📚 Interference, Diffraction and Polarisation | 干涉、衍射与偏振
Waves are everywhere in physics, and their behaviour reveals the most fundamental properties of light. Three wave phenomena — interference, diffraction and polarisation — are central to the IB Physics syllabus and are repeatedly tested in both Paper 1 and Paper 2. This article explains each concept clearly, with the mathematics you need, and contrasts them to help you avoid common confusions.
波在物理中无处不在，而波的行为揭示了光最基本的性质。干涉、衍射和偏振这三种波动现象是IB物理课程的核心内容，也常在Paper 1和Paper 2中反复考查。本文将清晰讲解每个概念及其所需数学，并通过对比帮助你避免常见混淆。
1. The Wave Nature of Light | 光的波动性
Light was long debated as either a particle or a wave. In the 19th century, Thomas Young's interference experiment and later Fresnel's diffraction studies provided convincing evidence that light behaves as a transverse wave. Later, Maxwell showed that light is an electromagnetic wave with mutually perpendicular electric and magnetic fields oscillating in phase.
光究竟是粒子还是波，曾长期争论不休。19世纪，托马斯·杨的干涉实验和后来菲涅耳的衍射研究为光是一种横波提供了有力证据。后来，麦克斯韦证明光是一种电磁波，其电场和磁场相互垂直并同相振荡。
For IB, you need to remember that visible light has wavelengths roughly between 400 nm (violet) and 700 nm (red). The wave model explains reflection, refraction, interference, diffraction and polarisation, while the particle model is needed for the photoelectric effect. Understanding which model applies in which situation is a key exam skill.
在IB课程中，你需要记住可见光波长大约在400纳米（紫光）到700纳米（红光）之间。波动模型可以解释反射、折射、干涉、衍射和偏振，而粒子模型则用于解释光电效应。理解在什么情境下使用哪种模型，是关键的考试技能。
2. The Principle of Superposition | 叠加原理
When two or more waves overlap in space, the resultant displacement at any point is the vector sum of the individual displacements. This is the principle of superposition. Mathematically, if two waves have displacements y₁ and y₂ at the same point, the resultant is:
当两列或多列波在空间重叠时，任意一点的合位移等于各列波位移的矢量和。这就是叠加原理。数学上，若两列波在同一点的位移分别为y₁和y₂，则合位移为：
y = y₁ + y₂
Superposition leads to two important effects: constructive interference occurs when waves arrive in phase, producing maximum amplitude; destructive interference occurs when waves arrive in anti-phase (phase difference of 180° or π radians), producing minimum amplitude. For coherent sources, the phase difference remains constant over time.
叠加产生两种重要效应：当两列波同相到达时发生相长干涉，振幅最大；当两列波反相（相位差为180°或π弧度）到达时发生相消干涉，振幅最小。对于相干波源，相位差随时间保持恒定。
3. Interference: Conditions and Path Difference | 干涉：条件与光程差
For observable interference, the wave sources must be coherent — they must have the same frequency and a constant phase difference. In practice, coherent sources are produced by splitting a single wave into two paths, for example in Young's double-slit experiment. The path difference is the extra distance one wave travels compared to the other.
要观察到稳定的干涉，波源必须相干，即频率相同且相位差恒定。实际中相干波源通常是通过将同一波分成两路得到的，例如杨氏双缝实验。光程差是指其中一列波比另一列波多传播的距离。
For constructive interference, the path difference equals an integer multiple of the wavelength:
相长干涉要求光程差等于波长的整数倍：
ΔL = nλ (n = 0, 1, 2, …)
For destructive interference, the path difference equals a half-integer multiple of the wavelength:
相消干涉要求光程差等于波长的半整数倍：
ΔL = (n + ½)λ (n = 0, 1, 2, …)
π)λ. In exams, always check whether the two waves start in phase or not, especially for reflection-induced phase changes.
