← Back to map Optics Review: Geometrical Optics, Wave Optics, EM Waves, and Quantum Basics Changed May 13, 2026 Auto translate Feedback Checking feedback… Latest feedback Suggest edit Suggest new note LaTeX PDF Open Contents 1 wave optics 1.1 Law of Reflection 1.2 Fermat’s Principle 1.3 Law of Refraction (Snell’s Law) 1.4 Total Internal Reflection 1.5 Numerical Aperture (NA) 1.6 Fermat’s Principle for Inhomogeneous Media 1.7 Mirrors 1.7.1 Plane Mirrors 1.7.2 Concave Mirrors 1.7.3 Imaging Equation & Magnification for cacave mirror: 1.7.4 Parabolic Mirros 1.8 Prism 1.8.1 Deflection Angle 1.8.2 Dispersion 1.8.3 The hange o fthe deflection angle with refractive index 1.9 Lenses 1.9.1 SPherical surface 1.9.2 Thin lens 1.9.3 Sign convention of a,b,R1 ,R2 for thin lens & spherical lens 1.9.4 Bessel’s method 1.9.5 Magnification of a lens 1.9.6 Thick lens 1.9.7 Imaging Equation for thick lens 1.9.8 Human’s eye’s refractive power (the unit is diopters(D)) 1.9.9 Resolution Limit of the eye 1.9.10 Evaluating the refractive error 1.9.11 Angular magnification 1.9.12 Magnifying glass 1.9.13 Two lens system 1.9.14 THe maginification of lens - eyepiece system 1.9.15 Light Gathering power 1.10 Imaging errors 1.10.1 Chromatic Aberration 1.10.2 Spherical aberration 1.10.3 Field Curvature 1.10.4 Coma 1.10.5 Astigmatism 1.10.6 Cushion Distortion 1.10.7 Barrel Distortion 1.11 Rainbow, single drop analysis 1.11.1 Primary and Secondary Rainbows 1.12 Wave Optics 1.12.1 Wave equation 1.12.2 Monochromatic wave 1.12.3 Intensity of waves 1.12.4 Optical Power P of a wave 1.12.5 Wave fronts 1.12.6 Plane waves 1.12.7 Dispersion Relation 1.12.8 In a Medium 1.12.9 Snells law 1.12.10 Spherical waves 1.13 Interference 1.13.1 Phase difference related to path difference between two waves 1.13.2 Coherence 1.13.3 Interferometers 1.13.4 Michelson Interferometer 1.13.5 Mach-Zehnder Interferometer 1.13.6 Application: Electro-Optic Modulators in Photonic Integrated Circuits 1.13.7 Sagnac Interferometer 1.13.8 Derivation and Application in Fiber-Optic Gyroscopes 1.14 Double Slit Interference 1.14.1 Two point sources 1.14.2 INterference Conditions for buouble slit 1.14.3 Intensity Distribution 1.14.4 Resolution 1.14.5 Fresnel Double Mirror 1.14.6 Fresnel Biprism 1.14.7 Basic Principle of Thin Film Interference 1.14.8 Normal incidence : α = 0 1.14.9 Thickness for constructive interference 1.14.10 Fixed thickness, understanding colored films 1.14.11 Anti-Reflection Coating 1.14.12 Newton Rings 1.14.13 Multiple Wave Interference with Constant Amplitude 1.14.14 Application: Diffraction Gratings 1.14.15 Wavevector Representation: A Powerful Geometric Insight 1.14.16 Multiple Wave Interference with Decreasing Amplitude 1.14.17 Fabry Perot Interferometer 1.14.18 Finesse and Spectral Properties 1.14.19 Ring Pattern Formation 1.14.20 Huygens Principle 1.14.21 Single Slit Diffraction 