📚 Diffraction of Light | 光的衍射
Light waves, like all waves, do not travel strictly in straight lines when they encounter obstacles or narrow openings. Instead, they spread out and bend around edges. This phenomenon is called diffraction. In the IGCSE Edexcel Physics syllabus, understanding diffraction is essential for explaining wave behaviour and interpreting experiments involving slits and gratings. This article unpacks the key learning points, typical examination questions, and the reasoning skills required to master light diffraction.
光波和所有波一样，当遇到障碍物或狭窄缝隙时，并不会完全沿直线传播，而是会绕过边缘向外扩散，这种现象称为衍射。在IGCSE Edexcel物理课程中，理解衍射对于解释波动行为和分析与狭缝、光栅相关的实验至关重要。本文将系统梳理考试重点、常见题型以及需要掌握的推理方法，帮助你彻底攻克光的衍射。
1. What is Diffraction? | 什么是衍射？
Diffraction is the spreading out of waves when they pass through a gap or move around an obstacle. For light, this spreading is usually very small because light has extremely short wavelengths. However, when the gap is comparable to the wavelength of the light, the effect becomes noticeable and produces bright and dark fringes on a screen.
衍射是指波在穿过缝隙或绕过障碍物时发生的扩散现象。对于光来说，由于波长极短，扩散通常非常微弱。但当缝隙大小与光的波长相近时，衍射效应就会变得显著，并在屏幕上形成明暗相间的条纹。
2. Conditions for Noticeable Diffraction | 明显衍射的条件
The amount of diffraction depends on the relative size of the gap or obstacle compared to the wavelength. Significant diffraction occurs when the gap width is approximately equal to or smaller than the wavelength. For light, this means the slit must be extremely narrow — on the order of micrometres. If the gap is much wider than the wavelength, the wave passes through almost unchanged, with only slight bending at the edges.
衍射的明显程度取决于缝隙或障碍物的尺寸与波长的比值。当缝隙宽度接近或小于波长时，衍射会非常显著。对于光而言，这就要求缝隙极其狭窄，达到微米级别。如果缝隙远大于波长，光波几乎不发生弯曲，仅边缘有微弱弯曲。
3. Diffraction Through a Single Slit | 单缝衍射
When monochromatic light passes through a single narrow slit, a characteristic diffraction pattern appears on a screen. The pattern consists of a broad, bright central maximum, flanked by a series of narrower, less intense bright fringes (secondary maxima), separated by completely dark fringes (minima). The central fringe is twice as wide as the other fringes. The intensity decreases as you move away from the centre.
当单色光通过一个狭窄的单缝时，屏幕上会出现特有的衍射图样。该图样由一个宽阔明亮的中央亮纹（中央极大）和两侧一系列较窄、较暗的次级亮纹组成，亮纹之间是完全黑暗的暗纹（极小）。中央亮纹的宽度约为其他亮纹的两倍，并且强度从中心向外逐渐减弱。
- Central maximum is brightest and widest | 中央极大最亮且最宽
- Secondary maxima are symmetrically placed and dimmer | 次级极大对称分布，亮度递减
- Dark fringes occur where waves cancel destructively | 暗纹出现在波相消干涉处
Condition for minima: a sin θ = nλ, where n = ±1, ±2, …
暗纹条件：a sin θ = nλ，其中 n = ±1, ±2, …
4. The Effect of Slit Width on Diffraction | 缝宽对衍射的影响
Reducing the slit width causes the waves to spread out more, making the central maximum wider and the entire pattern more spread out. However, the intensity of the central maximum decreases because less light can pass through. Conversely, widening the slit reduces the spreading, making the fringes narrower and sharper, while the intensity increases. There is a trade-off between fringe width and brightness.
减小缝宽会使波扩散更明显，中央亮纹变得更宽，整个图样更加伸展，但由于通过的光能减少，中央亮纹的强度会下降。反之，增大缝宽会减弱扩散，使条纹变窄、更清晰，强度增大。亮纹宽度与亮度之间存在此消彼长的关系。
5. The Effect of Wavelength | 波长对衍射的影响
For a fixed slit width, longer wavelengths (e.g. red light) diffract more than shorter wavelengths (e.g. blue light). This means the fringes for red light are more widely spaced than for blue light. Diffraction patterns therefore directly demonstrate that red light has a longer wavelength than blue light, a fact often tested in IGCSE physics experiments using lasers or colour filters.
