📚 Diffraction of Light – CCEA A-Level Physics Exam Focus | 光的衍射 CCEA A-Level 物理考点精讲
Diffraction is a fundamental wave phenomenon that provides striking evidence for the wave nature of light. In the CCEA A-Level Physics specification, mastering diffraction means understanding how light spreads when it passes through a narrow slit or around an obstacle, and how a diffraction grating can be used to split light into its component wavelengths. This examination-focused guide will walk you through single-slit patterns, the grating equation, experimental methods, and the key comparison with double-slit interference, ensuring you are fully prepared for both calculation and descriptive questions.
衍射是证实光具有波动性的重要波动现象。在 CCEA A-Level 物理考纲中，掌握衍射意味着要理解光通过狭缝或绕过障碍物时如何扩展，以及如何使用衍射光栅将光分解为不同波长的成分。本考点精讲将带你梳理单缝图样、光栅方程、实验方法以及与双缝干涉的关键对比，确保你为计算题和描述题做好全面准备。
1. Understanding Diffraction | 理解衍射
Diffraction is the spreading of waves when they encounter an obstacle or pass through a gap. The amount of spreading depends on the size of the gap relative to the wavelength. When the gap width is comparable to the wavelength, significant diffraction occurs; if the gap is much larger than the wavelength, the waves pass through with only slight bending at the edges.
衍射是波遇到障碍物或通过缝隙时发生扩展的现象。扩展的程度取决于缝隙尺寸与波长的比值。当缝隙宽度与波长可比时，发生明显的衍射；如果缝隙远大于波长，波通过时仅在边缘发生轻微弯曲。
2. Huygens’ Principle and Diffraction | 惠更斯原理与衍射
Huygens’ principle states that every point on a wavefront acts as a source of secondary spherical wavelets. The new wavefront is the envelope of these wavelets. When a plane wavefront meets a narrow slit, only a few secondary sources are exposed; the wavelets spread out, producing a curved new wavefront, which explains the diffraction pattern observed.
惠更斯原理指出，波前上的每一点都可以视为发射次级球面子波的波源，新的波前是这些子波的包络面。当平面波前遇到窄缝时，只有少部分次级波源暴露出来，子波向外扩展形成弯曲的新波前，这解释了观察到的衍射图样。
3. Single Slit Diffraction – Pattern & Conditions | 单缝衍射 — 图样与条件
When monochromatic light passes through a single narrow slit of width a, a diffraction pattern is formed on a distant screen. The pattern consists of a bright central maximum that is twice as wide as the secondary maxima, flanked by alternating dark and bright fringes of decreasing intensity. The condition for destructive interference (dark fringes) is given by a sinθ = nλ, where n = ±1, ±2, ±3…, with n = 0 corresponding to the central maximum.
当单色光通过宽度为 a 的窄缝时，在远处屏幕上形成衍射图样。图样包含一个中央亮纹，其宽度约为次级亮纹的两倍，两侧交替分布亮度递减的暗纹和亮纹。暗纹条件（相消干涉）为 a sinθ = nλ，其中 n = ±1, ±2, ±3…，n = 0 对应中央明纹。
4. Intensity Distribution in Single Slit | 单缝衍射的强度分布
The central maximum contains the majority of the light energy. The first secondary maximum has only about 4.7% of the central peak intensity. The angular half-width of the central maximum is the angle from the centre to the first dark fringe, given by θ ≈ λ/a for small angles. In the small-angle approximation, the linear width of the central maximum on a screen at distance D is w ≈ 2λD / a.
中央亮纹集中了绝大部分光能量。第一级次极大的强度仅约为中央峰值的 4.7%。中央明纹的角半宽是从中心到第一暗纹的角度，对于小角度有 θ ≈ λ/a。在小角度近似下，距离为 D 的屏幕上中央明纹的线宽度为 w ≈ 2λD / a。
5. Diffraction Grating – Construction and Working | 衍射光栅 — 构造与原理
A diffraction grating consists of a large number of equally spaced parallel slits (or rulings). The distance between adjacent slits, d, is called the grating spacing. When monochromatic light falls on the grating, each slit acts as a source of diffracted waves. The waves from all slits interfere constructively in certain directions, producing bright maxima that are much sharper and more widely separated than those from a double slit.
衍射光栅由大量等间距的平行狭缝（或刻线）组成，相邻狭缝的距离 d 称为光栅常数。当单色光照射光栅时，每个狭缝都成为衍射波的波源。来自所有狭缝的波在某些方向上产生相长干涉，形成明亮且尖锐的条纹，这些条纹比双缝干涉条纹更清晰、间距更大。
6. The Grating Equation d sinθ = nλ | 光栅方程 d sinθ = nλ
For a transmission grating, the condition for a principal maximum is d sinθ = nλ, where d is the slit separation, θ is the angle of diffraction measured from the normal, n is the order number (0, 1, 2…), and λ is the wavelength. This equation can be derived from the path difference between adjacent slits, which must equal a whole number of wavelengths for constructive interference.
