Interference of Light for IB WJEC Physics | IB WJEC 物理：光的干涉考点精讲

📚 Interference of Light for IB WJEC Physics | IB WJEC 物理：光的干涉考点精讲

Light interference is a cornerstone of wave physics, demonstrating that light behaves as a wave. For IB and WJEC students, mastering this topic means understanding superposition, coherence, and the conditions that produce stable interference patterns. This article breaks down every essential concept, from Young’s double-slit experiment to thin-film interference, with practical tips for your exams.

光的干涉是波动物理学的基石，证明光是一种波。对于 IB 和 WJEC 学生，掌握这一主题意味着理解叠加、相干性以及产生稳定干涉图样的条件。本文从杨氏双缝实验到薄膜干涉，逐一讲解每个基本概念，并提供实用的考试技巧。

1. Superposition and Interference | 叠加与干涉

Interference arises from the principle of superposition. When two or more waves overlap, the resultant displacement at any point is the vector sum of the individual displacements.

干涉源于叠加原理。当两个或更多波重叠时，任何一点的合位移都是各个位移的矢量和。

Constructive interference occurs when waves meet in phase, meaning their crests align. The amplitudes add up, producing a bright fringe for light. Destructive interference happens when waves meet out of phase by half a wavelength, cancelling each other to produce a dark fringe.

当波同相相遇时发生相长干涉，即波峰对齐。振幅相加，对光而言形成亮条纹。当波反相（相差半个波长）相遇时发生相消干涉，相互抵消形成暗条纹。

The phase relationship between waves is crucial. If the path difference is an integer multiple of the wavelength (0, λ, 2λ, …), the waves are in phase. If the path difference is an odd multiple of half-wavelength (λ/2, 3λ/2, …), they are out of phase.

波之间的相位关系至关重要。如果光程差是波长的整数倍（0, λ, 2λ, …），则波同相。如果光程差是半波长的奇数倍（λ/2, 3λ/2, …），则波反相。

2. Coherence and Monochromatic Light | 相干性与单色光

To observe a stable interference pattern, the sources must be coherent. Coherent sources emit waves with a constant phase difference and the same frequency. Laser light is highly coherent, while a filament bulb emits incoherent light.

要观察到稳定的干涉图样，光源必须具有相干性。相干光源发射具有恒定相位差和相同频率的波。激光是高度相干的，而灯丝灯泡发出的是非相干光。

In Young’s original experiment, coherence was achieved by illuminating two narrow slits with the same monochromatic source. Even if the primary source has random phase changes, the two secondary sources from the slits remain in step, creating a constant phase relationship.

在杨氏最初的实验中，通过用同一单色光源照射两条狭缝来实现相干性。即使主光源有随机的相位变化，从狭缝产生的两个次级光源仍保持同步，从而建立恒定的相位关系。

Monochromatic light contains a single wavelength or a very narrow band of wavelengths. A broader range of wavelengths causes overlapping patterns, washing out the fringes. Sodium lamps and lasers are common monochromatic sources.

单色光包含单一波长或非常窄的波长范围。较宽的波长范围会导致图样重叠，使条纹变得模糊。钠灯和激光是常见的单色光源。

3. Young’s Double-Slit Experiment | 杨氏双缝实验

Young’s double-slit experiment, first performed in 1801, provided convincing evidence for the wave nature of light. Light from a single source passes through two closely spaced slits, acting as two coherent sources. On a distant screen, alternating bright and dark fringes are observed.

杨氏双缝实验于 1801 年首次完成，为光的波动性提供了令人信服的证据。来自单一光源的光穿过两条靠得很近的狭缝，充当两个相干光源。在远处的屏幕上，可以观察到明暗相间的条纹。

The central bright fringe is called the zero-order maximum. Bright fringes on either side are labelled first-order, second-order maxima, and so on. The dark fringes in between are minima, where destructive interference occurs.

中央亮条纹称为零级极大。两侧的亮条纹分别标记为一级极大、二级极大等。中间的暗条纹是极小，即相消干涉发生的位置。

The symmetry of the pattern reflects the equal path differences on both sides. Understanding this setup is fundamental for deriving the fringe spacing formula and solving numerical problems.