如果波源之间存在初始相位差φ₀，则条件变为ΔL = (φ₀/2π)λ。在考试中，务必检查两列波是否从同相开始，特别要注意反射引起的相位突变。
4. Young's Double-Slit Experiment | 杨氏双缝实验
In Young's experiment, monochromatic light passes through two narrow slits separated by distance d, and the interference pattern is observed on a screen a distance D away. The bright fringes occur at angles satisfying:
在杨氏实验中，单色光通过间距为d的两条窄缝，在距离D远的屏上观察干涉图样。明纹出现在满足以下条件的角度：
d sin θ = nλ
where θ is the angle of the nth-order fringe measured from the central maximum. For small angles, the fringe separation Δy (distance between adjacent bright fringes) is given by:
其中θ是第n级明纹相对于中央最大亮纹的角度。对于小角度，相邻明纹间距Δy为：
Δy = (λD) / d
This equation is extremely important. It shows that increasing the slit separation d decreases the fringe spacing; increasing the wavelength λ or the screen distance D increases it. The fringes are equally spaced, which distinguishes double-slit interference from single-slit diffraction.
这个公式极为重要。它表明增大缝间距d会减小条纹间距；增大波长λ或屏距D会增大条纹间距。双缝干涉条纹等间距，这与单缝衍射条纹不同。
In IB experiments, you might use a laser as a coherent light source. The pattern consists of a series of bright and dark lines of similar width. Ensure you understand how to calculate λ from measured values of d, D and Δy, including uncertainties.
在IB实验中，通常使用激光作为相干光源。干涉图样由一系列宽度相近的明暗条纹组成。确保你理解如何利用测得的d、D和Δy计算λ并处理不确定度。
5. Diffraction: Bending of Waves | 衍射：波的弯曲
Diffraction is the spreading of waves when they pass through a gap or around an obstacle. The amount of spreading depends on the ratio of the wavelength λ to the gap width a. When λ is comparable to or larger than a, diffraction is significant. If the gap is much wider than λ, the wave passes through with little spreading.
衍射是波通过狭缝或绕过障碍物时发生的展宽现象。衍射程度取决于波长λ与缝宽a的比值。当λ与a相差不多或更大时，衍射显著；若缝宽远大于λ，则波几乎不发生展宽地通过。
Diffraction explains why we can hear sound around corners but cannot see light around corners. Sound waves have wavelengths of the order of metres, comparable to door openings, while light wavelengths are sub-micrometres, much smaller than typical obstacles.
衍射解释了为什么我们能听到拐角处的声音却看不到拐角处的光。声波波长在米量级，与门洞尺寸相当；而光波波长在亚微米量级，远小于日常障碍物。
For IB, the key is Huygens' principle: every point on a wavefront acts as a secondary source of spherical wavelets. The new wavefront is the envelope of these wavelets. This idea explains both diffraction and refraction.
IB课程的关键是惠更斯原理：波前上的每一点都可以看作发出球面子波的新波源，新的波前是这些子波的包络。这个原理既解释衍射也解释折射。
6. Single-Slit Diffraction | 单缝衍射
When monochromatic light passes through a narrow slit of width a, the intensity pattern on a distant screen has a central bright maximum, which is twice as wide as the subsidiary maxima, and much brighter. The first dark fringe occurs when the path difference between light from the two edges equals one wavelength:
当单色光通过宽度为a的窄缝时，远处屏上的强度图样中央是一个明亮的中央极大，其宽度是次级极大的两倍，且亮度远高。第一暗纹出现在来自缝两边缘的光程差等于一个波长时：
a sin θ = mλ (for dark fringes, m = 1, 2, 3, …)
rapidly away from the centre. You should be able to sketch this pattern and label the minima positions.
中央极大的角宽度为2θ₁，其中θ₁满足a sin θ₁ = λ。强度随离中心距离增大而迅速减小。你应该能够画出这个图样并标出各级暗纹位置。
If the slit is very wide compared to λ, the diffraction pattern is barely visible, and geometrical optics is a good approximation. As the slit width decreases, the central maximum spreads out more. If you reduce the wavelength, the pattern becomes narrower.
若缝宽远大于λ，衍射图样几乎不可见，几何光学近似成立。随着缝宽减小，中央极大变得更宽。若减小波长，衍射图样会变窄。
7. Diffraction Grating | 衍射光栅
A diffraction grating consists of many equally spaced parallel slits. The sharp bright maxima occur at angles satisfying:
衍射光栅由许多等间距平行狭缝组成。尖锐的明纹出现在满足以下条件的角度：
d sin θ = nλ (n = 0, 1, 2, …)
eger n is the order of the maximum. The maximum order is limited by sin θ ≤ 1, so n ≤ d/λ.