1.14.22 Circular Aperture 1.14.23 Application: Diffraction Grating 1.14.24 Properties of the Diffraction Pattern 1.15 Diffraction in Applications 1.15.1 Rayleighʼs Criterion for Resolution 1.15.2 Abbeʼs Criterion 1.16 Fresnel Zones 1.16.1 Fresnel Zone Plate 1.16.2 Diffraction Integral 2 Electromagnetic Optics 2.0.1 Electromagnetic Spectrum 2.0.2 Maxwell Equations 2.0.3 Deriving the Wave Equation 2.0.4 Michelson-Morley Experiment 2.0.5 Plane waves 2.0.6 Spherical Waves 2.1 Polarization of EM Waves 2.1.1 Linearly Polarized waves 2.1.2 Circularly Polarized Waves 2.1.3 Elliptically Polarized Waves 2.2 Unpolarized Light 2.2.1 Analyzing Polarization & Law of Malus 2.2.2 The Three Polarizer Paradox 2.3 Energy Transport and Momentum Transport of EM waves 2.3.1 Energy Transport 2.3.3 Intensity and Measurement 2.3.4 Momentum Transport and Radiation Pressure 2.3.5 Microscopic Picture of Dielectric Response 2.3.6 Single Atom Response 2.3.7 Macroscopic Description of Dielectric Materials 2.3.8 クラウジウス・モソッティの関係式 (Clausius-Mossotti Relation) 2.3.9 Maxwellʼs Equations in Matter 2.3.10 構成方程式 (Constitutive Relations): 2.3.11 物質中の波動伝搬 (Wave Propagation in Non-conducting Matter) 2.3.12 特殊なケース：負の屈折 (Negative Refraction) 2.3.13 負の屈折率物質中のエネルギー流 (Energy Flow) 2.3.14 メタマテリアルの実現 (Metamaterial Realization) 2.3.15 Interaction Model & Approximations 2.3.16 吸収とランベルト・ベールの法則 (Absorption & Lambert-Beer Law) 2.3.17 Dispersion: Phase & Group Velocity 2.3.18 Normal & Anomalous Dispersion 2.3.19 超光速群速度 (Superluminal Group Velocity) 2.3.20 クラマース・クローニッヒの関係式 (Kramers-Kronig Relations) 2.4 Reflection and Refraction of Electromagnetic Waves 2.4.1 Effect of the Refractive Index 2.4.2 反射と屈折の一般的記述 (General Description of Reflection and Refraction) 2.4.3 境界条件 (Boundary Conditions) 2.4.4 反射と屈折 (Reflection/Refraction) - 周波数と波数の整合 (matching) 2.5 Fresnel Equations 2.5.1 Reflection 2.5.2 s 偏光 (s-polarized light) 2.5.3 S polaized light 2.5.4 空気からガラスへの反射と位相 (Air to Glass) 2.5.5 ガラスから空気への反射：全反射 (Total Internal Reflection) 2.5.6 エバネッセント波 (Evanescent Wave) 2.5.7 強度 (Intensities) 2.5.8 Electromagnetic Waves in Metals 2.5.9 ドルーデモデル (Drude Model) 2.5.10 複素屈折率と導電率 (Complex Refractive Index & Conductivity) 2.5.11 Reflectivity of Metals 2.5.12 分散関係と表皮効果 (Dispersion Relation & Skin Depth) 2.5.13 プラズモニクス (Plasmonics) 2.6 Anisotropic Materials 2.6.1 Light propagation 2.6.2 誘電率テンソルと主座標系 (Dielectric Tensor and Principal Coordinate System) 2.6.3 主座標系（Principal Coordinate System） 2.6.4 エネルギーの流れと位相の伝搬 (Energy Flow vs Phase Propagation) 2.6.5 結晶の対称性と分類 (Symmetries: Uniaxial and Biaxial) 2.6.6 固有モード：常光線と異常光線 (Normal Modes: Ordinary and Extraordinary rays) . 2.6.7 k 曲面（波数ベクトル曲面）と分散関係 (The k-surface) 2.6.8 複屈折（Birefringence） 2.6.9 波長板（Wave Retarders） 2.7 Optical Activity and Rotatory Dispersion 2.7.1 電磁気学的メカニズム：双極子モーメントの結合 2.7.2 円複屈折とその電子的起源 Circular Birefringence (円複屈折) 2.7.3 量子力学的基礎 Quantum Mechanical Foundation 2.7.4 コットン効果と波長依存性 The Cotton Effect (コットン効果) 2.7.5 砂糖水溶液におけるケーススタディ Sugar Solutions 2.7.6 温度効果と応用 Temperature Effects & Applications 2.8 Dipole Radiation 2.8.1 1. 