Diffraction of Waves: Phenomena and Conditions Explained | 波的衍射现象与条件详解

📚 Diffraction of Waves: Phenomena and Conditions Explained | 波的衍射现象与条件详解

Diffraction is one of the most characteristic properties of waves. It describes the way waves spread out when they pass through a gap or around an obstacle, and it helps distinguish wave behaviour from simple particle behaviour.

衍射是波动最典型的性质之一。它描述的是波通过狭缝或绕过障碍物时发生的展宽现象，也有助于区分波动行为与简单的粒子行为。

In Cambridge CIE A-Level Physics, diffraction is examined for water waves, sound waves and light waves. You need to understand not only what diffraction looks like, but also the precise condition that makes diffraction obvious: the size of the gap or obstacle must be comparable to the wavelength.

在剑桥 CIE A-Level 物理考试中，水波、声波和光波的衍射都会被考查。你不仅需要了解衍射的特征，更需掌握使衍射变得明显的精确条件：狭缝或障碍物的尺寸必须与波长相当。

1. What Is Diffraction? | 什么是衍射？

Diffraction is the bending and spreading of waves as they pass through an aperture or around the edge of an obstacle. The wavefront is no longer a straight line or a simple circular arc; instead, it extends into the region that would otherwise be in the geometric shadow.

衍射是波通过孔隙或绕过障碍物边缘时发生的弯曲和展宽现象。波前不再是一条直线或简单的圆弧，而是扩展到原本会处于几何阴影的区域。

For example, plane water waves passing through a narrow gap emerge as circular waves centred on the gap. This spreading is diffraction, not reflection or refraction.

例如，平面水波通过一个狭窄的缺口后，会变成以缺口为中心的弧形波向外扩展。这种展宽就是衍射，而不是反射或折射。

Diffraction occurs for all types of waves, including mechanical waves such as sound and water waves, and electromagnetic waves such as light.

所有类型的波都会发生衍射，包括声波、水波等机械波，以及光这样的电磁波。

2. The Huygens Principle and Diffraction | 惠更斯原理与衍射

The Huygens principle states that every point on a wavefront can be considered as a source of secondary wavelets. The new wavefront is the envelope of these wavelets after a small time interval.

惠更斯原理指出，波前上的每一点都可以视为产生次级子波的点波源。经过一小段时间后，这些子波的包络面就是新的波前。

When a wave encounters a gap, only the unobstructed points on the wavefront act as secondary sources. These secondary wavelets spread into the shadow region, producing the observed diffraction pattern.

当波遇到障碍物或缝隙时，只有未被遮挡的波前点能发出次级子波。这些子波向阴影区域传播，从而形成观察到的衍射图样。

Huygens’ construction explains why the amount of spreading depends on the size of the gap relative to the wavelength. A narrow gap limits the wavefront to a small number of sources, so the wavelets spread through a large angle.

惠更斯作图法解释了为什么衍射程度取决于缝隙尺寸与波长的相对大小。窄缝只保留少数波前点作为子波源，因此子波会以较大角度向外扩展。

3. Conditions for Significant Diffraction | 明显衍射的条件

For diffraction to be significant, the size of the gap or obstacle must be of the same order as the wavelength of the wave.

要使衍射明显，缝隙或障碍物的尺寸必须与波的波长处于同一数量级。

Use this rule: if the gap width a is much greater than the wavelength λ, the wave passes through almost without spreading, and a sharp shadow is formed.

判断规则是：如果缝宽 a 远大于波长 λ，波几乎不发生展宽地穿过，会形成清晰的阴影。

If a is comparable to λ, diffraction is strong and the wave spreads widely into the geometric shadow.

如果 a 与 λ 相差不多，衍射很强，波会明显扩展到几何阴影区域内。

If a is much smaller than λ, diffraction also occurs and the gap acts almost like a point source, but the transmitted intensity may become very small.

如果 a 远小于 λ，衍射同样会发生，缝隙几乎像一个点波源，但透射强度可能会变得非常小。

a ≈ λ → significant diffraction

a ≈ λ → 明显衍射

This condition explains everyday observations: sound diffracts around doorways because sound wavelengths are around 0.1 m to 1 m, similar to a door width. Light waves have wavelengths around 500 nm, so ordinary doorways are far too wide to produce noticeable diffraction.