在缝宽固定的情况下，波长较长的光（如红光）比波长较短的光（如蓝光）衍射更显著。这意味着红光的条纹间距比蓝光的更大。衍射图样因此直接证明了红光的波长大于蓝光，这一知识点常通过使用激光或滤色片的实验在IGCSE物理考试中出现。
6. Diffraction Grating: An Extension | 衍射光栅（考点延伸）
cing very sharp, bright maxima at specific angles. The grating equation nλ = d sin θ links the wavelength λ, the grating spacing d, the diffraction angle θ, and the order of maximum n. For a fixed grating, measuring θ allows us to calculate the wavelength of the light.
衍射光栅由大量紧密排列的平行狭缝组成。当光通过时，来自相邻狭缝的波发生干涉，在特定角度产生非常锐利明亮的极大值。光栅方程 nλ = d sin θ 将波长 λ、光栅常数 d、衍射角 θ 和亮纹级数 n 联系在一起。对于已知光栅常数的光栅，通过测量 θ 即可计算出光的波长。
nλ = d sin θ
A typical IGCSE question may ask you to deduce which colour of light produces a larger angle for the same order. Since sin θ ∝ λ, red light always gives a larger θ than blue light for the same n and d.
典型的IGCSE题目可能会问：对于同一级次，哪一颜色的光会产生更大的衍射角。由于 sin θ 与 λ 成正比，在 n 和 d 相同的情况下，红光总是比蓝光产生更大的 θ。
7. White Light Diffraction | 白光的衍射
When a beam of white light is diffracted through a single slit or a diffraction grating, the bright central maximum remains white because all wavelengths overlap at the centre. However, the outer fringes show a continuous spectrum — red on the outside edge and violet on the inside — because different wavelengths are diffracted by different amounts. This separation of colours is a clear demonstration that white light is composed of a range of wavelengths.
当白光通过单缝或衍射光栅发生衍射时，中央亮纹仍为白色，因为所有波长的光在中心重叠。但是，两侧的亮纹会呈现出从内紫到外红的连续光谱，这是因为不同波长的光的衍射角不同。这种色散现象清楚表明白光是由多种波长的光复合而成。
8. Comparing Diffraction and Interference | 衍射与干涉的比较
| Aspect | 方面 | Diffraction | 衍射 | Interference | 干涉 |
|---|---|---|
| Cause | 成因 | Wave bending around obstacle or through a gap | 波遇障碍物或缝隙弯曲 | Superposition of two or more coherent wave trains | 两个或多个相干波列叠加 |
| Pattern | 图样 | Broad central maximum, dimmer secondary fringes | 宽阔中央亮纹，次级条纹较暗 | Equally spaced, equally bright fringes (Young's slits) | 等间距、等亮度的条纹（杨氏双缝） |
| Fringe spacing formula | 条纹间距公式 | Minima: a sin θ = nλ | 暗纹：a sin θ = nλ | Maxima: d sin θ = nλ | 亮纹：d sin θ = nλ |
It is crucial to not confuse single-slit diffraction with double-slit interference. Both produce patterns of light and dark, but their origins and distributions differ distinctly. Exam questions frequently test this comparison.
切勿混淆单缝衍射和双缝干涉。两者都产生明暗条纹，但其成因和分布特征截然不同。这是考试中常出现的比较类考点。
9. Applications of Diffraction | 衍射的实际应用
Diffraction plays a pivotal role in many technologies. In spectroscopy, diffraction gratings are used to separate light into its component wavelengths for identifying elements in stars or analysing chemical compositions. X-ray diffraction reveals the atomic structure of crystals. Even the resolving power of microscopes and telescopes is limited by diffraction — the Airy disk places a fundamental limit on how close two points can be and still be distinguished.
