📚 Light Diffraction: IB & Edexcel Physics Revision | 光的衍射：IB与Edexcel物理考点精讲
Diffraction is a fundamental wave phenomenon that reveals the nature of light itself. Both IB and Edexcel Physics syllabuses place strong emphasis on single‑slit diffraction, diffraction gratings, and the conditions for observable patterns. Mastering these concepts requires a clear understanding of wave superposition, path difference, and the use of concise mathematical relations — skills that are frequently tested in examinations.
衍射是揭示光本质的基本波动现象。IB 和 Edexcel 物理大纲都特别强调单缝衍射、衍射光栅以及可观察图样的条件。掌握这些概念需要清晰理解波的叠加、光程差，并能熟练运用简洁的数学关系——这些技能在考试中备受青睐。
1. What is Diffraction? | 什么是衍射？
Diffraction is the spreading of waves when they pass through a narrow aperture or around an obstacle. For visible light, the effect becomes pronounced when the size of the aperture or obstacle is comparable to the wavelength. Unlike geometrical optics, which predicts sharp shadows, diffraction demonstrates the wave nature of light by producing alternating bright and dark fringes.
衍射是指波通过窄缝或绕过障碍物时发生的扩展现象。对于可见光，当缝隙或障碍物的尺寸与波长可比拟时，衍射效应变得显著。与预测锐利阴影的几何光学不同，衍射通过明暗交替的条纹证明了光的波动性。
2. Huygens–Fresnel Principle | 惠更斯–菲涅耳原理
Every point on a wavefront acts as a source of secondary spherical wavelets. The new wavefront is the envelope of these wavelets. In diffraction, the interference of countless such secondary sources gives rise to the observed intensity pattern. This principle provides the theoretical foundation for predicting both single‑slit and multiple‑slit diffraction.
波前上的每一点都可视为次球面子波的波源，新波前是这些子波的包络面。在衍射中，无数次级波源相互干涉，形成观测到的强度分布。这一原理为单缝和多缝衍射提供了理论基础。
3. Single‑Slit Diffraction Pattern | 单缝衍射图样
When monochromatic light passes through a single narrow slit of width a, a central bright fringe much wider and brighter than the subsidiary maxima is observed on a screen. On either side, dark fringes appear at specific angles where destructive interference is complete. The intensity drops rapidly away from the centre, with the first secondary maximum less than 5% of the central peak intensity.
当单色光通过宽度为 a 的窄缝时，在屏幕上可观察到比次级明纹宽且亮得多的中央明纹。两侧特定角度处出现暗纹，此时发生完全相消干涉。强度从中心向外迅速衰减，第一级次级明纹强度不及中央主极大的 5%。
4. Single‑Slit Dark Fringe Condition | 单缝暗纹条件
Destructive interference in a single slit occurs when the path difference between wavelets from the top and the centre of the slit is an integer multiple of half‑wavelengths. The condition for the n‑th order dark fringe is:
a sin θ = n λ, n = ±1, ±2, ±3, …
Here θ is the angle measured from the centre of the slit to the dark fringe, and a is the slit width. Note that n = 0 corresponds to the central maximum, not a minimum. This equation is identical in form to the grating maxima condition, but careful interpretation separates their physical meaning.
单缝中发生相消干涉的条件是：从缝顶和缝中点发出的子波之间的光程差等于半波长的整数倍。第 n 级暗纹的条件为：
a sin θ = n λ, n = ±1, ±2, ±3, …
其中 θ 是从缝中心量起的暗纹角，a 是缝宽。注意 n = 0 对应中央明纹而非暗纹。该方程在形式上与光栅亮纹条件相同，但解读时物理含义截然不同。
5. Effect of Slit Width and Wavelength | 缝宽与波长的影响
Increasing the slit width a narrows the central maximum and reduces fringe spacing, making the pattern more geometric. Conversely, longer wavelengths produce broader diffraction patterns. The angular width of the central maximum is approximately 2λ/a (for small angles), which is why red light diffracts more than blue light through the same slit.
增大缝宽 a 会使中央明纹变窄、条纹间距缩小，图样趋近几何投影。反之，波长越长衍射图样越宽。中央明纹的角宽度在小角度近似下约为 2λ/a，因此同一狭缝下红光的衍射比蓝光更明显。
6. Introduction to Diffraction Grating | 衍射光栅简介
A diffraction grating consists of many equally spaced parallel slits, with the slit separation d acting as the grating spacing. When illuminated, each slit acts as a coherent source, and the superposition of waves from all slits yields very sharp principal maxima separated by wide dark regions. Gratings provide precise wavelength measurements, making them essential in spectroscopy.
衍射光栅由大量等间距的平行狭缝构成，缝间距 d 即为光栅常数。光照下每个狭缝相当于相干光源，所有缝发出的波叠加，产生非常锐利的主极大，其间隔着宽阔的暗区。光栅可实现高精度波长测量，因而在光谱学中不可或缺。
7. Diffraction Grating Equation | 光栅方程
For a transmission grating, constructive interference occurs when the path difference between adjacent slits equals an integer number of wavelengths. The grating equation is:
d sin θ = n λ, n = 0, ±1, ±2, ±3, …
Here d is the grating spacing (1 / number of lines per metre), θ is the angle of the n‑th order maximum, and λ is the wavelength. This equation is central to exam problems: students must be able to calculate line density, wavelength, or the number of visible orders given the experimental geometry.