图样的对称性反映了两侧光程差相等。理解这一装置是推导条纹间距公式和解决数值问题的基础。

4. Fringe Pattern and Path Difference | 干涉条纹与光程差

The path difference between waves from the two slits to a point on the screen determines whether a bright or dark fringe appears. For constructive interference (bright fringe), the path difference Δ = nλ, where n is an integer (0, 1, 2, …).

从双缝到屏幕上某一点的波之间的光程差决定了出现亮条纹还是暗条纹。对于相长干涉（亮条纹），光程差 Δ = nλ，其中 n 为整数（0, 1, 2, …）。

For destructive interference (dark fringe), the path difference is Δ = (n + ½)λ. The central bright fringe corresponds to n = 0, with zero path difference, meaning the waves travel exactly the same distance.

对于相消干涉（暗条纹），光程差为 Δ = (n + ½)λ。中央亮条纹对应 n = 0，光程差为零，即两列波走过的距离完全相同。

Using trigonometry, the path difference can be approximated by Δ ≈ d sin θ, where d is the slit separation and θ is the angle from the central axis. For small angles, sin θ ≈ tan θ ≈ x/D, a crucial simplification linking fringe position x, slit-to-screen distance D, and slit separation d.

利用三角学，光程差可近似为 Δ ≈ d sin θ，其中 d 是缝距，θ 是偏离中心轴的角度。对于小角度，sin θ ≈ tan θ ≈ x/D，这是将条纹位置 x、缝到屏距离 D 和缝距 d 联系起来的关键简化。

5. Fringe Spacing Formula | 条纹间距公式

The fringe spacing Δx, also called fringe width, is the distance between adjacent bright (or dark) fringes. The standard formula is:

条纹间距 Δx（也称条纹宽度）是相邻亮（或暗）条纹之间的距离。标准公式为：

Δx = λD / d

where λ is the wavelength, D is the distance from the slits to the screen, and d is the slit separation.

其中 λ 是波长，D 是双缝到屏幕的距离，d 是双缝之间的距离。

This formula assumes that D is much larger than d, so the small-angle approximation holds. Students often confuse D and d – remember: D is the large distance to the screen, d is the tiny gap between slits.

该公式假设 D 远大于 d，因此小角度近似成立。学生常混淆 D 和 d——请记住：D 是到屏幕的大距离，d 是狭缝之间的微小间隙。

From Δx = λD / d, we see that increasing wavelength or screen distance increases fringe spacing, while increasing slit separation decreases fringe spacing. This relationship is frequently tested in examination calculations.

从 Δx = λD / d 可以看出，增加波长或屏幕距离会增加条纹间距，而增加缝距则会减小条纹间距。这种关系在考试计算中经常出现。

6. Effect of Slit Separation and Wavelength | 缝距与波长的影响

Let’s interpret the formula physically. A smaller slit separation d means the two sources are closer, so the angular separation between bright fringes increases, spreading out the pattern. This makes fringes easier to measure but reduces intensity at any single point.

让我们从物理上理解该公式。缝距 d 越小，两个光源越靠近，亮条纹之间的角分离就越大，使图样分散开。这使得条纹更容易测量，但会降低任何一个点的强度。

A longer wavelength λ also produces wider spaced fringes. Red light gives a broader pattern than blue light. If you were to use white light, you would see a central white fringe with coloured fringes on either side (more in the next section).

较长的波长 λ 也会产生更宽的条纹间距。红光比蓝光产生更宽的图样。如果使用白光，你会看到中央白色条纹，两侧带有彩色条纹（下一节详述）。

The distance D appears linearly — doubling the screen distance doubles the fringe spacing. This offers a direct experimental method to determine an unknown wavelength by measuring Δx, D, and d, then using λ = Δx d / D.

