Guidage de la lumi\u00e8re dans une fibre optique<\/title>\n<style>\n :root{\n --bg:#ffffff; --panel:#f7f8fa; --border:#e0e3e8;\n --text:#1c1f26; --muted:#6b7280; --accent:#c0392b;\n --core:#eaf4ff; --clad:#fff3e6; --air:#ffffff;\n --guided:#1f9d55; --lost:#c0392b;\n }\n @media (prefers-color-scheme: dark){\n :root{\n --bg:#14161a; --panel:#1c1f26; --border:#2c313a;\n --text:#e7e9ee; --muted:#9aa2b1; --accent:#ff6b5e;\n --core:#16324a; --clad:#3a2a17; --air:#14161a;\n }\n }\n *{box-sizing:border-box;}\n body{\n margin:0; padding:20px; background:var(--bg); color:var(--text);\n font-family: system-ui, -apple-system, \"Segoe UI\", Roboto, Helvetica, Arial, sans-serif;\n }\n .wrap{max-width:900px; margin:0 auto;}\n h1{font-size:1.25rem; font-weight:600; margin:0 0 4px;}\n p.sub{color:var(--muted); font-size:0.92rem; margin:0 0 18px;}\n .panel{\n background:var(--panel); border:1px solid var(--border); border-radius:12px;\n padding:16px; margin-bottom:16px;\n }\n svg{width:100%; height:auto; display:block; background:var(--air); border-radius:8px;}\n .controls{display:grid; grid-template-columns:1fr; gap:14px;}\n .ctrl-row{display:flex; align-items:center; gap:12px;}\n .ctrl-row label{flex:0 0 220px; font-size:0.92rem;}\n .ctrl-row input[type=range]{flex:1;}\n .ctrl-row .val{flex:0 0 70px; text-align:right; font-variant-numeric:tabular-nums; font-weight:600;}\n .status{\n display:flex; flex-wrap:wrap; gap:8px 22px; margin-top:14px; font-size:0.92rem;\n }\n .status div{display:flex; gap:6px;}\n .status span.k{color:var(--muted);}\n .status span.v{font-weight:600; font-variant-numeric:tabular-nums;}\n .badge{\n display:inline-block; padding:2px 10px; border-radius:999px; font-size:0.82rem; font-weight:600;\n }\n .badge.ok{background:rgba(31,157,85,0.15); color:var(--guided);}\n .badge.no{background:rgba(192,57,43,0.15); color:var(--lost);}\n footer{color:var(--muted); font-size:0.8rem; text-align:center; margin-top:10px;}\n<\/style>\n<\/head>\n<body>\n<div class=\"wrap\">\n <h1>Guidage de la lumi\u00e8re dans une fibre optique \u00e0 saut d’indice<\/h1>\n <p class=\"sub\">Faites varier l’angle d’incidence et les indices pour observer le guidage par r\u00e9flexion totale \u2014 et sa disparition au-del\u00e0 de l’angle d’acceptance.<\/p>\n\n <div class=\"panel\">\n <svg id=\"scene\" viewBox=\"0 0 900 320\" preserveAspectRatio=\"xMidYMid meet\"><\/svg>\n <div class=\"status\" id=\"status\"><\/div>\n <\/div>\n\n <div class=\"panel controls\">\n <div class=\"ctrl-row\">\n <label for=\"i\">Angle d’incidence <i>i<\/i> (air \u2192 c\u0153ur)<\/label>\n <input type=\"range\" id=\"i\" min=\"0\" max=\"89\" step=\"0.5\" value=\"20\">\n <span class=\"val\" id=\"iVal\">20\u00b0<\/span>\n <\/div>\n <div class=\"ctrl-row\">\n <label for=\"n1\">Indice du c\u0153ur n\u2081<\/label>\n <input type=\"range\" id=\"n1\" min=\"1.30\" max=\"1.75\" step=\"0.005\" value=\"1.456\">\n <span class=\"val\" id=\"n1Val\">1.456<\/span>\n <\/div>\n <div class=\"ctrl-row\">\n <label for=\"n2\">Indice de la gaine n\u2082<\/label>\n <input type=\"range\" id=\"n2\" min=\"1.20\" max=\"1.70\" step=\"0.005\" value=\"1.410\">\n <span class=\"val\" id=\"n2Val\">1.410<\/span>\n <\/div>\n <\/div>\n\n <footer>S. Benlhajlahsen \u2014 PCSI \u00b7 Guidage par