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<title>Formulas for IPhO 日本語版: Section 7 | Toshiki's Note</title>
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collapsible has-active" data-v-c79ccefa data-v-b05232f3><div class="item" role="button" data-v-b05232f3><div class="indicator" data-v-b05232f3></div><a class="VPLink link" data-v-b05232f3 data-v-30c06bd3><!--[--><h2 class="text" data-v-b05232f3>IPhO Formulas: JP Ver.</h2><!--]--><!----></a><div class="caret" role="button" data-v-b05232f3><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" viewbox="0 0 24 24" class="caret-icon" data-v-b05232f3><path d="M9,19c-0.3,0-0.5-0.1-0.7-0.3c-0.4-0.4-0.4-1,0-1.4l5.3-5.3L8.3,6.7c-0.4-0.4-0.4-1,0-1.4s1-0.4,1.4,0l6,6c0.4,0.4,0.4,1,0,1.4l-6,6C9.5,18.9,9.3,19,9,19z"></path></svg></div></div><div class="items" data-v-b05232f3><!--[--><div class="VPSidebarItem level-1 is-link" data-v-b05232f3 data-v-b05232f3><div class="item" data-v-b05232f3><div class="indicator" data-v-b05232f3></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/1" data-v-b05232f3 data-v-30c06bd3><!--[--><p class="text" data-v-b05232f3>1: 数学</p><!--]--><!----></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b05232f3 data-v-b05232f3><div class="item" data-v-b05232f3><div class="indicator" data-v-b05232f3></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/2" data-v-b05232f3 data-v-30c06bd3><!--[--><p class="text" data-v-b05232f3>2: 一般的な推奨事</p><!--]--><!----></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b05232f3 data-v-b05232f3><div class="item" data-v-b05232f3><div class="indicator" data-v-b05232f3></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/3" data-v-b05232f3 data-v-30c06bd3><!--[--><p class="text" data-v-b05232f3>3: 運動学</p><!--]--><!----></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b05232f3 data-v-b05232f3><div class="item" data-v-b05232f3><div class="indicator" data-v-b05232f3></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/4" data-v-b05232f3 data-v-30c06bd3><!--[--><p class="text" data-v-b05232f3>4: 力学</p><!--]--><!----></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b05232f3 data-v-b05232f3><div class="item" data-v-b05232f3><div class="indicator" data-v-b05232f3></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/5" data-v-b05232f3 data-v-30c06bd3><!--[--><p class="text" data-v-b05232f3>5: 振動と波</p><!--]--><!----></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b05232f3 data-v-b05232f3><div class="item" data-v-b05232f3><div class="indicator" data-v-b05232f3></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/6" data-v-b05232f3 data-v-30c06bd3><!--[--><p class="text" data-v-b05232f3>6: 幾何光学，測光</p><!--]--><!----></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link is-active has-active" data-v-b05232f3 data-v-b05232f3><div class="item" data-v-b05232f3><div class="indicator" data-v-b05232f3></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/7" data-v-b05232f3 data-v-30c06bd3><!--[--><p class="text" data-v-b05232f3>7: 波動光学</p><!--]--><!----></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b05232f3 data-v-b05232f3><div class="item" data-v-b05232f3><div class="indicator" data-v-b05232f3></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/8" data-v-b05232f3 data-v-30c06bd3><!--[--><p class="text" data-v-b05232f3>8: 電気回路</p><!--]--><!----></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b05232f3 data-v-b05232f3><div class="item" data-v-b05232f3><div class="indicator" data-v-b05232f3></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/9" data-v-b05232f3 data-v-30c06bd3><!--[--><p class="text" data-v-b05232f3>9: 電磁気学</p><!--]--><!----></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b05232f3 data-v-b05232f3><div class="item" data-v-b05232f3><div class="indicator" data-v-b05232f3></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/10" data-v-b05232f3 data-v-30c06bd3><!--[--><p class="text" data-v-b05232f3>10: 熱力</p><!--]--><!----></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b05232f3 data-v-b05232f3><div class="item" data-v-b05232f3><div class="indicator" data-v-b05232f3></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/11" data-v-b05232f3 data-v-30c06bd3><!--[--><p class="text" data-v-b05232f3>11: 量子力学</p><!--]--><!