加速電荷による電場の発生 (Electric Field of an Accelerated Charge) 2.8.2 エネルギーの流れとポインティング・ベクトル (Energy Flow & Poynting Vector) 2.8.3 ラーモアの公式 (Larmor’s Formula): 2.8.4 振動双極子とレイリー散乱 (Oscillating Dipole & Rayleigh Scattering) 2.8.5 ミー散乱とメタマテリアル (Mie Scattering & Metamaterials) 2.9 Black Body Radiation 2.9.1 黒体とキルヒホッフの法則 (Blackbody and Kirchhoff’s Law) 2.9.2 モード密度の導出 (Derivation of Spectral Density of Modes) 2.9.3 レイリー・ジーンズの法則 (Rayleigh-Jeans Law) 2.9.4 プランクの法則 (Planck’s Law) 2.9.5 プランクの放射公式 2.9.6 プランク定数の測定 (Measuring Planck’s Constant) 2.9.7 関連する法則と応用 (Related Laws and Applications) 2.10 The Wave Character of Particles, Electron diffraction and de brogile wavelength 2.10.1 The Wave Character of Particles & de Broglie Wavelength 2.10.2 荷電粒子の加速 Accelerating Charged Particles 2.10.3 デビソン＝ガーマーの実験 Experiment by Davisson and Germer 2.10.4 ブラッグの法則 (Bragg’s Law) 2.10.5 原子および分子の回折 Atomic and Molecular Diffraction 2.11 Matter Waves 2.11.1 平面波 2.11.2 ウェーブパケット (Wave Packets / Wave Trains) 2.11.3 重ね合わせの式 2.11.4 群速度 (Group Velocity) 2.11.5 一定振幅のウェーブパケット (Constant Amplitude Wave Packets) 2.11.6 物質波の統計的解釈 (Statistical Interpretation of Matter Waves) 2.11.7 測定との関係 (Relation to Measurement) 2.12 Heisenbergs Uncertainty Relation 2.12.1 Position-momentum uncertainty 2.12.2 エネルギーと時間の不確定性 (Energy-time uncertainty) 2.13 The Structure of Atoms and the Bohr Model 2.13.2 原子スペクトル (Atomic Spectra) 2.13.3 ボーア・モデル (The Bohr Model) 2.13.4 ボーア・ゾンマーフェルト・モデル (The Bohr-Sommerfeld Model) 2.13.5 フランク・ヘルツの実験 (Franck-Hertz Experiment) 2.14 The Schrödinger Equation 2.14.2 定常シュレーディンガー方程式 (Stationary Schrödinger Equation) 2.14.3 境界条件 (Boundary Conditions) 2.14.4 ポテンシャル障壁：ステップ型 (A Potential Barrier / Step) 2.15 Potential barriers and wells 2.15.1 ポテンシャル障壁とトンネル効果 (Potential Barrier & Tunneling Effect) 2.15.2 トンネル効果 (The Tunneling Effect) 2.15.3 トンネル効果の応用 (Applications) 2.15.4 無限井戸型ポテンシャル (Potential Well with Infinite Depth) 2.15.5 有限井戸型ポテンシャル (Potential Well with Finite Depth) 2.16 The harmonic oscillator 2.17 Angular Momentum and Spherical Potentials 2.18 Parametric Downconversion 2.18.1 1. パラメトリック下方変換 (Parametric Downconversion: PDC) 2.18.2 2. 非線形光学の基礎 (Nonlinear Optics Primer) 2.18.3 3. 位相整合条件 (Phase Matching Condition) 2.18.4 4. Type-I と Type-II の違い (Type-I vs Type-II PDC) 2.18.5 5. 量子もつれ (Quantum Entanglement) 2.18.6 6. CHSH 不等式 (CHSH Inequality) 2.18.7 まとめ 2.19 The Quantum Zeno Effect 2.19.1 導入と歴史的背景 (Introduction and Historical Background) 2.19.2 理論的枠組みと導出 (Theoretical Framework) 2.19.3 対比：偏光の段階的回転 (Gradual Polarization Rotation) 2.19.4 断熱発展と段階的測定 (Adiabatic Evolution and Gradual Measurements) 2.19.5 実験結果と現在の研究 (Experimental Results and Current Research) 2.19.6 応用例：液晶ディスプレイ (Liquid Crystal Displays - LCD)
