Reflections on Refraction (Geometrical Optics)
. Consider an optical system made of an unknown number N of layers of homogeneous transparent plates with different unknown refraction indices. Observing beams of monochromatic light through the system, find the number N of plates together with their respective indices and their thicknesses. The mat...
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| Veröffentlicht in: | Annales Henri Poincaré 2008, Vol.9 (4), p.625-638 |
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| container_end_page | 638 |
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| container_issue | 4 |
| container_start_page | 625 |
| container_title | Annales Henri Poincaré |
| container_volume | 9 |
| creator | France, Michel Mendès Sebbar, Ahmed |
| description | .
Consider an optical system made of an unknown number
N
of layers of homogeneous transparent plates with different unknown refraction indices. Observing beams of monochromatic light through the system, find the number
N
of plates together with their respective indices and their thicknesses. The mathematical analysis of the problem involves the so-called Hadamard quotient of two power series.
We shall also discuss fractal optical systems consisting of infinitely many infinitely thin plates. If the index of refraction varies in an erratic way there may be multiple refraction. These systems could be called “refractals".
We conclude the paper with independent considerations on a general system consisting of one plate with continuous varying index
n
(
x
,
y
) ≥ 1. To determine the function
seems to be a difficult problem. Our contribution to solving it is thus very modest. |
| doi_str_mv | 10.1007/s00023-008-0367-7 |
| format | Article |
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Consider an optical system made of an unknown number
N
of layers of homogeneous transparent plates with different unknown refraction indices. Observing beams of monochromatic light through the system, find the number
N
of plates together with their respective indices and their thicknesses. The mathematical analysis of the problem involves the so-called Hadamard quotient of two power series.
We shall also discuss fractal optical systems consisting of infinitely many infinitely thin plates. If the index of refraction varies in an erratic way there may be multiple refraction. These systems could be called “refractals".
We conclude the paper with independent considerations on a general system consisting of one plate with continuous varying index
n
(
x
,
y
) ≥ 1. To determine the function
seems to be a difficult problem. Our contribution to solving it is thus very modest.</description><identifier>ISSN: 1424-0637</identifier><identifier>EISSN: 1424-0661</identifier><identifier>DOI: 10.1007/s00023-008-0367-7</identifier><language>eng</language><publisher>Basel: SP Birkhäuser Verlag Basel</publisher><subject>Classical and Quantum Gravitation ; Dynamical Systems and Ergodic Theory ; Elementary Particles ; Exact sciences and technology ; Mathematical and Computational Physics ; Mathematical Methods in Physics ; Other topics in mathematical methods in physics ; Physics ; Physics and Astronomy ; Quantum Field Theory ; Quantum Physics ; Relativity Theory ; Theoretical</subject><ispartof>Annales Henri Poincaré, 2008, Vol.9 (4), p.625-638</ispartof><rights>Birkhaueser 2008</rights><rights>2015 INIST-CNRS</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c395t-71bbf5440dd4314f578c779088eeb49815f708febeb78f1c8b09c1eb830b5fb63</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00023-008-0367-7$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00023-008-0367-7$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>230,314,780,784,885,27924,27925,41488,42557,51319</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=20436124$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://hal.science/hal-00293661$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>France, Michel Mendès</creatorcontrib><creatorcontrib>Sebbar, Ahmed</creatorcontrib><title>Reflections on Refraction (Geometrical Optics)</title><title>Annales Henri Poincaré</title><addtitle>Ann. Henri Poincaré</addtitle><description>.
Consider an optical system made of an unknown number
N
of layers of homogeneous transparent plates with different unknown refraction indices. Observing beams of monochromatic light through the system, find the number
N
of plates together with their respective indices and their thicknesses. The mathematical analysis of the problem involves the so-called Hadamard quotient of two power series.
We shall also discuss fractal optical systems consisting of infinitely many infinitely thin plates. If the index of refraction varies in an erratic way there may be multiple refraction. These systems could be called “refractals".