----></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b05232f3 data-v-b05232f3><div class="item" data-v-b05232f3><div class="indicator" data-v-b05232f3></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/12" data-v-b05232f3 data-v-30c06bd3><!--[--><p class="text" data-v-b05232f3>12: Keplerの法則</p><!--]--><!----></a><!----></div><!----></div><div class="VPSidebarItem level-1 is-link" data-v-b05232f3 data-v-b05232f3><div class="item" data-v-b05232f3><div class="indicator" data-v-b05232f3></div><a class="VPLink link link" href="/academic/physics/ipho-formulas-jpn/13" data-v-b05232f3 data-v-30c06bd3><!--[--><p class="text" data-v-b05232f3>13: 相対性理論</p><!--]--><!----></a><!----></div><!----></div><!--]--></div></section></div><!--]--><!--[--><!--]--></nav></aside><div class="VPContent has-sidebar" id="VPContent" data-v-93a960b4 data-v-0bd490fb><div class="VPDoc has-sidebar has-aside" data-v-0bd490fb data-v-c5936a1e><div class="container" data-v-c5936a1e><div class="aside" data-v-c5936a1e><div class="aside-curtain" data-v-c5936a1e></div><div class="aside-container" data-v-c5936a1e><div class="aside-content" data-v-c5936a1e><div class="VPDocAside" data-v-c5936a1e data-v-cdc66372><!--[--><!--]--><!--[--><!--]--><div class="VPDocAsideOutline" data-v-cdc66372 data-v-5dd9d5f6><div class="content" data-v-5dd9d5f6><div class="outline-marker" data-v-5dd9d5f6></div><div class="outline-title" data-v-5dd9d5f6>TOC</div><nav aria-labelledby="doc-outline-aria-label" data-v-5dd9d5f6><span class="visually-hidden" id="doc-outline-aria-label" data-v-5dd9d5f6> Table of Contents for current page </span><ul class="root" data-v-5dd9d5f6 data-v-1188541a><!--[--><!--]--></ul></nav></div></div><!--[--><!--]--><div class="spacer" data-v-cdc66372></div><!--[--><!--]--><!----><!--[--><!--]--><!--[--><!--[--><!--[--><!--[--><div class="VPDocAsideSponsors"><div class="VPSponsors vp-sponsor aside"><!--[--><section class="vp-sponsor-section"><!----><div class="VPSponsorsGrid vp-sponsor-grid medium"><!--[--><div class="vp-sponsor-grid-item"><a class="vp-sponsor-grid-link" target="_blank" rel="sponsored noopener"><article class="vp-sponsor-grid-box"><h4 class="visually-hidden"></h4><img class="vp-sponsor-grid-image" 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href="#formulas-for-ipho-日本語版-section-7" aria-hidden="true">#</a></h1><h2 id="_7-波動光学" tabindex="-1">7: 波動光学 <a class="header-anchor" href="#_7-波動光学" aria-hidden="true">#</a></h2><h3 id="_7-1-huygens-の原理に基づいた回折" tabindex="-1">7.1: Huygens の原理に基づいた回折 <a class="header-anchor" href="#_7-1-huygens-の原理に基づいた回折" aria-hidden="true">#</a></h3><ol><li>Huygens の原理に基づいた回折 : 障害物が波面を切断 すると波面は小さな断片に分割され，それが仮想的な 点波源となり，観測点での波の振幅はこれらの波源か らの寄与の重ね合わせとなる.</li></ol><h3 id="_7-2-二重スリット" tabindex="-1">7.2: 二重スリット <a class="header-anchor" href="#_7-2-二重スリット" aria-hidden="true">#</a></h3><ol start="2"><li>二重スリット（幅は <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>d</mi><mo>≪</mo><mi>a</mi><mo separator="true">,</mo><mi>λ</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">d \ll a, \lambda)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≪</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">a</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">λ</span><span class="mclose">)</span></span></span></span> による干渉:強 め合う角 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>φ</mi><mi>max</mi><mo>⁡</mo></msub><mo>=</mo><mi>arcsin</mi><mo>⁡</mo><mo stretchy="false">(</mo><mi>n</mi><mi>λ</mi><mi mathvariant="normal">/</mi><mi>d</mi><mo stretchy="false">)</mo><mo separator="true">,</mo><mi>n</mi><mo>∈</mo><mi mathvariant="double-struck">Z</mi><mi mathvariant="normal">.</mi><mi>I</mi><mo>∝</mo></mrow><annotation encoding="application/x-tex">\varphi_{\max }=\arcsin (n \lambda / d), n \in \mathbb{Z} . I \propto</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal">φ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mop mtight"><span class="mtight">m</span><span class="mtight">a</span><span class="mtight">x</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">arcsin</span><span class="mopen">(</span><span class="mord mathnormal">nλ</span><span class="mord">/</span><span class="mord mathnormal">d</span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6889em;"></span><span class="mord mathbb">Z</span><span class="mord">.