r\u00e9flexion totale dans une fibre \u00e0 saut d’indice<\/footer>\n<\/div>\n\n<script>\nconst svg = document.getElementById('scene');\nconst NS = 'http:\/\/www.w3.org\/2000\/svg';\n\n\/\/ --- geometry constants (svg units) ---\nconst X0 = 130; \/\/ entrance face x\nconst XMAX = 880; \/\/ right edge\nconst AXIS_Y = 160; \/\/ fiber axis height\nconst HALF_CORE = 45; \/\/ core half-thickness\nconst CLAD_T = 45; \/\/ cladding thickness (each side)\n\nfunction el(tag, attrs){\n const e = document.createElementNS(NS, tag);\n for(const k in attrs) e.setAttribute(k, attrs[k]);\n return e;\n}\n\nfunction build(){\n svg.innerHTML = '';\n\n \/\/ cladding bands\n svg.appendChild(el('rect',{x:X0,y:AXIS_Y-HALF_CORE-CLAD_T,width:XMAX-X0,height:CLAD_T,fill:'var(--clad)'}));\n svg.appendChild(el('rect',{x:X0,y:AXIS_Y+HALF_CORE,width:XMAX-X0,height:CLAD_T,fill:'var(--clad)'}));\n \/\/ core band\n svg.appendChild(el('rect',{x:X0,y:AXIS_Y-HALF_CORE,width:XMAX-X0,height:2*HALF_CORE,fill:'var(--core)'}));\n\n \/\/ interfaces\n svg.appendChild(el('line',{x1:X0,y1:AXIS_Y-HALF_CORE,x2:XMAX,y2:AXIS_Y-HALF_CORE,stroke:'var(--border)','stroke-width':1.5}));\n svg.appendChild(el('line',{x1:X0,y1:AXIS_Y+HALF_CORE,x2:XMAX,y2:AXIS_Y+HALF_CORE,stroke:'var(--border)','stroke-width':1.5}));\n svg.appendChild(el('line',{x1:X0,y1:AXIS_Y-HALF_CORE-CLAD_T,x2:XMAX,y2:AXIS_Y-HALF_CORE-CLAD_T,stroke:'var(--border)','stroke-width':1,'stroke-dasharray':'2,4'}));\n svg.appendChild(el('line',{x1:X0,y1:AXIS_Y+HALF_CORE+CLAD_T,x2:XMAX,y2:AXIS_Y+HALF_CORE+CLAD_T,stroke:'var(--border)','stroke-width':1,'stroke-dasharray':'2,4'}));\n \/\/ entrance face\n svg.appendChild(el('line',{x1:X0,y1:AXIS_Y-HALF_CORE-CLAD_T,x2:X0,y2:AXIS_Y+HALF_CORE+CLAD_T,stroke:'var(--text)','stroke-width':1.5}));\n \/\/ axis (dashed)\n svg.appendChild(el('line',{x1:X0,y1:AXIS_Y,x2:XMAX,y2:AXIS_Y,stroke:'var(--muted)','stroke-width':1,'stroke-dasharray':'4,4'}));\n\n \/\/ labels\n const t1 = el('text',{x:XMAX-6,y:AXIS_Y-HALF_CORE-14,'text-anchor':'end','font-size':'13',fill:'var(--muted)'});\n t1.textContent = 'gaine (n\u2082)'; svg.appendChild(t1);\n const t2 = el('text',{x:XMAX-6,y:AXIS_Y+4,'text-anchor':'end','font-size':'13',fill:'var(--muted)'});\n t2.textContent = 'c\u0153ur (n\u2081)'; svg.appendChild(t2);\n const t3 = el('text',{x:XMAX-6,y:AXIS_Y+HALF_CORE+28,'text-anchor':'end','font-size':'13',fill:'var(--muted)'});\n t3.textContent = 'gaine (n\u2082)'; svg.appendChild(t3);\n const t4 = el('text',{x:X0-6,y:AXIS_Y-HALF_CORE-CLAD_T-10,'text-anchor':'start','font-size':'13',fill:'var(--muted)'});\n t4.textContent = 'air (n\u2080=1,00)'; svg.appendChild(t4);\n}\n\nfunction rayPath(points, color, width, dashed){\n const d = points.map((p,idx)=> (idx===0?'M':'L') + p[0].toFixed(2) + ',' + p[1].toFixed(2)).join(' ');\n const attrs = {d, fill:'none', stroke:color, 'stroke-width':width};\n if(dashed) attrs['stroke-dasharray'] = '5,4';\n svg.appendChild(el('path', attrs));\n}\n\nfunction arrowHead(p1, p2, color){\n const ang = Math.atan2(p2[1]-p1[1], p2[0]-p1[0]);\n const len = 10, spread = 0.45;\n const x = p2[0], y = p2[1];\n const p3 = [x - len*Math.cos(ang-spread), y - len*Math.sin(ang-spread)];\n const p4 = [x - len*Math.cos(ang+spread), y - len*Math.sin(ang+spread)];\n