📚 Diffraction of Light | 光的衍射
Diffraction is a fundamental wave phenomenon observed when light passes through a narrow slit or around an obstacle, causing the light to spread out and form a characteristic pattern of bright and dark regions. This topic is a key part of the CCEA IGCSE Physics specification, linking the wave nature of light to practical observations and measurements.
衍射是光波通过窄缝或绕过障碍物时发生的一种基本波动现象，光会扩散并形成独特的明暗条纹图样。这是CCEA IGCSE物理大纲中的重点内容，将光的波动性与实际观察和测量紧密联系起来。
1. What is Diffraction? | 什么是衍射？
Diffraction is the spreading out of waves when they pass through a narrow gap or move around the edge of an obstacle. Unlike reflection or refraction, diffraction does not involve a change in medium; it occurs purely due to the wave nature of light. The amount of spreading is most noticeable when the size of the gap or obstacle is similar to the wavelength of the wave.
衍射是指波通过窄缝或绕过障碍物边缘时发生的扩散现象。与反射和折射不同，衍射不涉及介质变化，纯粹源于光的波动性。当缝隙或障碍物的尺寸与波长相当时，扩散效果最为明显。
2. Conditions for Noticeable Diffraction | 产生明显衍射的条件
For light diffraction to be easily observed, the width of the slit (or obstacle) must be very small – typically of the same order of magnitude as the light's wavelength, which is around 400–700 nm. If the slit is much wider than the wavelength, the wave passes through almost unchanged and the spreading is minimal. This explains why we do not normally see light bending around everyday objects; doors and windows are millions of times larger than the wavelength of light.
要清晰观察到光的衍射，狭缝（或障碍物）的宽度必须非常小，通常与光波长（约400–700 nm）处在同一数量级。如果狭缝远宽于波长，光几乎无变化地通过，扩散极不明显。这解释了为什么日常生活中我们看不到光绕过门框或窗户——它们的尺寸比光波长大数百万倍。
3. Single-Slit Diffraction: Experimental Setup | 单缝衍射实验装置
A typical classroom demonstration uses a monochromatic light source, such as a laser, directed at a single narrow slit. The slit is often created by two razor blades taped closely together or by a precision-manufactured single slit on a slide. A screen is placed several metres beyond the slit. When the laser beam passes through the slit, a diffraction pattern appears on the screen, consisting of a bright central region flanked by alternating dark and bright fringes.
典型的课堂演示使用单色光源（如激光）照射单个窄缝。通常用两片紧靠的剃须刀片或精密制作的单缝玻片来制造狭缝，在几米外放置屏幕。激光穿过狭缝后，屏幕上便出现由中央亮区和两侧交替明暗条纹组成的衍射图样。
4. The Single-Slit Diffraction Pattern | 单缝衍射图样
The pattern has a central bright fringe (central maximum) that is about twice as wide as the secondary bright fringes on either side. Moving away from the centre, the bright fringes become progressively dimmer. The dark fringes (minima) are points of complete destructive interference. A simplified diagram labels the central maximum, first-order dark fringe, first-order bright fringe, and so on.
图样中央有一道明亮的中央亮条纹（中央极大），其宽度约为两侧次级亮条纹的两倍。离中心越远，亮条纹逐渐变暗。暗条纹（极小值）是完全相消干涉的位置。简化的示意图会标出中央极大、第一级暗纹、第一级亮纹等。
Central maximum – the brightest and widest part of the pattern.
中央极大 – 图样中最亮、最宽的部分。
First-order dark fringes – located symmetrically on either side of the central maximum.
第一级暗纹 – 对称地分布在中央极大两侧。
Second-order bright fringes – dimmer than the first-order ones.
第二级亮纹 – 比第一级亮纹更暗。
5. Explaining the Pattern with Huygens' Principle | 用惠更斯原理解释图样
According to Huygens' principle, every point on a wavefront acts as a source of secondary spherical wavelets. When light reaches the slit, each point within the slit opening sends out wavelets. These wavelets overlap and interfere with each other. In some directions, they arrive in phase and produce constructive interference (bright fringes); in other directions, they arrive out of phase and cause destructive interference (dark fringes). The central bright fringe occurs where all wavelets travel the same distance and hence arrive in phase.