</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∝</span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mrow><mi>cos</mi><mo>⁡</mo></mrow><mn>2</mn></msup><mrow><mo fence="true">(</mo><mi>k</mi><mfrac><mi>a</mi><mn>2</mn></mfrac><mi>sin</mi><mo>⁡</mo><mi>φ</mi><mo fence="true">)</mo></mrow><mo separator="true">,</mo><mo stretchy="false">(</mo><mi>k</mi><mo>=</mo><mn>2</mn><mi>π</mi><mi mathvariant="normal">/</mi><mi>λ</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\cos ^2\left(k \frac{a}{2} \sin \varphi\right),(k=2 \pi / \lambda)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2em;vertical-align:-0.35em;"></span><span class="mop"><span class="mop">cos</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size1">(</span></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6954em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">a</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">sin</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">φ</span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mord mathnormal" style="margin-right:0.03588em;">π</span><span class="mord">/</span><span class="mord mathnormal">λ</span><span class="mclose">)</span></span></span></span></li></ol><h3 id="_7-3-単スリット-弱め合う角" tabindex="-1">7.3: 単スリット-弱め合う角 <a class="header-anchor" href="#_7-3-単スリット-弱め合う角" aria-hidden="true">#</a></h3><ol start="3"><li>単スリット:弱め合う角: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>φ</mi><mtext>min </mtext></msub><mo>=</mo><mi>arcsin</mi><mo>⁡</mo><mo stretchy="false">(</mo><mi>n</mi><mi>λ</mi><mi mathvariant="normal">/</mi><mi>d</mi><mo stretchy="false">)</mo><mo separator="true">,</mo><mi>n</mi><mo>∈</mo></mrow><annotation encoding="application/x-tex">\varphi_{\text {min }}=\arcsin (n \lambda / d), n \in</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal">φ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3175em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">min </span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">arcsin</span><span class="mopen">(</span><span class="mord mathnormal">nλ</span><span class="mord">/</span><span class="mord mathnormal">d</span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∈</span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="double-struck">Z</mi><mo separator="true">,</mo><mi>n</mi><mo mathvariant="normal">≠</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">\mathbb{Z}, n \neq 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathbb">Z</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel"><span class="mrel"><span class="mord vbox"><span class="thinbox"><span class="rlap"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="inner"><span class="mord"><span class="mrel"></span></span></span><span class="fix"></span></span></span></span></span><span class="mrel">=</span></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span>. 中央の強め合う部分は <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mo>=</mo><mo>±</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">n=\pm 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">±</span><span class="mord">1</span></span></span></span> の間である ことに注意せよ. <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>I</mi><mo>∝</mo><msup><mrow><mi>sin</mi><mo>⁡</mo></mrow><mn>2</mn></msup><mrow><mo fence="true">(</mo><mi>k</mi><mfrac><mi>d</mi><mn>2</mn></mfrac><mi>sin</mi><mo>⁡</mo><mi>φ</mi><mo fence="true">)</mo></mrow><mi mathvariant="normal">/</mi><mi>sin</mi><mo>⁡</mo><mi>φ</mi></mrow><annotation encoding="application/x-tex">I \propto \sin ^2\left(k \frac{d}{2} \sin \varphi\right) / \sin \varphi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∝</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2301em;vertical-align:-0.35em;"></span><span class="mop"><span class="mop">sin</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8719em;"><span style="top:-3.1208em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size1">(</span></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8801em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">sin</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">φ</span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">/</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">sin</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">φ</span></span></span></span></li></ol><h3 