对于透射光栅，相邻缝的光程差等于波长的整数倍时发生相长干涉。光栅方程为：
d sin θ = n λ, n = 0, ±1, ±2, ±3, …
其中 d 是光栅常数（即每米刻线数的倒数），θ 是第 n 级主极大的角度，λ 为波长。该方程是考试的核心：学生须能根据实验几何计算线密度、波长或可见的级数。
8. Intensity Distribution and Missing Orders | 强度分布与缺级
The overall intensity envelope of a diffraction grating pattern is modulated by the single‑slit diffraction envelope from each slit. If a principal maximum from the grating equation coincides with a single‑slit minimum, that order is missing. The condition for m‑th order missing is d/a = rational ratio such that the grating angle satisfies both d sin θ = nλ and a sin θ = mλ. This subtle interplay is a favourite in higher‑tier questions.
衍射光栅图样的强度包络受到每条单缝衍射包络的调制。若光栅方程给出的某一主极大恰好与单缝暗纹重合，该级次便会缺级。缺级条件为 d/a 呈有理比，使得角度同时满足 d sin θ = nλ 和 a sin θ = mλ。这种微妙相互作用是高阶考题的热点。
9. Rayleigh Criterion and Resolution | 瑞利判据与分辨率
Two adjacent point sources are said to be just resolved when the central maximum of one diffraction pattern falls on the first minimum of the other. For a circular aperture of diameter D, the angular resolution limit is:
θ ≈ 1.22 λ / D
This criterion applies to telescopes, microscopes, and the human eye. Shortening the wavelength or increasing the aperture size improves resolution. Both IB and Edexcel syllabuses require students to discuss the significance of the Rayleigh criterion in optical instruments.
当一个衍射图样的中央极大恰好落在另一个的第一暗纹上时，两个相邻点光源被认为刚好可分辨。对于直径为 D 的圆孔，角分辨率极限为：
θ ≈ 1.22 λ / D
此判据适用于望远镜、显微镜和人眼。缩短波长或增大孔径可提升分辨率。IB 和 Edexcel 大纲均要求学生讨论瑞利判据在光学仪器中的意义。
10. Diffraction vs. Interference – Key Distinction | 衍射与干涉的核心区别
A common exam pitfall is confusing diffraction with interference. Interference arises from the superposition of waves from a small number of discrete coherent sources, such as two slits. Diffraction refers to the spreading and superposition of wavelets from a continuous wavefront passing through a single aperture. In a double‑slit experiment, the fringe envelope arises from single‑slit diffraction, while the fine fringes inside are due to interference. Recognising this distinction is crucial for accurate graph sketching and explaining observations.
考试常见误区是混淆衍射与干涉。干涉源自少量分立相干源（如双缝）的波叠加，而衍射则指连续波前通过单个孔径时子波的扩展与叠加。双缝实验中，条纹包络来自单缝衍射，内部的细条纹则为干涉所致。清晰辨认这一区别对准确作图与解释现象至关重要。
11. Experimental Determination of Wavelength | 波长测定的实验方法
A standard practical task uses a laser, a diffraction grating of known line spacing, and a distant screen. By measuring the distance from the grating to the screen L and the distance from the central maximum to the n‑th order spot y, tan θ = y/L can be used. For small angles, sin θ ≈ tan θ, allowing λ = d y / (n L). Precision can be increased by measuring multiple orders and calculating an average. The experiment reinforces the grating equation and source coherence concepts.
标准的实验任务使用激光、已知线间距的衍射光栅和远处的屏幕。测量光栅到屏幕的距离 L 以及中央明纹到第 n 级亮点的距离 y，可利用 tan θ = y/L。小角度下 sin θ ≈ tan θ，由此 λ = d y / (n L)。通过测量多级并取平均值可提高精度。该实验巩固了光栅方程及光源相干性的概念。
12. Common Examination Tips and Pitfalls | 高频考点与易错提醒
Students often forget that the single‑slit equation gives minima while the grating equation gives maxima. In multiple‑choice questions, watch for units: grating spacing d must be in metres when used with wavelength in metres. Ensure you correctly identify the angle θ from the diagram — it is measured from the normal, not from the screen centre. For the Rayleigh criterion, note the factor 1.22 applies only to circular apertures; for a single slit, the resolution limit is λ/a. Pay close attention to significant figures when using experimental data.
学生常忘记单缝公式给出的是 暗纹 而光栅方程给出的是 明纹。选择题中要注意单位：光栅常数 d 须与波长单位统一为米。确保从图中正确识别角度 θ——它是从法线而非从屏幕中心量起的。瑞利判据中的系数 1.22 仅 适用于圆孔；对单缝而言，分辨率极限为 λ/a。使用实验数据时务必注意有效数字。
Published by TutorHao | Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导