对于透射光栅，主极大条件为 d sinθ = nλ，其中 d 为狭缝间距，θ 为从法线量起的衍射角，n 为级数（0, 1, 2…），λ 为波长。该方程可由相邻狭缝的光程差推导得出，相长干涉要求光程差等于波长的整数倍。
7. Measuring Wavelength Using a Grating | 用光栅测量波长
A typical exam experiment involves using a spectrometer with a diffraction grating. The grating is placed perpendicular to the collimated beam, and the angles θ for the first-order (and possibly second-order) maxima on each side are measured. The wavelength is then calculated using λ = d sinθ / n. Measurements on both sides are averaged to reduce systematic error. Students must be able to state precautions such as ensuring the grating is normal to the incident beam and using a dark room for clearer viewing.
典型的考试实验涉及使用分光计和衍射光栅。将光栅垂直于准直光束放置，测量两侧一级（有时为二级）明纹的角度 θ，然后利用 λ = d sinθ / n 计算波长。取两侧测量结果的平均值可减小系统误差。学生需要能够说出注意事项，例如确保光栅垂直于入射光束、在暗室中操作以获得更清晰的观察效果。
8. Diffraction Grating vs. Double Slit | 衍射光栅与双缝干涉的比较
Although both produce interference patterns, a diffraction grating yields maxima that are significantly sharper (narrower) and brighter than those from a double slit. This is because many slits contribute, making the constructive interference condition very strict. In a double-slit setup, the maxima are broader and the intensity fades only gradually, while a grating’s maxima are well-separated narrow lines. This sharpness makes the grating ideal for precise wavelength measurements.
虽然两者都产生干涉图样，但衍射光栅产生的亮纹明显比双缝更尖锐（更窄）且更亮。这是因为众多狭缝的贡献使得相长干涉条件非常严格。在双缝装置中，亮纹较宽且强度逐渐衰减，而光栅的亮纹是分隔清晰的细线。这种尖锐特性使光栅成为精确测量波长的理想工具。
| Feature | Diffraction Grating | Double Slit |
|---|---|---|
| Maxima width | Very narrow (sharp) | Broad |
| Separation | Large angular separation | Smaller overlapping fringes |
| Intensity | High, concentrated | Lower, more spread out |
The table summarises the main differences. In CCEA exams, you may be asked to justify why a grating is preferred when determining an unknown wavelength with high precision.
上表总结了主要区别。在 CCEA 考试中，你可能会被要求说明为什么在需要高精度测定未知波长时优先选用光栅。
9. Diffraction Effects on Resolution | 衍射对分辨率的影响
Diffraction limits the ability of optical instruments to resolve two close objects. According to the Rayleigh criterion, two point sources are just resolved when the central maximum of one coincides with the first minimum of the other. For a circular aperture of diameter D, the minimum resolvable angle is approximately θ ≈ 1.22λ / D. This concept explains why telescopes need large apertures to distinguish fine details in astronomical observations.
衍射限制了光学仪器分辨两个靠近物体的能力。根据瑞利判据，当一个点源的中共极大恰好落在另一个点源的第一极小时，两个点源恰好能被分辨。对于直径为 D 的圆孔，最小可分辨角约为 θ ≈ 1.22λ / D。这一概念解释了为什么望远镜需要大孔径才能在天文观测中分辨精细结构。
10. Common Exam Questions and Tips | 常见考题与技巧
CCEA exam questions on diffraction often require you to: identify the diffraction pattern from a single slit, label the central maximum and first minimum, use the grating equation to calculate wavelength or slit spacing, and describe an experiment to determine wavelength using a grating and spectrometer. Pay careful attention to units: ensure d is in metres and angles are in degrees or radians as appropriate. Remember that n must be an integer; non-integer values do not correspond to principal maxima. When drawing graphs, show intensity versus angle with a tall central peak and much smaller secondary peaks.
CCEA 考试中关于衍射的题目通常要求：识别单缝衍射图样，标注中央明纹和第一暗纹；使用光栅方程计算波长或狭缝间距；描述利用光栅和分光计测定波长的实验。请特别注意单位：确保 d 以米为单位，角度按需要以度或弧度表示。记住 n 必须是整数，非整数值不对应主极大。画图时，要体现出强度随角度变化中突出的中央峰和极小的次级峰。
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