这一条件解释了日常现象：声音能绕过门口衍射，因为声波波长约为 0.1 m 到 1 m，与门宽相近。光波的波长约为 500 nm，因此普通门缝远大于波长，难以产生明显衍射。

4. Diffraction of Water Waves | 水波的衍射

Water waves are often used in the laboratory to investigate diffraction using a ripple tank. A straight wavefront is directed at a barrier with a gap, and the wave pattern is observed on a screen or with a stroboscope.

水波通常用波动槽（ripple tank）在实验室中研究衍射。让直线波前射向带缺口的障碍物，并观察所形成的水波图样。

When the gap is wide compared with the wavelength, the waves beyond the gap remain almost straight, with only slight bending at the edges.

当缝隙宽度远大于波长时，缝隙后方的波仍近似为直线，只在边缘有轻微弯曲。

When the gap is narrowed until it is approximately equal to the wavelength, the transmitted waves spread out as circular waves with a large angle of diffraction.

当缝隙减小到与波长差不多时，透过的波会以较大衍射角扩展为近似圆弧形波。

Diffraction also occurs around obstacles. A small obstacle, such as a post in a ripple tank, casts a surprisingly small “shadow” because waves bend around it and meet behind it.

障碍物周围也会发生衍射。例如，波动槽中的一根小柱子产生的“阴影”很小，因为波会绕过柱子并在其后重新汇合。

5. Diffraction of Sound Waves | 声波的衍射

Sound waves have relatively long wavelengths, so audible sound is strongly diffracted by everyday objects such as doors, pillars and building corners.

声波的波长较长，因此可听见的声音很容易被门、柱子、建筑拐角等日常物体强烈衍射。

At 20 °C, the speed of sound in air is about 340 m s⁻¹. A sound wave of frequency 1000 Hz has a wavelength of about 0.34 m.

在 20 °C 时，空气中的声速约为 340 m s⁻¹。频率为 1000 Hz 的声波波长约为 0.34 m。

λ = v / f = 340 / 1000 = 0.34 m

This is why you can hear someone speaking even when you cannot see them, because sound bends around a doorway or the corner of a building.

这就是为什么即使看不见说话的人，你也能听到声音，因为声波会绕过门口或建筑拐角发生衍射。

Low-frequency sounds diffract more than high-frequency sounds because their wavelengths are longer. That is why bass notes from a band are heard more easily from behind a wall than high-pitched notes.

低频声波比高频声波衍射更明显，因为低频声波的波长更长。这就是为什么在墙后更容易听到乐队的低音而不是高音。

6. Diffraction of Light Waves | 光的衍射

Light waves have very short wavelengths, roughly 400–700 nm. To observe significant diffraction of light, the aperture must be extremely narrow, comparable to the wavelength of light.

光波的波长非常短，约为 400–700 nm。要观察到明显的光衍射，狭缝必须极窄，与光波长相当。

When light passes through a narrow single slit, it spreads out into a pattern of bright and dark fringes on a distant screen. This is called a single-slit diffraction pattern.

当光通过窄单缝时，会在远处的屏幕上形成明暗相间的条纹图样，这称为单缝衍射图样。

The central bright fringe is the brightest and about twice as wide as the other bright fringes. The intensity decreases rapidly for fringes further from the centre.

中央亮纹最亮，宽度约为其他亮纹的两倍。离中心越远的亮纹，光强衰减越快。

Diffraction of light limits the resolution of optical instruments. In a telescope, light passing through the circular objective aperture is diffracted, producing a central Airy disc rather than a perfect point image.

光的衍射限制了光学仪器的分辨能力。在望远镜中，光通过圆形物镜孔径时发生衍射，形成中央艾里斑，而不是理想的点像。

7. Single-Slit Diffraction Pattern | 单缝衍射图样

Consider a single slit of width a illuminated by monochromatic light of wavelength λ. The resulting intensity pattern on a screen far away shows a central maximum and alternating minima and secondary maxima.

考虑宽度为 a 的单缝被波长为 λ 的单色光照亮。远处屏幕上形成的强度图样包括一个中央极大、交替出现的暗纹和次级极大。

The condition for dark fringes in single-slit diffraction is given by:

单缝衍射暗纹的条件为：

a sin θ = n λ, where n = 1, 2, 3, …

a sin θ = n λ，其中 n = 1, 2, 3, …

Here θ is the angle between the direction of the incident wave and the direction of the diffracted wave. The first dark fringe occurs at n = 1.

这里 θ 是入射波方向与衍射方向之间的夹角。第一暗纹对应于 n = 1。

The angular width of the central maximum is twice the angle of the first minimum. A narrower slit produces a broader central maximum, but the overall intensity is lower.