svg.appendChild(el('polygon',{points:`${x},${y} ${p3[0]},${p3[1]} ${p4[0]},${p4[1]}`, fill:color}));\n}\n\nfunction update(){\n const iDeg = parseFloat(document.getElementById('i').value);\n const n1 = parseFloat(document.getElementById('n1').value);\n let n2 = parseFloat(document.getElementById('n2').value);\n if(n2 >= n1) n2 = n1 - 0.01; \/\/ garde-fou : la gaine doit rester moins refringente\n\n document.getElementById('iVal').textContent = iDeg.toFixed(1) + '\u00b0';\n document.getElementById('n1Val').textContent = n1.toFixed(3);\n document.getElementById('n2Val').textContent = n2.toFixed(3);\n\n const n0 = 1.0;\n const iRad = iDeg * Math.PI\/180;\n\n build();\n\n \/\/ acceptance cone (visual wedge at entrance)\n const ia = Math.asin(Math.min(1, Math.sqrt(Math.max(0,n1*n1-n2*n2))\/n0));\n const coneLen = 90;\n const topY = AXIS_Y - coneLen*Math.sin(ia);\n const botY = AXIS_Y + coneLen*Math.sin(ia);\n svg.appendChild(el('polygon',{\n points:`${X0},${AXIS_Y} ${X0-coneLen*Math.cos(ia)},${topY} ${X0-coneLen*Math.cos(ia)},${botY}`,\n fill:'rgba(31,157,85,0.12)'\n }));\n\n \/\/ theta = angle from axis inside the core\n const sinTheta = n0*Math.sin(iRad)\/n1;\n const theta = Math.asin(Math.min(1,sinTheta));\n const thetaDeg = theta*180\/Math.PI;\n\n \/\/ guiding condition: cos(theta) >= n2\/n1\n const guided = Math.cos(theta) >= n2\/n1;\n\n \/\/ incident ray in air, arriving at entry point (axis center), angle i above axis\n const entry = [X0, AXIS_Y];\n const Lin = 110;\n const start = [X0 - Lin*Math.cos(iRad), AXIS_Y - Lin*Math.sin(iRad)];\n rayPath([start, entry], 'var(--accent)', 2.4, false);\n arrowHead(start, entry, 'var(--accent)');\n\n \/\/ build zigzag inside core\n let pts = [entry];\n let x = X0, y = AXIS_Y;\n let goingDown = true; \/\/ first bounce toward bottom interface (matches incoming angle > 0)\n let guidedColor = guided ? 'var(--guided)' : 'var(--accent)';\n\n if(guided){\n \/\/ distance to first boundary from axis\n let dyFirst = HALF_CORE;\n let dx = dyFirst\/Math.tan(theta);\n x += dx; y = AXIS_Y + HALF_CORE;\n pts.push([x,y]);\n let dir = 1; \/\/ 1 = going down last, next goes up\n while(x < XMAX - 5){\n const dy = 2*HALF_CORE;\n const dx2 = dy\/Math.tan(theta);\n x += dx2;\n y = dir>0 ? AXIS_Y - HALF_CORE : AXIS_Y + HALF_CORE;\n if(x > XMAX){\n \/\/ clip last segment\n const prev = pts[pts.length-1];\n const frac = (XMAX - prev[0])\/(x - prev[0]);\n x = XMAX; y = prev[1] + frac*(y-prev[1]);\n pts.push([x,y]);\n break;\n }\n pts.push([x,y]);\n dir *= -1;\n }\n rayPath(pts, guidedColor, 2.6, false);\n for(let k=1;k<pts.length;k++) arrowHead(pts[k-1], pts[k], guidedColor);\n } else {\n \/\/ hits first interface then escapes into the cladding (refraction)\n let dx = HALF_CORE\/Math.tan(theta);\n x += dx; y = AXIS_Y + HALF_CORE;\n pts.push([x,y]);\n rayPath(pts, 'var(--core)'.startsWith('#')?'