We conclude the paper with independent considerations on a general system consisting of one plate with continuous varying index
n
(
x
,
y
) ≥ 1. To determine the function
seems to be a difficult problem. Our contribution to solving it is thus very modest.</description><subject>Classical and Quantum Gravitation</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Elementary Particles</subject><subject>Exact sciences and technology</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Methods in Physics</subject><subject>Other topics in mathematical methods in physics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Field Theory</subject><subject>Quantum Physics</subject><subject>Relativity Theory</subject><subject>Theoretical</subject><issn>1424-0637</issn><issn>1424-0661</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><recordid>eNp9kEFLwzAYhoMoOKc_wFsvgjtkfl-TNulxDN2EwUD0HJIs0Y6uHUkV_PdmVnr0lHzJ-3zwvITcIswRQDxEAMgZBZAUWCmoOCMT5DmnUJZ4Pt6ZuCRXMe4BMJesmpD5i_ONs33dtTHr2iyNQf-O2f3KdQfXh9rqJtse-9rG2TW58LqJ7ubvnJK3p8fX5Zputqvn5WJDLauKngo0xhecw27HGXJfCGmFqEBK5wyvJBZegPTOOCOkRysNVBadkQxM4U3JpmQ27P3QjTqG-qDDt-p0rdaLjTq9JduKJbUvTFkcsjZ0MQbnRwBBncpRQzmJkepUjhKJuRuYo45JLzm3to4jmANnJeY85fIhF9NX--6C2nefoU3q_yz_AQ2Gcg0</recordid><startdate>2008</startdate><enddate>2008</enddate><creator>France, Michel Mendès</creator><creator>Sebbar, Ahmed</creator><general>SP Birkhäuser Verlag Basel</general><general>Springer</general><general>Springer Verlag</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope></search><sort><creationdate>2008</creationdate><title>Reflections on Refraction (Geometrical Optics)</title><author>France, Michel Mendès ; Sebbar, Ahmed</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c395t-71bbf5440dd4314f578c779088eeb49815f708febeb78f1c8b09c1eb830b5fb63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>Classical and Quantum Gravitation</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Elementary Particles</topic><topic>Exact sciences and technology</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Methods in Physics</topic><topic>Other topics in mathematical methods in physics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Field Theory</topic><topic>Quantum Physics</topic><topic>Relativity Theory</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>France, Michel Mendès</creatorcontrib><creatorcontrib>Sebbar, Ahmed</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Annales Henri Poincaré</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>France, Michel Mendès</au><au>Sebbar, Ahmed</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Reflections on Refraction (Geometrical Optics)</atitle><jtitle>Annales Henri Poincaré</jtitle><stitle>Ann. Henri Poincaré</stitle><date>2008</date><risdate>2008</risdate><volume>9</volume><issue>4</issue><spage>625</spage><epage>638</epage><pages>625-638</pages><issn>1424-0637</issn><eissn>1424-0661</eissn><abstract>.
Consider an optical system made of an unknown number
N
of layers of homogeneous transparent plates with different unknown refraction indices. Observing beams of monochromatic light through the system, find the number
N
of plates together with their respective indices and their thicknesses. The mathematical analysis of the problem involves the so-called Hadamard quotient of two power series.
We shall also discuss fractal optical systems consisting of infinitely many infinitely thin plates. If the index of refraction varies in an erratic way there may be multiple refraction. These systems could be called “refractals".
We conclude the paper with independent considerations on a general system consisting of one plate with continuous varying index
n
(
x
,
y
) ≥ 1. To determine the function
seems to be a difficult problem. Our contribution to solving it is thus very modest.</abstract><cop>Basel</cop><pub>SP Birkhäuser Verlag Basel</pub><doi>10.1007/s00023-008-0367-7</doi><tpages>14</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Annales Henri Poincaré, 2008, Vol.9 (4), p.625-638 |
| issn | 1424-0637 1424-0661 |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Classical and Quantum Gravitation Dynamical Systems and Ergodic Theory Elementary Particles Exact sciences and technology Mathematical and Computational Physics Mathematical Methods in Physics Other topics in mathematical methods in physics Physics Physics and Astronomy Quantum Field Theory Quantum Physics Relativity Theory Theoretical |
| title | Reflections on Refraction (Geometrical Optics) |
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