id="_7-4-回折格子" tabindex="-1">7.4: 回折格子 <a class="header-anchor" href="#_7-4-回折格子" aria-hidden="true">#</a></h3><ol start="4"><li>回折格子：主な強め合う角はポイント 2 と同じで, 主 な強め合う角の幅は <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>d</mi></mrow><annotation encoding="application/x-tex">d</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">d</span></span></span></span> を回折格子の正味の長さとすれ ばポイント 3 と同じ. <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span></span></span></span> 番目の明線のスペクトルの分 解能は，溝の総数を <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>N</mi></mrow><annotation encoding="application/x-tex">N</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span></span></span></span> 本として <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mi>λ</mi><mrow><mi mathvariant="normal">Δ</mi><mi>λ</mi></mrow></mfrac><mo>=</mo><mi>n</mi><mi>N</mi></mrow><annotation encoding="application/x-tex">\frac{\lambda}{\Delta \lambda}=n N</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2251em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8801em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">λ</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">λ</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">n</span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span></span></span></span>.</li></ol><h3 id="_7-5-分光器の分解能" tabindex="-1">7.5: 分光器の分解能 <a class="header-anchor" href="#_7-5-分光器の分解能" aria-hidden="true">#</a></h3><ol start="5"><li>分光器の分解能 : 最短の光線と最長の光線の光学距離 の差を <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi></mrow><annotation encoding="application/x-tex">L</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">L</span></span></span></span> として, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mi>λ</mi><mrow><mi mathvariant="normal">Δ</mi><mi>λ</mi></mrow></mfrac><mo>=</mo><mfrac><mi>L</mi><mi>λ</mi></mfrac></mrow><annotation encoding="application/x-tex">\frac{\lambda}{\Delta \lambda}=\frac{L}{\lambda}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2251em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8801em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">λ</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">λ</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2173em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8723em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">λ</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">L</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span>.</li></ol><h3 id="_7-6-プリズムの分解能" tabindex="-1">7.6: プリズムの分解能 <a class="header-anchor" href="#_7-6-プリズムの分解能" aria-hidden="true">#</a></h3><ol start="7"><li>プリズムの分解能 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>:</mo><mfrac><mi>λ</mi><mrow><mi mathvariant="normal">Δ</mi><mi>λ</mi></mrow></mfrac><mo>=</mo><mi>a</mi><mfrac><mrow><mi mathvariant="normal">d</mi><mi>n</mi></mrow><mrow><mrow><mtext> </mtext><mi mathvariant="normal">d</mi></mrow><mi>λ</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">: \frac{\lambda}{\Delta \lambda}=a \frac{\mathrm{d} n}{\mathrm{~d} \lambda}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2251em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8801em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">λ</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">λ</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2251em;vertical-align:-0.345em;"></span><span class="mord mathnormal">a</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8801em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mspace nobreak mtight"><span class="mtight"> </span></span><span class="mord mathrm mtight">d</span></span><span class="mord mathnormal mtight">λ</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathrm mtight">d</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></li></ol><h3 id="_7-7-角度距離" tabindex="-1">7.7: 角度距離 <a class="header-anchor" href="#_7-7-角度距離" aria-hidden="true">#</a></h3><ol start="7"><li>理想的な望遠鏡 (レンズ) で 2 点を解像するときの角度距離 : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>φ</mi><mo>≈</mo><mn>1.22</mn><mi>λ</mi><mi mathvariant="normal">/</mi><mi>d</mi></mrow><annotation encoding="application/x-tex">\varphi \approx 1.22 \lambda / d</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6776em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">φ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1.22</span><span class="mord mathnormal">λ</span><span class="mord">/</span><span class="mord mathnormal">d</span></span></span></span>. この角度では, 一方の点の中 心が他方の点の最初の回折最小值に当たる.