其中d是光栅常数（相邻狭缝间距），通常给出每毫米线数N，则d = 1/N（单位毫米，需换算为米）。整数n为极大级次。最大级次受sin θ ≤ 1限制，因此n ≤ d/λ。
The main difference in the pattern compared to double-slit interference is that the grating maxima are much sharper and brighter because of the large number of superposing beams. Between the principal maxima there are many weak secondary maxima, but these are often too faint to observe.
与双缝干涉图样相比，光栅图样的最主要区别是主极大更锐利、更明亮，这是因为大量光束叠加。主极大之间有许多微弱的次级极大，但通常太弱难以观察到。
Diffraction gratings are used in spectrometers to measure wavelengths of light. When white light passes through a grating, each order becomes a continuous spectrum, with violet closest to the central maximum and red furthest away.
衍射光栅被用于光谱仪测量光波长。当白光通过光栅时，每一级都形成连续光谱，紫光最靠近中央极大，红光离得最远。
8. Polarisation: Transverse Wave Evidence | 偏振：横波的证据
Polarisation is the restriction of oscillations of a transverse wave to a single plane. Longitudinal waves cannot be polarised because their oscillations are along the direction of propagation. Therefore, demonstrating that light can be polarised proves that light is a transverse wave.
偏振是将横波的振动限制在单一平面内的现象。纵波不能发生偏振，因为其振动方向沿传播方向。因此，证明光可以被偏振，就证明了光是横波。
Unpolarised light consists of electric field vectors oscillating in all directions perpendicular to the direction of propagation. A polarising filter transmits only the component of the electric field parallel to its transmission axis. If the transmission axis is vertical, only vertically polarised light passes through.
非偏振光的电场矢量在垂直于传播方向的所有方向上都振动。偏振滤光片只透射与其透振方向平行的电场分量。如果透振方向竖直，则只有竖直偏振的光能通过。
When two polarising filters are crossed (their transmission axes at 90°), no light passes through because the first filter produces polarised light, and the second filter blocks it. The intensity of light transmitted through a polariser at angle θ to its axis is given by Malus's law:
当两个偏振片正交放置（透振方向成90°）时，没有光透过，因为第一个偏振片产生偏振光，第二个偏振片将其阻挡。透过透振方向与偏振方向成θ角的偏振片的强度由马吕斯定律给出：
I = I₀ cos²θ
where I₀ is the intensity of the incident polarised light. If unpolarised light of intensity I₀ passes through a single polariser, the transmitted intensity is I₀/2, because only one component remains.
其中I₀是入射偏振光的强度。如果强度为I₀的非偏振光通过单个偏振片，透射强度为I₀/2，因为只剩一个分量。
9. Applications of Polarisation | 偏振的应用
Polarisation has many practical uses. In photography, polarising filters reduce glare from reflective surfaces such as water or glass, because reflected light is often partially polarised in a horizontal direction. Rotating the filter can block this glare.
偏振有许多实际应用。摄影中，偏振滤光片可以减少水面或玻璃等反射表面的眩光，因为反射光通常是水平方向部分偏振的。旋转滤光片可以阻挡这种眩光。
In liquid crystal displays (LCDs), two crossed polarisers with a liquid crystal layer rotate the plane of polarisation to control brightness. Sunglasses with polarising lenses reduce horizontal glare from roads and water, improving visibility and reducing eye strain.
液晶显示器（LCD）中，两个正交偏振片之间夹一层液晶，通过旋转偏振面来控制亮度。偏光太阳镜能减少路面和水面的水平眩光，提高能见度并减轻眼睛疲劳。
In chemistry and astronomy, optical activity and polarised light from stars are studied. Car headlights and sun glare are minimised using polarising filters. Also, 3D cinema uses two images polarised at right angles, and glasses with corresponding polarisers separate them for each eye.
在化学和天文学中，会研究旋光性和恒星发出的偏振光。车灯和太阳眩光也使用偏振滤光片来减弱。此外，3D影院使用两幅偏振方向互相垂直的图像，而观众的眼镜上装有对应的偏振片，从而为每只眼睛分离图像。
10. Comparing Interference, Diffraction and Polarisation | 三者比较
Interference and diffraction both arise from the superposition of waves, but they are often treated separately. Interference specifically involves the superposition of waves from a small number of coherent sources (two slits or two sources). Diffraction involves the superposition of an infinite number of secondary wavelets from a continuous aperture or obstacle.