衍射在许多技术中发挥着关键作用。在光谱学中，衍射光栅用于将光分解为不同波长，以鉴定恒星中的元素或分析化学成分。X射线衍射则揭示了晶体的原子结构。哪怕是显微镜和望远镜的分辨本领，也受到衍射极限的制约——艾里斑决定了两个点能被分辨的最小距离。
10. Key Equations and Calculations | 关键公式与常见计算
distance from the centre to the first minimum and L is the distance from the slit to the screen. Combining yields a(x/L) ≈ λ, hence the width of the central fringe is 2x ≈ 2λL/a. Students are expected to use these relationships to determine either wavelength or slit width.
对于单缝衍射，第一暗纹的位置由 a sin θ = λ 给出。大多数IGCSE实验中角度很小，因此可近似 sin θ ≈ θ ≈ x/L，其中 x 为中央到第一暗纹的距离，L 为缝到屏的距离。代入可得 a(x/L) ≈ λ，因此中央亮纹宽度 2x ≈ 2λL/a。学生需要能够运用这些关系求出波长或缝宽。
Fringe width w = 2λL / a (for central maximum)
中央亮纹宽度 w = 2λL / a
ocal of the number of lines per millimetre, e.g. 300 lines/mm means d = 1/300 mm = 3.33 × 10⁻⁶ m. Ensure units are consistent when plugging numbers into the equation.
对于衍射光栅，最常见的计算是由测得的 θ 求 λ：λ = d sin θ / n。光栅常数 d 通常用每毫米线条数的倒数表示，例如 300 线/mm 意味着 d = 1/300 mm = 3.33 × 10⁻⁶ m。代入公式时需特别注意单位统一。
11. Common Exam Pitfalls | 常见考试误区
- Confusing slit width with wavelength effect: A narrower slit increases spreading, while a longer wavelength does the same — but they are two independent factors. Students often mix up the cause of wider fringes in a given scenario. | 混淆缝宽与波长的影响：缝变窄会增加扩散，而波长变长也会增加扩散——两者是独立的影响因素。许多学生在具体情景中会张冠李戴。
- Forgetting that white central maximum stays white: With a grating or single slit, the zero-order maximum for white light is always white, not coloured. Only higher-order spectra show dispersion. | 忘记中央亮纹保持白色：对于光栅或单缝，白光的零级极大永远是白色，只有高级次光谱才会出现色散。
- Misapplying the grating formula to single slits dark fringes of a single slit use a sin θ = nλ. Be alert to which apparatus is described. | 将光栅公式错误用于单缝：nλ = d sin θ 用于光栅的亮纹，单缝暗纹使用 a sin θ = nλ。务必根据器材选择正确公式。
- Ignoring the small-angle approximation ≈ x/L. Neglecting this simplification can lead to unnecessarily complicated calculations. | 忽视小角度近似：当 θ 很小时，sin θ ≈ θ ≈ x/L。不使用这一近似会让计算变得十分繁琐。
12. Summary Mind Map | 思维导图总结
| Core concept | 核心概念 | Wave spreading when passing through a gap or around an obstacle | 波通过缝隙或绕过障碍物的扩散 | ||
|---|---|---|---|
| Key factors | 关键因素 | Gap width a ≈ λ for strong diffraction | 缝宽 a ≈ λ 时衍射显著 | Longer λ → greater spreading | 波长越长，扩散越明显 | Smaller a → wider fringes | 缝越窄，条纹越宽 |
| Single slit pattern | 单缝图样 | Broad central maximum | 宽阔中央亮纹 | Dark fringes at a sin θ = nλ | 暗纹满足 a sin θ = nλ | Width of central max = 2λL/a | 中央亮纹宽度 2λL/a |
| Grating formula | 光栅方程 | nλ = d sin θ | nλ = d sin θ | Sharp bright maxima | 锐利明亮极大 | d = 1 / lines per metre | d = 1/每米线数 |
| White light | 白光 | Central fringe white | 中央条纹白色 | Outer fringes show spectra | 外侧为彩色光谱 | Red deviates most | 红光偏折最大 |
Knowing these relationships and patterns will enable you to tackle both descriptive and calculation questions confidently. Practise past paper questions, paying special attention to the command words 'explain', 'compare' and 'calculate', which guide the depth of your answer.
掌握以上关系和图样特征，你就能从容应对描述题和计算题。多做往年真题，尤其注意“explain”、“compare”、“calculate”这类指令词，它们决定了作答需达到的深度。
Published by TutorHao | IGCSE Edexcel Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图