</li></ol><h3 id="_7-8-bragg-の法則" tabindex="-1">7.8: Bragg の法則 <a class="header-anchor" href="#_7-8-bragg-の法則" aria-hidden="true">#</a></h3><ol start="8"><li>Bragg の法則：間隔が <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>d</mi></mrow><annotation encoding="application/x-tex">d</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">d</span></span></span></span> の平行な結晶面の組は, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mi>d</mi><mi>sin</mi><mo>⁡</mo><mi>θ</mi><mo>=</mo><mi>n</mi><mi>λ</mi></mrow><annotation encoding="application/x-tex">2 d \sin \theta=n \lambda</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">2</span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">sin</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">nλ</span></span></span></span> ならば <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">X</mi></mrow><annotation encoding="application/x-tex">\mathrm{X}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathrm">X</span></span></span></span> 線を反射する. ここで <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>θ</mi></mrow><annotation encoding="application/x-tex">\theta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span></span></span></span> は結 晶面と X 線がなす角 (かすめ角).</li></ol><h3 id="_7-9-高密度電体媒質反射" tabindex="-1">7.9: 高密度電体媒質反射 <a class="header-anchor" href="#_7-9-高密度電体媒質反射" aria-hidden="true">#</a></h3><ol start="9"><li>光学的に高密度な誘電体媒質による反射 : 位相が <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">π</span></span></span></span> ず れる. 半透明の薄膜では <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ϕ</mi><mo lspace="0em" rspace="0em">→</mo></msub><mo>+</mo><msub><mi>ϕ</mi><mo lspace="0em" rspace="0em">←</mo></msub><mo>=</mo><mi>π</mi></mrow><annotation encoding="application/x-tex">\phi_{\rightarrow}+\phi_{\leftarrow}=\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal">ϕ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1068em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mrel mtight">→</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal">ϕ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1068em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mrel mtight">←</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">π</span></span></span></span>. ここで <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ϕ</mi><mo lspace="0em" rspace="0em">→</mo></msub></mrow><annotation encoding="application/x-tex">\phi_{\rightarrow}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal">ϕ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1068em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mrel mtight">→</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> と <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ϕ</mi><mo lspace="0em" rspace="0em">←</mo></msub></mrow><annotation encoding="application/x-tex">\phi_{\leftarrow}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal">ϕ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1068em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mrel mtight">←</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> は反射波と透過波の位相差（矢印は入射方向を 示す)</li></ol><h3 id="_7-10-fabry-perot-干渉計" tabindex="-1">7.10: Fabry-Pérot 干渉計 <a class="header-anchor" href="#_7-10-fabry-perot-干渉計" aria-hidden="true">#</a></h3><ol start="10"><li>Fabry-Pérot 干渉計 : 高い反射率 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>r</mi><mo>≪</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">r(1-r \ll 1)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≪</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mclose">)</span></span></span></span> を持 つ 2 枚の平行な半透明の鏡. 