干涉和衍射都源于波的叠加，但通常分开讨论。干涉特指来自少数相干波源（双缝或双源）的波叠加；衍射涉及来自连续孔径或障碍物的无数子波的叠加。
Polarisation is fundamentally different: it is a property of transverse waves only, describing the direction of oscillation. It does not require superposition, although interference and diffraction of polarised light can be observed.
偏振则根本不同：它是横波特有的性质，描述振动方向。它不依赖叠加原理，尽管偏振光也可以发生干涉和衍射。
| Phenomenon | Cause | Evidence |
| Interference | Coherent sources overlap | Light as a wave |
| Diffraction | Wave spreading at edges | Wave theory of light |
| Polarisation | Transverse oscillation orientation | Light is transverse |
Remember: interference and diffraction require path differences and produce spatial patterns of intensity. Polarisation changes intensity based on angle, and can be used to identify whether a wave is transverse or longitudinal.
请记住：干涉和衍射需要光程差并产生空间强度图样；偏振根据角度改变强度，可用于判断波是横波还是纵波。
11. Common Exam Pitfalls | 常见考试误区
ximum in single-slit diffraction is twice as wide as the other maxima, but in double-slit interference all bright fringes are equally spaced.
许多学生混淆双缝干涉和单缝衍射的公式。双缝干涉中，d sin θ = nλ对应明纹；单缝衍射中，a sin θ = mλ对应暗纹（m ≥ 1）。此外，单缝衍射中央极大宽度是其他极大的两倍，而双缝干涉所有明纹等间距。
hat polarisation only applies to transverse waves. Sound cannot be polarised, but light can. Also, Malus' ght that is already polarised. For unpolarised light passing through a single ideal polariser, the intensity is halved, not reduced by cos²θ.
另一个常见错误是忘记偏振只适用于横波。声波不能偏振，而光可以。另外，马吕斯定律I = I₀ cos²θ要求入射光已经是偏振光。对于非偏振光通过单个理想偏振片，强度减半，而不是按cos²θ减小。
When solving grating problems, always convert the lines per millimetre into spacing in metres. Check that sin θ does not exceed 1. If the required order gives sin θ > 1, that order does not exist. Include units and significant figures in your answers.
解光栅问题时，务必把每毫米线数换算成以米为单位的间距。检查sin θ不超过1。若某级计算得到sin θ > 1，则该级不存在。答题时注意单位与有效数字。
12. Exam Tips and Final Summary | 考试技巧与总结
Here are concise revision points for your exams:
以下是供复习的简明要点：
- Interference and diffraction prove wave nature; polarisation proves transverse nature.
- Path difference determines constructive/destructive interference: nλ or (n + ½)λ.
- Double-slit: d sin θ = nλ; fringe separation Δy = λD/d.
- Single-slit dark fringes: a sin θ = mλ (m = 1, 2, 3…).
- Diffraction grating: d sin θ = nλ, with d = 1/N.
- Malus's law: I = I₀ cos²θ; remember I₀/2 for unpolarised light through one polariser.
- Draw clear labelled diagrams for each experiment.
- 干涉和衍射证明波动性；偏振证明横波性。
- 光程差决定相长/相消干涉：nλ 或 (n + ½)λ。
- 双缝：d sin θ = nλ；条纹间距 Δy = λD/d。
- 单缝暗纹：a sin θ = mλ（m = 1, 2, 3…）。
- 光栅：d sin θ = nλ，其中 d = 1/N。
- 马吕斯定律：I = I₀ cos²θ；注意非偏振光通过一个偏振片后强度为 I₀/2。
- 为每个实验画出清晰标注的示意图。
Master these concepts, practice past-paper questions, and you will be well prepared for any interference, diffraction or polarisation question. Always link the physics to the evidence it provides for the nature of light.
掌握这些概念，练习历年真题，你就能从容应对任何关于干涉、衍射和偏振的问题。始终将物理原理与其为光的本质提供的证据联系起来。
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