根据惠更斯原理，波前上的每一点都可视为次级球面子波的波源。当光到达狭缝时，缝内各点都发出子波。这些子波相互重叠并发生干涉。在某些方向上，它们同相到达，形成相长干涉（亮纹）；在另一些方向上，它们异相到达，形成相消干涉（暗纹）。中央亮纹出现在所有子波传播距离相等、因此同相到达的位置。
6. Effect of Slit Width on the Diffraction Pattern | 缝宽对衍射图样的影响
The width of the single slit, often denoted by w or a, directly affects the spacing and width of the fringes. As the slit becomes narrower, the central maximum spreads out more, and the angular separation between successive minima increases. If the slit is made wider, the central maximum becomes narrower and the whole pattern compresses towards the centre. This relationship can be summarised in a table.
单缝的宽度（常记作w或a）直接影响条纹的间距和宽度。缝越窄，中央极大铺展得越开，相邻极小值之间的角距离增大。缝越宽，中央极大变窄，整个图样向中心压缩。这一关系可用表格总结。
| Change in Slit Width | Effect on Pattern |
|---|---|
| Decrease slit width 减小缝宽 | Wider central maximum, greater fringe spacing 中央极大变宽，条纹间距增大 |
| Increase slit width 增大缝宽 | Narrower central maximum, reduced fringe spacing 中央极大变窄，条纹间距减小 |
7. Effect of Wavelength on the Diffraction Pattern | 波长对衍射图样的影响
ore compact pattern. The position of the first dark fringe is given approximately by the relationship:
光的波长λ也起着关键作用。对于同一缝宽，较长波长（如红光，λ ≈ 650 nm）产生的图样更发散，中央极大更宽，暗纹之间的角距离更大。较短波长（如蓝光，λ ≈ 450 nm）形成的图样更紧凑。第一暗纹的位置近似满足：
w sin θ = λ
where w w x / D, where x is the distance from the centre to the first dark fringe on the screen and D is the slit-to-screen distance.
其中 w 是缝宽，θ 是第一极小值偏离中心的角度。对于小角度，sin θ ≈ θ ≈ x/D，因此 λ ≈ w x / D，其中 x 是屏幕上第一暗纹到中心的距离，D 是缝到屏幕的距离。
8. White Light Diffraction through a Single Slit | 白光通过单缝的衍射
When a narrow slit is illuminated with white light, each component wavelength diffracts by a different amount. The central maximum remains white because all colours overlap there. On either side of the central white fringe, continuous spectra appear. In each spectrum, violet light (shorter wavelength) is diffracted less and appears closer to the centre, while red light (longer wavelength) is diffracted more and lies farther outward. The overlapping of spectra from different orders can cause colours to blend, but the distinct sequence from violet to red is always observed.
用白光照射窄缝时，每一种波长的单色光衍射程度不同。中央极大仍然呈白色，因为所有颜色在此重合。在中央白色条纹两侧，出现连续光谱。在每个光谱中，紫光（波长较短）衍射角度较小，出现在靠近中心的位置；红光（波长较长）衍射角度较大，分布在更外侧。不同级次光谱的重叠会导致颜色混合，但总能观察到从紫到红的清晰序列。
9. Diffraction around Obstacles | 绕过障碍物的衍射
Light does not only diffract when passing through a gap; it also bends around the edges of obstacles. For example, a laser beam directed at the sharp edge of a razor blade will produce faint bright and dark fringes in the geometric shadow region of the blade. This occurs because the edge acts as a secondary source of wavelets that bend into the shadow. Small particles, such as dust or water droplets in the air, can also produce diffraction patterns known as coronae or glory effects around the Sun or Moon.
光不仅通过缝隙时会发生衍射，遇到障碍物边缘时也会弯曲。例如，激光照射到剃须刀片的锋利边缘时，在几何阴影区域内会产生微弱的明暗条纹。这是因为边缘充当了次级子波源，使光弯曲进入阴影区。空气中的微小颗粒（如尘埃或水滴）也能产生衍射图样，如日华或月华（日冕或月冕现象）。
10. Introduction to the Diffraction Grating | 衍射光栅简介
A diffraction grating consists of a large number of equally spaced, parallel slits. When monochromatic light passes through a grating, it produces a pattern of very sharp and well-separated bright maxima. The positions of these maxima are given by the grating equation:
衍射光栅由大量等间距的平行狭缝组成。当单色光通过光栅时，会产生非常尖锐且分得很开的亮条纹（极大值）。这些极大值的位置由光栅方程给出：
d sin θ = nλ
where d grating spacing), θ is the angle of the nth-order maximum, n is the order number (0, 1, 2, … e, and higher orders appear symmetrically on either side. Because the maxima are narrow and bright, the grating is an excellent tool for measuring light wavelengths precisely.