#3b6ea5':'#3b6ea5', 2.6, false);\n \/\/ redraw properly (core segment) in blue-ish guided-like color before leak\n svg.lastChild.remove();\n rayPath(pts, '#2f7dd1', 2.6, false);\n arrowHead(entry, [x,y], '#2f7dd1');\n\n \/\/ angle from the interface normal (vertical) = 90-theta ; refract into cladding\n const angFromNormal = Math.PI\/2 - theta;\n const sinOut = (n1\/n2)*Math.sin(angFromNormal);\n if(sinOut <= 1){\n const angOut = Math.asin(sinOut); \/\/ from normal, in cladding\n const thetaClad = Math.PI\/2 - angOut; \/\/ from horizontal\n const Lout = 140;\n const end = [x + Lout*Math.cos(thetaClad), y + Lout*Math.sin(thetaClad)];\n const clippedEnd = [Math.min(end[0], XMAX), end[1] + (Math.min(end[0],XMAX)-x)\/(end[0]-x)*0 ];\n \/\/ simple straight clip to XMAX\n let ex = end[0], ey = end[1];\n if(ex > XMAX){\n const frac = (XMAX - x)\/(ex-x);\n ex = XMAX; ey = y + frac*(end[1]-y);\n }\n rayPath([[x,y],[ex,ey]], 'var(--accent)', 2.6, true);\n arrowHead([x,y],[ex,ey],'var(--accent)');\n }\n }\n\n \/\/ status readouts\n const st = document.getElementById('status');\n const betaDeg = 90 - thetaDeg;\n const NA = Math.sqrt(Math.max(0,n1*n1-n2*n2));\n st.innerHTML = `\n <div><span class=\"k\">\u03b8 (depuis l'axe) :<\/span><span class=\"v\">${thetaDeg.toFixed(1)}\u00b0<\/span><\/div>\n <div><span class=\"k\">angle sur l'interface c\u0153ur\/gaine :<\/span><span class=\"v\">${betaDeg.toFixed(1)}\u00b0<\/span><\/div>\n <div><span class=\"k\">angle d'acceptance i_a :<\/span><span class=\"v\">${(ia*180\/Math.PI).toFixed(1)}\u00b0<\/span><\/div>\n <div><span class=\"k\">ouverture num\u00e9rique ON :<\/span><span class=\"v\">${NA.toFixed(3)}<\/span><\/div>\n <div><span class=\"badge ${guided?'ok':'no'}\">${guided ? 'Guid\u00e9 (r\u00e9flexion totale)' : 'Non guid\u00e9 (fuite dans la gaine)'}<\/span><\/div>\n `;\n}\n\n['i','n1','n2'].forEach(id=>{\n document.getElementById(id).addEventListener('input', update);\n});\nupdate();\n<\/script>\n<\/body>\n<\/html>\n","protected":false},"excerpt":{"rendered":"<p>Guidage de la lumi\u00e8re dans une fibre optique Guidage de la lumi\u00e8re dans une fibre optique \u00e0 saut d’indice Faites varier l’angle d’incidence et les indices pour observer le guidage par r\u00e9flexion totale \u2014 et sa disparition au-del\u00e0 de l’angle d’acceptance. Angle d’incidence i (air \u2192 c\u0153ur) 20\u00b0 Indice du c\u0153ur n\u2081 1.456 Indice de … <a href=\"https:\/\/benlhajlahsen.fr\/index.php\/fibre-optique\/\" class=\"more-link\">Continuer la lecture<span class=\"screen-reader-text\"> de « Fibre optique »<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-276","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/benlhajlahsen.fr\/index.php\/wp-json\/wp\/v2\/pages\/276","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/benlhajlahsen.fr\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/benlhajlahsen.fr\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/benlhajlahsen.fr\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/benlhajlahsen.fr\/index.php\/wp-json\/wp\/v2\/comments?post=276"}],"version-history":[{"count":1,"href":"https:\/\/benlhajlahsen.fr\/index.php\/wp-json\/wp\/v2\/pages\/276\/revisions"}],"predecessor-version":[{"id":278,"href":"https:\/\/benlhajlahsen.fr\/index.php\/wp-json\/wp\/v2\/pages\/276\/revisions\/278"}],"wp:attachment":[{"href":"https:\/\/benlhajlahsen.fr\/index.php\/wp-json\/wp\/v2\/media?parent=276"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