中央极大的角宽度等于第一暗纹角度的两倍。狭缝越窄，中央亮纹越宽，但总的光强更弱。

For the diffraction pattern to be clearly observed, the slit width should be small enough so that the central maximum spreads over a measurable angle.

要清晰观察衍射图样，缝宽应足够小，使中央极大能扩展到可测量的角度范围。

8. Diffraction Grating | 衍射光栅

A diffraction grating consists of many equally spaced parallel slits. When monochromatic light passes through a grating, the diffracted waves from all slits interfere constructively at specific angles.

衍射光栅由许多等间距的平行狭缝组成。当单色光通过光栅时，来自所有狭缝的衍射波会在特定角度上发生相长干涉。

The grating equation for constructive interference is:

光栅方程的相长干涉条件为：

d sin θ = n λ, where n = 0, 1, 2, 3, …

d sin θ = n λ，其中 n = 0, 1, 2, 3, …

Here d is the grating spacing, θ is the angle of the diffracted beam from the normal, n is the order of the maximum, and λ is the wavelength.

其中 d 是光栅常数（相邻缝间距），θ 是衍射光束与法线的夹角，n 是极大级数，λ 是波长。

The grating spacing d is related to the number of lines per metre N by:

光栅常数 d 与每米刻线数 N 的关系为：

d = 1 / N

A grating produces very sharp, bright maxima because the interference involves thousands of slits. This makes the grating very useful for measuring wavelengths of light precisely.

光栅包含数千条狭缝，因此产生的极大非常尖锐明亮。这使光栅非常适用于精确测量光的波长。

Since different wavelengths have different angles for the same order, a grating can separate white light into a spectrum, with blue light diffracted less than red light.

因为不同波长在同一级数下的衍射角不同，光栅可以把白光分离成光谱，蓝光衍射角小于红光。

9. Applications and Exam Tips | 应用与考试要点

Diffraction is not just a classroom phenomenon. Radio waves diffract around hills and buildings, which is why AM radio can often be received in areas without a direct line of sight to the transmitter.

衍射不只是课堂现象。无线电波会绕过高山和建筑物衍射，这就是为什么中波广播在没有直射路径的地方也能被接收到。

Ultrasound imaging uses the reflection and diffraction of high-frequency sound waves to build images of internal body structures.

超声成像利用高频声波的反射和衍射来构建体内结构的图像。

For CIE exam questions, always compare the wavelength with the aperture size. State clearly that significant diffraction requires the gap width to be comparable to the wavelength.

应对 CIE 考题时，务必比较波长与孔径尺寸。要明确指出：明显衍射要求缝宽与波长相当。

When describing diffraction patterns, use the terms “central maximum”, “minima”, and “intensity” precisely. Avoid saying that diffraction is “bending of light” without explaining the size condition.

在描述衍射图样时，要准确使用“中央极大”“暗纹”“强度”等术语。避免只说光“弯曲”而不解释尺寸条件。

Remember that waves diffract around obstacles as well as through gaps. The obstacle size must also be comparable to the wavelength.

请记住，波在障碍物周围和通过缝隙时都会发生衍射，且障碍物尺寸也必须与波长相当。

10. Common Misconceptions | 常见误区

Misconception 1: Diffraction only occurs for light. In fact, all waves diffract, including sound, water, seismic waves and matter waves.

误区一：只有光才会发生衍射。事实上，所有波都会衍射，包括声波、水波、地震波和物质波。

Misconception 2: A narrow slit always makes a wider diffraction pattern. Yes, the angular spread becomes larger, but the transmitted intensity becomes smaller, so the pattern may become too faint to see.

误区二：缝越窄，衍射图样一定越清晰。确实角展宽会增大，但透射强度变小，图样可能过暗而难以观察。

Misconception 3: In single-slit diffraction, the bright fringes have equal intensity. In fact, the central maximum is much brighter than the secondary maxima, whose intensity falls rapidly with distance from the centre.

误区三：单缝衍射中所有亮纹强度相等。事实上，中央极大远亮于次级极大，次级极大的强度随离中心距离增大而迅速下降。

Misconception 4: Diffraction and interference are completely different phenomena. They are closely related: diffraction arises from the interference of secondary wavelets from different parts of the same wavefront.

误区四：衍射和干涉是完全不同的现象。二者密切相关：衍射源于同一波前不同部分发射的子波之间的干涉。

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Diffraction of Waves: Phenomena and Conditions Explained | 波的衍射现象与条件详解