其中 d 是相邻狭缝的间距（光栅常数），θ 是第 n 级极大的衍射角，n 是级数（0, 1, 2, …），λ 是波长。零级（n=0）是中央亮线，更高级的亮线对称分布在两侧。由于极大值又窄又亮，光栅成为精确测量光波长的极佳工具。
11. Key Equations and Calculations | 关键公式与计算
In CCEA IGCSE Physics, you are expected to use the grating equation d sin θ = nλ light (λ = 6.5 × 10⁻⁷ m), sin θ = (1 × 6.5 × 10⁻⁷) / (3.33 × 10⁻⁶) = 0.195, so θ ≈ 11.2°.
在CCEA IGCSE物理中，你需要运用光栅方程 d sin θ = nλ 进行未知量的计算。还可能要求你根据每毫米的刻线数确定光栅常数，关系为 d = 1/N，其中 N 是单位长度的线数。例如，一个每毫米300线的光栅，d = 1/300 mm = 3.33 × 10⁻⁶ m。对于红光（λ = 6.5 × 10⁻⁷ m）的第一级极大（n=1），sin θ = (1 × 6.5 × 10⁻⁷) / (3.33 × 10⁻⁶) = 0.195，故 θ ≈ 11.2°。
12. Comparison: Diffraction and Interference | 对比：衍射与干涉
Diffraction and interference are both manifestations of the wave nature of light, but they are distinct phenomena. Diffraction refers to the bending of waves around obstacles or through slits, leading to a characteristic pattern due to the superposition of wavelets from the same wavefront. Interference, on the other hand, typically refers to the superposition of waves from two or more distinct coherent sources, such as in Young's double-slit experiment. The table below highlights the key differences.
衍射和干涉都是光波动性的表现，但它们是不同的现象。衍射指波绕过障碍物或穿过缝隙时的弯曲，由同一波前上各子波的叠加形成特征图样；而干涉通常指来自两个或多个不同相干光源（如杨氏双缝实验）的波的叠加。下表总结了主要区别。
| Aspect | Diffraction | Interference |
|---|---|---|
| Caused by 起因 | Single wavefront encountering a gap or obstacle 单一波前遇到缝隙或障碍物 | Superposition of waves from two (or more) separate coherent sources 来自两个（或多个）独立相干源的波叠加 |
| Typical setup 典型装置 | Single slit or sharp edge 单缝或锋利边缘 | Double slit (Young's experiment) 双缝（杨氏实验） |
| Fringe width 条纹宽度 | Central fringe widest; intensity falls off rapidly 中央条纹最宽；强度迅速衰减 | All bright fringes ideally of equal intensity and spacing (with narrow slits) 理想情况下所有亮条纹强度相等且等间距（窄缝时） |
| Key equation 关键方程 | w sin θ = nλ (for minima) w sin θ = nλ（极小值） | d sin θ = nλ (for maxima in double slit at small angles) d sin θ = nλ（双缝中极大值，小角度下） |
13. Applications of Diffraction | 衍射的应用
Diffraction has numerous real-world applications. Diffraction gratings are used in spectrometers to analyse the composition of light from stars, flames, and chemical samples. The iridescent colours on a CD or DVD surface are due to the diffraction of white light by the closely spaced tracks. In medicine, X-ray diffraction is used to determine crystal structures, though that is beyond the IGCSE scope. Understanding diffraction also helps in the design of microscopes and telescopes to minimise the blurring caused by diffraction at apertures.
衍射有众多实际应用。衍射光栅用于光谱仪中，分析来自恒星、火焰和化学样品的光的组成。CD或DVD表面的虹彩颜色就是由密集轨道对白光的衍射产生的。在医学领域，X射线衍射用于确定晶体结构（不过这超出了IGCSE范围）。理解衍射还有助于设计显微镜和望远镜，以减小孔径衍射造成的图像模糊。
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