{"id":276,"date":"2026-09-14T20:17:54","date_gmt":"2026-09-14T18:17:54","guid":{"rendered":"https:\/\/benlhajlahsen.fr\/?page_id=276"},"modified":"2026-09-14T20:17:54","modified_gmt":"2026-09-14T18:17:54","slug":"fibre-optique","status":"publish","type":"page","link":"https:\/\/benlhajlahsen.fr\/index.php\/fibre-optique\/","title":{"rendered":"Fibre optique"},"content":{"rendered":"\n\n\n\n\n\nGuidage de la lumi\u00e8re dans une fibre optique<\/title>\n<style>\n :root{\n --bg:#ffffff; --panel:#f7f8fa; --border:#e0e3e8;\n --text:#1c1f26; --muted:#6b7280; --accent:#c0392b;\n --core:#eaf4ff; --clad:#fff3e6; --air:#ffffff;\n --guided:#1f9d55; --lost:#c0392b;\n }\n @media (prefers-color-scheme: dark){\n :root{\n --bg:#14161a; --panel:#1c1f26; --border:#2c313a;\n --text:#e7e9ee; --muted:#9aa2b1; --accent:#ff6b5e;\n --core:#16324a; --clad:#3a2a17; --air:#14161a;\n }\n }\n *{box-sizing:border-box;}\n body{\n margin:0; padding:20px; background:var(--bg); color:var(--text);\n font-family: system-ui, -apple-system, \"Segoe UI\", Roboto, Helvetica, Arial, sans-serif;\n }\n .wrap{max-width:900px; margin:0 auto;}\n h1{font-size:1.25rem; font-weight:600; margin:0 0 4px;}\n p.sub{color:var(--muted); font-size:0.92rem; margin:0 0 18px;}\n .panel{\n background:var(--panel); border:1px solid var(--border); border-radius:12px;\n padding:16px; margin-bottom:16px;\n }\n svg{width:100%; height:auto; display:block; background:var(--air); border-radius:8px;}\n .controls{display:grid; grid-template-columns:1fr; gap:14px;}\n .ctrl-row{display:flex; align-items:center; gap:12px;}\n .ctrl-row label{flex:0 0 220px; font-size:0.92rem;}\n .ctrl-row input[type=range]{flex:1;}\n .ctrl-row .val{flex:0 0 70px; text-align:right; font-variant-numeric:tabular-nums; font-weight:600;}\n .status{\n display:flex; flex-wrap:wrap; gap:8px 22px; margin-top:14px; font-size:0.92rem;\n }\n .status div{display:flex; gap:6px;}\n .status span.k{color:var(--muted);}\n .status span.v{font-weight:600; font-variant-numeric:tabular-nums;}\n .badge{\n display:inline-block; padding:2px 10px; border-radius:999px; font-size:0.82rem; font-weight:600;\n }\n .badge.ok{background:rgba(31,157,85,0.15); color:var(--guided);}\n .badge.no{background:rgba(192,57,43,0.15); color:var(--lost);}\n footer{color:var(--muted); font-size:0.8rem; text-align:center; margin-top:10px;}\n<\/style>\n<\/head>\n<body>\n<div class=\"wrap\">\n <h1>Guidage de la lumi\u00e8re dans une fibre optique \u00e0 saut d’indice<\/h1>\n <p class=\"sub\">Faites varier l’angle d’incidence et les indices pour observer le guidage par r\u00e9flexion totale \u2014 et sa disparition au-del\u00e0 de l’angle d’acceptance.<\/p>\n\n <div class=\"panel\">\n <svg id=\"scene\" viewBox=\"0 0 900 320\" preserveAspectRatio=\"xMidYMid meet\"><\/svg>\n <div class=\"status\" id=\"status\"><\/div>\n <\/div>\n\n <div class=\"panel controls\">\n <div class=\"ctrl-row\">\n <label for=\"i\">Angle d’incidence <i>i<\/i> (air \u2192 c\u0153ur)<\/label>\n <input type=\"range\" id=\"i\" min=\"0\" max=\"89\" step=\"0.5\" value=\"20\">\n <span class=\"val\" id=\"iVal\">20\u00b0<\/span>\n <\/div>\n <div class=\"ctrl-row\">\n <label for=\"n1\">Indice du c\u0153ur n\u2081<\/label>\n <input type=\"range\" id=\"n1\" min=\"1.30\" max=\"1.75\" step=\"0.005\" value=\"1.456\">\n <span class=\"val\" id=\"n1Val\">1.456<\/span>\n <\/div>\n <div class=\"ctrl-row\">\n <label for=\"n2\">Indice de la gaine n\u2082<\/label>\n <input