjee, Chandan Debnath This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3870062/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This communication presents the generalized laws of reflection and refraction in vectorial form with simple derivation. A few relations related to reflection and refraction in vectorial form have been included. The photon theory as well as the principle of conservation of momentum has been used for the derivation of these vectorial laws of reflection and refraction. The application of these laws in metamaterial has been discussed. Generalized laws reflection and refraction vector calculus momentum conservation metamaterial Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3870062","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":267563987,"identity":"a9cf382b-baf3-4d81-bc9f-728a29d2576b","order_by":0,"name":"Anchal Debnath","email":"","orcid":"","institution":"IIT Madras","correspondingAuthor":false,"prefix":"","firstName":"Anchal","middleName":"","lastName":"Debnath","suffix":""},{"id":267563988,"identity":"3d3e398c-0f73-434d-a5fa-75d24058d528","order_by":1,"name":"Debajyoti Bhattacharjee","email":"","orcid":"","institution":"Tripura University","correspondingAuthor":false,"prefix":"","firstName":"Debajyoti","middleName":"","lastName":"Bhattacharjee","suffix":""},{"id":267563989,"identity":"15537e76-bab2-441b-ada3-94dd4f222d17","order_by":2,"name":"Chandan Debnath","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9ElEQVRIiWNgGAWjYFCCBAZmIMnDwMD//cMHIIuNnXgtDGaMM0BamInUAgJmzCCNDIS08LfnHntc2FYnw99/IO2xza9t8nzMDIwfPubg1iJx5l268cy2wzwSNxKOG+f23TZsY2Zglpy5DbcWA4kcM2netgM8BhKMDdK5PbcZgVrYmHkJa6njMeA/zCBt2XPbnlgtzDwGDGls0gw/bicS1CJx5o25Mc85kF9ymA17G24ntzEzNuP1C397jtljnrI6e/7+M4wPfvy5bTu/vfngh494tAABGwMjG5TJ2AYmG/CqB2th+ANj/8GncBSMglEwCkYqAADj9UkG4yRCDwAAAABJRU5ErkJggg==","orcid":"","institution":"Tripura University","correspondingAuthor":true,"prefix":"","firstName":"Chandan","middleName":"","lastName":"Debnath","suffix":""}],"badges":[],"createdAt":"2024-01-16 14:16:59","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3870062/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3870062/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":50720014,"identity":"c84cf746-cc9e-4090-b9f7-f8f9aac0ac4e","added_by":"auto","created_at":"2024-02-06 09:37:26","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":361499,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3870062/v1_covered_946b410e-5299-4915-b54c-e30fafac7f82.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Generalized form of vectorial laws of reflection and refraction and application to meta material","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Generalized laws, reflection and refraction, vector calculus, momentum conservation, metamaterial","lastPublishedDoi":"10.21203/rs.3.rs-3870062/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3870062/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis communication presents the generalized laws of reflection and refraction in vectorial form with simple derivation. 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