分解能は <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mi>ν</mi><mrow><mi mathvariant="normal">Δ</mi><mi>ν</mi></mrow></mfrac><mo>≈</mo><mfrac><mrow><mn>2</mn><mi>a</mi></mrow><mrow><mi>λ</mi><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>r</mi><mo stretchy="false">)</mo></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{\nu}{\Delta \nu} \approx \frac{2 a}{\lambda(1-r)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0404em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6954em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">Δ</span><span class="mord mathnormal mtight" style="margin-right:0.06366em;">ν</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.06366em;">ν</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.3651em;vertical-align:-0.52em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">λ</span><span class="mopen mtight">(</span><span class="mord mtight">1</span><span class="mbin mtight">−</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mclose mtight">)</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span><span class="mord mathnormal mtight">a</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.52em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span>. 5 つの平面波 (干渉計の前で左右に進む波, 内部を左右 に進む波，後ろを進む波）を設定して境界条件を課す ことで，透過スペクトルを求められる.</li></ol><h3 id="_7-11-コヒーレントな電磁波" tabindex="-1">7.11: コヒーレントな電磁波 <a class="header-anchor" href="#_7-11-コヒーレントな電磁波" aria-hidden="true">#</a></h3><ol start="11"><li>コヒーレントな電磁波: 電場をベクトル为で表し, ベク トル間の角度を位相差とする. 屈折率が <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mo>=</mo><mi>n</mi><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><mo>=</mo></mrow><annotation encoding="application/x-tex">n=n(\omega)=</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">n</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msqrt><mrow><mi>ε</mi><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo></mrow></msqrt></mrow><annotation encoding="application/x-tex">\sqrt{\varepsilon(\omega)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.24em;vertical-align:-0.305em;"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.935em;"><span class="svg-align" style="top:-3.2em;"><span class="pstrut" style="height:3.2em;"></span><span class="mord" style="padding-left:1em;"><span class="mord mathnormal">ε</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose">)</span></span></span><span style="top:-2.895em;"><span class="pstrut" style="height:3.2em;"></span><span class="hide-tail" style="min-width:1.02em;height:1.28em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.28em" viewBox="0 0 400000 1296" preserveAspectRatio="xMinYMin slice"><path d="M263,681c0.7,0,18,39.7,52,119
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M1001 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.305em;"><span></span></span></span></span></span></span></span></span> (普通 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>μ</mi><mo>≈</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\mu \approx 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6776em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">μ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span> ) であることに注意せよ. エネ ルギー流密度（単位面積を通過する単位時間あたりの エネルギー）: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>I</mi><mo>=</mo><mi>c</mi><mi>n</mi><msub><mi>ε</mi><mn>0</mn></msub><msup><mi>E</mi><mn>2</mn></msup><mo>=</mo><mfrac><mi>c</mi><mrow><mi>n</mi><msub><mi>μ</mi><mn>0</mn></msub></mrow></mfrac><msup><mi>B</mi><mn>2</mn></msup><mo stretchy="false">(</mo><mi>E</mi></mrow><annotation encoding="application/x-tex">I=c n \varepsilon_0 E^2=\frac{c}{n \mu_0} B^2(E</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.9641em;vertical-align:-0.15em;"></span><span class="mord mathnormal">c</span><span class="mord mathnormal">n</span><span class="mord"><span class="mord mathnormal">ε</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2952em;vertical-align:-0.4811em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6954em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mord mtight"><span class="mord mathnormal mtight">μ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">c</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4811em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span></span></span></span> と <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>B</mi></mrow><annotation encoding="application/x-tex">B</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span></span></span></span> は実 効值)</li></ol><h3 id="_7-12-malus-の法則" tabindex="-1">7.12: Malus の法則 <a class="header-anchor" href="#_7-12-malus-の法則" aria-hidden="true">#</a></h3><ol start="12"><li>Malus の法則 : 直線偏光が角度 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>φ</mi></mrow><annotation