type=\"range\" id=\"n2\" min=\"1.20\" max=\"1.70\" step=\"0.005\" value=\"1.410\">\n <span class=\"val\" id=\"n2Val\">1.410<\/span>\n <\/div>\n <\/div>\n\n <footer>S. Benlhajlahsen \u2014 PCSI \u00b7 Guidage par r\u00e9flexion totale dans une fibre \u00e0 saut d’indice<\/footer>\n<\/div>\n\n<script>\nconst svg = document.getElementById('scene');\nconst NS = 'http:\/\/www.w3.org\/2000\/svg';\n\n\/\/ --- geometry constants (svg units) ---\nconst X0 = 130; \/\/ entrance face x\nconst XMAX = 880; \/\/ right edge\nconst AXIS_Y = 160; \/\/ fiber axis height\nconst HALF_CORE = 45; \/\/ core half-thickness\nconst CLAD_T = 45; \/\/ cladding thickness (each side)\n\nfunction el(tag, attrs){\n const e = document.createElementNS(NS, tag);\n for(const k in attrs) e.setAttribute(k, attrs[k]);\n return e;\n}\n\nfunction build(){\n svg.innerHTML = '';\n\n \/\/ cladding bands\n svg.appendChild(el('rect',{x:X0,y:AXIS_Y-HALF_CORE-CLAD_T,width:XMAX-X0,height:CLAD_T,fill:'var(--clad)'}));\n svg.appendChild(el('rect',{x:X0,y:AXIS_Y+HALF_CORE,width:XMAX-X0,height:CLAD_T,fill:'var(--clad)'}));\n \/\/ core band\n svg.appendChild(el('rect',{x:X0,y:AXIS_Y-HALF_CORE,width:XMAX-X0,height:2*HALF_CORE,fill:'var(--core)'}));\n\n \/\/ interfaces\n svg.appendChild(el('line',{x1:X0,y1:AXIS_Y-HALF_CORE,x2:XMAX,y2:AXIS_Y-HALF_CORE,stroke:'var(--border)','stroke-width':1.5}));\n svg.appendChild(el('line',{x1:X0,y1:AXIS_Y+HALF_CORE,x2:XMAX,y2:AXIS_Y+HALF_CORE,stroke:'var(--border)','stroke-width':1.5}));\n svg.appendChild(el('line',{x1:X0,y1:AXIS_Y-HALF_CORE-CLAD_T,x2:XMAX,y2:AXIS_Y-HALF_CORE-CLAD_T,stroke:'var(--border)','stroke-width':1,'stroke-dasharray':'2,4'}));\n svg.appendChild(el('line',{x1:X0,y1:AXIS_Y+HALF_CORE+CLAD_T,x2:XMAX,y2:AXIS_Y+HALF_CORE+CLAD_T,stroke:'var(--border)','stroke-width':1,'stroke-dasharray':'2,4'}));\n \/\/ entrance face\n svg.appendChild(el('line',{x1:X0,y1:AXIS_Y-HALF_CORE-CLAD_T,x2:X0,y2:AXIS_Y+HALF_CORE+CLAD_T,stroke:'var(--text)','stroke-width':1.5}));\n \/\/ axis (dashed)\n svg.appendChild(el('line',{x1:X0,y1:AXIS_Y,x2:XMAX,y2:AXIS_Y,stroke:'var(--muted)','stroke-width':1,'stroke-dasharray':'4,4'}));\n\n \/\/ labels\n const t1 = el('text',{x:XMAX-6,y:AXIS_Y-HALF_CORE-14,'text-anchor':'end','font-size':'13',fill:'var(--muted)'});\n t1.textContent = 'gaine (n\u2082)'; svg.appendChild(t1);\n const t2 = el('text',{x:XMAX-6,y:AXIS_Y+4,'text-anchor':'end','font-size':'13',fill:'var(--muted)'});\n t2.textContent = 'c\u0153ur (n\u2081)'; svg.appendChild(t2);\n const t3 = el('text',{x:XMAX-6,y:AXIS_Y+HALF_CORE+28,'text-anchor':'end','font-size':'13',fill:'var(--muted)'});\n t3.textContent = 'gaine (n\u2082)'; svg.appendChild(t3);\n const t4 = el('text',{x:X0-6,y:AXIS_Y-HALF_CORE-CLAD_T-10,'text-anchor':'start','font-size':'13',fill:'var(--muted)'});\n t4.textContent = 'air (n\u2080=1,00)'; svg.appendChild(t4);\n}\n\nfunction rayPath(points, color, width, dashed){\n const d = points.map((p,idx)=> (idx===0?'M':'L') + p[0].toFixed(2) + ',' + p[1].toFixed(2)).join(' ');\n const attrs = {d, fill:'none', stroke:color, 'stroke-width':width};\n if(dashed) attrs['stroke-dasharray'] = '5,4';\n svg.appendChild(el('path', attrs));\n}\n\nfunction arrowHead(p1, p2, color){\n const ang = Math.atan2(p2[1]-p1[1], p2[0]-p1[0]);\n const len = 10, spread = 0.45;\n const x = p2[0], y = p2[1];\n const p3 = [x - len*Math.cos(ang-spread), y - len*Math.sin(ang-spread)];\n const p4 = [x - len*Math.cos(ang+spread), y - len*Math.sin(ang+spread)];\n svg.appendChild(el('polygon',{points:`${x},${y} ${p3[0]},${p3[1]} ${p4[0]},${p4[1]}`, fill:color}));\n}\n\nfunction update(){\n const iDeg = parseFloat(document.getElementById('i').value);\n const n1 = parseFloat(document.getElementById('n1').value);\n let n2 = parseFloat(document.getElementById('n2').value);\n if(n2 >= n1) n2 = n1 - 0.01; \/\/ garde-fou : la gaine doit rester moins refringente\n\n document.getElementById('iVal').textContent = iDeg.toFixed(1) + '\u00b0';\n document.getElementById('n1Val').textContent = n1.toFixed(3);\n document.getElementById('n2Val').textContent = n2.toFixed(3);\n\n const n0 = 1.0;\n const iRad = iDeg * Math.PI\/180;\n\n build();\n\n \/\/ acceptance cone (visual wedge at entrance)\n const ia = Math.asin(Math.min(1, Math.sqrt(Math.max(0,n1*n1-n2*n2))\/n0));\n const coneLen = 90;\n const topY = AXIS_Y - coneLen*Math.sin(ia);\n const botY = AXIS_Y + coneLen*Math.sin(ia);\n svg.appendChild(el('polygon',{\n points:`${X0},${AXIS_Y} ${X0-coneLen*Math.cos(ia)},${topY} ${X0-coneLen*Math.cos(ia)},${botY}`,\n fill:'rgba(31,157,85,0.12)'\n }));\n\n \/\/ theta = angle from axis inside the core\n const sinTheta = n0*Math.sin(iRad)\/n1;\n const theta = Math.asin(Math.min(1,sinTheta));\n const thetaDeg = theta*180\/Math.PI;\n\n \/\/ guiding condition: cos(theta) >= n2\/n1\n const guided = Math.cos(theta) >= n2\/n1;\n\n \/\/ incident ray in air, arriving at entry point (axis center), angle i above axis\n const entry = [X0, AXIS_Y];\n const Lin = 110;\n const start = [X0 - Lin*Math.cos(iRad), AXIS_Y - Lin*Math.sin(iRad)];\n rayPath([start, entry], 'var(--accent)', 2.4, false);\n arrowHead(start, entry, 'var(--accent)');\n\n \/\/ build zigzag inside core\n let pts = [entry];\n let x = X0, y = AXIS_Y;\n let goingDown = true; \/\/ first bounce toward bottom interface (matches incoming angle > 0)\n let guidedColor = guided ? 'var(--guided)' : 'var(--accent)';\n\n if(guided){\n \/\/ distance to first boundary from axis\n let dyFirst = HALF_CORE;\n let dx = dyFirst\/Math.tan(theta);\n x += dx; y = AXIS_Y + HALF_CORE;\n pts.push([x,y]);\n let dir = 1; \/\/ 1 = going down last, next goes up\n while(x < XMAX - 5){\n const dy = 2*HALF_CORE;\n const dx2 = dy\/Math.tan(theta);\n x += dx2;\n y = dir>0 ? AXIS_Y - HALF_CORE : AXIS_Y + HALF_CORE;\n if(x > XMAX){\n \/\/ clip last segment\n const prev = pts[pts.length-1];\n const frac = (XMAX - prev[0])\/(x - prev[0]);\n x = XMAX; y = prev[1] + frac*(y-prev[1]);\n pts.push([x,y]);\n break;\n }\n pts.push([x,y]);\n dir *= -1;\n }\n rayPath(pts, guidedColor, 2.6, false);\n for(let k=1;k<pts.length;k++) arrowHead(pts[k-1], pts[k], guidedColor);\n } else {\n \/\/ hits first interface then escapes into the cladding (refraction)\n let dx = HALF_CORE\/Math.tan(theta);\n x += dx; y = AXIS_Y + HALF_CORE;\n pts.push([x,y]);\n rayPath(pts, 'var(--core)'.startsWith('#')?'