encoding="application/x-tex">\varphi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">φ</span></span></span></span> で偏光板を通過する と <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>I</mi><mo>=</mo><msub><mi>I</mi><mn>0</mn></msub><msup><mrow><mi>cos</mi><mo>⁡</mo></mrow><mn>2</mn></msup><mi>φ</mi></mrow><annotation encoding="application/x-tex">I=I_0 \cos ^2 \varphi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0085em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop"><span class="mop">cos</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">φ</span></span></span></span></li></ol><h3 id="_7-13-1-4-波長版" tabindex="-1">7.13: 1/4 波長版 <a class="header-anchor" href="#_7-13-1-4-波長版" aria-hidden="true">#</a></h3><ol start="13"><li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mi mathvariant="normal">/</mi><mn>4</mn></mrow><annotation encoding="application/x-tex">1 / 4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1/4</span></span></span></span> 波長版 : 直線偏光成分間の位相が <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi><mi mathvariant="normal">/</mi><mn>2</mn></mrow><annotation encoding="application/x-tex">\pi / 2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">π</span><span class="mord">/2</span></span></span></span> ずれる.</li></ol><h3 id="_7-14-brewster-角" tabindex="-1">7.14: Brewster 角 <a class="header-anchor" href="#_7-14-brewster-角" aria-hidden="true">#</a></h3><ol start="14"><li>Brewster 角: 入射角が <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>tan</mi><mo>⁡</mo><mi>φ</mi><mo>=</mo><mi>n</mi></mrow><annotation encoding="application/x-tex">\tan \varphi=n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8095em;vertical-align:-0.1944em;"></span><span class="mop">tan</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">φ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span></span></span></span> を満たすとき, 反 射波と屈折波が垂直になり反射波は直線偏光となる.</li></ol><h3 id="_7-15-光学素子による回折" tabindex="-1">7.15: 光学素子による回折 <a class="header-anchor" href="#_7-15-光学素子による回折" aria-hidden="true">#</a></h3><ol start="15"><li>光学素子による回折 : レンズやプリズムなどを通る光 の光学距離を計算する必要はなく, 図形的に考える. 例えば，双プリズムは二重スリットによる回折と同じ 回折をする.</li></ol><h3 id="_7-16-光ファイバー" tabindex="-1">7.16: 光ファイバー <span class="VPBadge tip" data-v-350d3852><!--[-->supplemental<!--]--></span> <a class="header-anchor" href="#_7-16-光ファイバー" aria-hidden="true">#</a></h3><ol start="17"><li>光ファイバー：Mach-Zehnder 干渉計は二重スリッ トによる干渉と, 円形共振器は Fabry-Pérot 干渉計 と似ている. Bragg フィルターは <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">X</mi></mrow><annotation encoding="application/x-tex">\mathrm{X}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathrm">X</span></span></span></span> 線の場合と同 じように働く. シングルモードの光ファイバーでは, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mi>n</mi><mi mathvariant="normal">/</mi><mi>n</mi><mo>≈</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo stretchy="false">(</mo><mi>λ</mi><mi mathvariant="normal">/</mi><mi>d</mi><msup><mo stretchy="false">)</mo><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">\Delta n / n \approx \frac{1}{2}(\lambda / d)^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">Δ</span><span class="mord mathnormal">n</span><span class="mord">/</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1901em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mopen">(</span><span class="mord mathnormal">λ</span><span class="mord">/</span><span class="mord mathnormal">d</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span>.</li></ol></div></div></main><!--[--><!--[--><!--[--><!----><!--]--><!--]--><!--]--><footer class="VPDocFooter" data-v-c5936a1e data-v-e033cd21><div class="edit-info" data-v-e033cd21><div class="edit-link" data-v-e033cd21><a class="VPLink link edit-link-button" href="https://github.com/andatoshiki/toshiki-notebook/edit/master/docs/academic/physics/ipho-formulas-jpn/7.md" target="_blank" rel="noreferrer" data-v-e033cd21 data-v-30c06bd3><!--[--><svg xmlns="http://www.w3.org/2000/svg" viewbox="0 0 24 24" class="edit-link-icon" data-v-e033cd21><path d="M18,23H4c-1.7,0-3-1.3-3-3V6c0-1.7,1.3-3,3-3h7c0.6,0,1,0.4,1,1s-0.4,1-1,1H4C3.4,5,3,5.4,3,6v14c0,0.6,0.4,1,1,1h14c0.6,0,1-0.4,1-1v-7c0-0.6,0.4-1,1-1s1,0.4,1,1v7C21,21.7,19.7,23,18,23z"></path><path 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