#3b6ea5':'#3b6ea5', 2.6, false);\n \/\/ redraw properly (core segment) in blue-ish guided-like color before leak\n svg.lastChild.remove();\n rayPath(pts, '#2f7dd1', 2.6, false);\n arrowHead(entry, [x,y], '#2f7dd1');\n\n \/\/ angle from the interface normal (vertical) = 90-theta ; refract into cladding\n const angFromNormal = Math.PI\/2 - theta;\n const sinOut = (n1\/n2)*Math.sin(angFromNormal);\n if(sinOut <= 1){\n const angOut = Math.asin(sinOut); \/\/ from normal, in cladding\n const thetaClad = Math.PI\/2 - angOut; \/\/ from horizontal\n const Lout = 140;\n const end = [x + Lout*Math.cos(thetaClad), y + Lout*Math.sin(thetaClad)];\n const clippedEnd = [Math.min(end[0], XMAX), end[1] + (Math.min(end[0],XMAX)-x)\/(end[0]-x)*0 ];\n \/\/ simple straight clip to XMAX\n let ex = end[0], ey = end[1];\n if(ex > XMAX){\n const frac = (XMAX - x)\/(ex-x);\n ex = XMAX; ey = y + frac*(end[1]-y);\n }\n rayPath([[x,y],[ex,ey]], 'var(--accent)', 2.6, true);\n arrowHead([x,y],[ex,ey],'var(--accent)');\n }\n }\n\n \/\/ status readouts\n const st = document.getElementById('status');\n const betaDeg = 90 - thetaDeg;\n const NA = Math.sqrt(Math.max(0,n1*n1-n2*n2));\n st.innerHTML = `\n <div><span class=\"k\">\u03b8 (depuis l'axe) :<\/span><span class=\"v\">${thetaDeg.toFixed(1)}\u00b0<\/span><\/div>\n <div><span class=\"k\">angle sur l'interface c\u0153ur\/gaine :<\/span><span class=\"v\">${betaDeg.toFixed(1)}\u00b0<\/span><\/div>\n <div><span class=\"k\">angle d'acceptance i_a :<\/span><span class=\"v\">${(ia*180\/Math.PI).toFixed(1)}\u00b0<\/span><\/div>\n <div><span class=\"k\">ouverture num\u00e9rique ON :<\/span><span class=\"v\">${NA.toFixed(3)}<\/span><\/div>\n <div><span class=\"badge ${guided?'ok':'no'}\">${guided ? 'Guid\u00e9 (r\u00e9flexion totale)' : 'Non guid\u00e9 (fuite dans la gaine)'}<\/span><\/div>\n `;\n}\n\n['i','n1','n2'].forEach(id=>{\n document.getElementById(id).addEventListener('input', update);\n});\nupdate();\n<\/script>\n<\/body>\n<\/html>\n","protected":false},"excerpt":{"rendered":"<p>Guidage de la lumi\u00e8re dans une fibre optique Guidage de la lumi\u00e8re dans une fibre optique \u00e0 saut d’indice Faites varier l’angle d’incidence et les indices pour observer le guidage par r\u00e9flexion totale \u2014 et sa disparition au-del\u00e0 de l’angle d’acceptance. Angle d’incidence i (air \u2192 c\u0153ur) 20\u00b0 Indice du c\u0153ur n\u2081 1.456 Indice de … <a href=\"https:\/\/benlhajlahsen.fr\/index.php\/fibre-optique\/\" class=\"more-link\">Continuer la lecture<span class=\"screen-reader-text\"> de « Fibre optique »<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-276","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/benlhajlahsen.fr\/index.php\/wp-json\/wp\/v2\/pages\/276","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/benlhajlahsen.fr\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/benlhajlahsen.fr\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/benlhajlahsen.fr\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/benlhajlahsen.fr\/index.php\/wp-json\/wp\/v2\/comments?post=276"}],"version-history":[{"count":1,"href":"https:\/\/benlhajlahsen.fr\/index.php\/wp-json\/wp\/v2\/pages\/276\/revisions"}],"predecessor-version":[{"id":278,"href":"https:\/\/benlhajlahsen.fr\/index.php\/wp-json\/wp\/v2\/pages\/276\/revisions\/278"}],"wp:attachment":[{"href":"https:\/\/benlhajlahsen.fr\/index.php\/wp-json\/wp\/v2\/media?parent=276"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}