距离 D 以线性关系出现——将屏幕距离加倍会使条纹间距加倍。这提供了一种直接的实验方法，通过测量 Δx、D 和 d，然后使用 λ = Δx d / D 来确定未知波长。

7. White Light Interference | 白光干涉

If a white light source is used in Young’s experiment, the pattern becomes more colourful. The central bright fringe is white because all wavelengths overlap constructively there (zero path difference).

如果在杨氏实验中使用白光光源，图样会变得更加多彩。中央亮条纹是白色的，因为所有波长在那里发生相长干涉（光程差为零）。

On either side of the central maximum, a few coloured fringes appear, with violet closest to the centre and red farthest, because violet light has a shorter wavelength and forms narrower fringes. Further away, the fringes overlap and merge into a uniform white background.

在中央极大的两侧，会出现一些彩色条纹，紫色最靠近中心，红色最远，因为紫光波长较短，形成的条纹较窄。再远一些，条纹会重叠并融合成均匀的白色背景。

This colour sequence provides qualitative evidence that Δx ∝ λ. It also explains why monochromatic light is preferred for precise measurements — coloured fringes are harder to measure accurately and only a few orders are visible.

这一颜色序列定性证明了 Δx ∝ λ。这也解释了为什么精确测量更倾向于使用单色光——彩色条纹难以精确测量，而且只能看到少数几级。

8. Thin Film Interference | 薄膜干涉

Thin film interference occurs when light reflects off the top and bottom surfaces of a thin transparent film, such as a soap bubble or an oil slick. The two reflected waves travel different path lengths and interfere, producing vibrant colours in white light.

当光从薄膜（如肥皂泡或油膜）的上下表面反射时，就会发生薄膜干涉。两列反射波经过不同的路程长度并发生干涉，在白光下产生鲜艳的颜色。

The condition for constructive interference depends on the film thickness t, the refractive index n, and the wavelength λ. For a film in air, with no phase change at both surfaces (e.g., a thin glass plate in air), the condition is 2nt = mλ for constructive, and 2nt = (m + ½)λ for destructive, where m = 0, 1, 2, …

相长干涉的条件取决于薄膜厚度 t、折射率 n 和波长 λ。对于空气中两面均无相位变化的薄膜（如空气中的薄玻璃板），相长条件为 2nt = mλ，相消条件为 2nt = (m + ½)λ，其中 m = 0, 1, 2, …

However, phase changes on reflection can flip these conditions. If one reflection undergoes a 180° phase change (e.g., soap bubble in air, where the top surface has a phase change and the bottom does not), then 2nt = (m + ½)λ becomes constructive, and 2nt = mλ destructive.

然而，反射时的相位变化可能会颠倒这些条件。如果一次反射发生 180° 相位变化（例如空气中肥皂泡，上表面有相位变化而下表面没有），则 2nt = (m + ½)λ 为相长，2nt = mλ 为相消。

Situation / 情况	Constructive / 相长	Destructive / 相消
No net phase change (e.g., glass in air) / 无净相位变化（如空气中玻璃）	2nt = mλ	2nt = (m + ½)λ
Net 180° phase change (e.g., soap bubble) / 净 180° 相位变化（如肥皂泡）	2nt = (m + ½)λ	2nt = mλ

9. Phase Change on Reflection | 反射时的相位变化

When light reflects off a medium with a higher refractive index, it undergoes a phase change of π radians (180°). This is equivalent to an extra path difference of half a wavelength. Conversely, reflecting off a medium of lower refractive index causes no phase change.

当光从折射率较高的介质反射时，会发生 π 弧度（180°）的相位变化。这相当于额外的半个波长的光程差。反之，从折射率较低的介质反射时不发生相位变化。

In thin film interference, both reflections must be analysed. For a soap film in air, the top reflection (air to soap, n increases) gives a phase change; the bottom reflection (soap to air, n decreases) gives no phase change. Therefore, there is a net 180° phase difference between the two reflected rays, inverting the interference conditions.

在薄膜干涉中，必须分析两次反射。对于空气中的肥皂膜，上表面反射（从空气到肥皂，n 增大）产生相位变化；下表面反射（从肥皂到空气，n 减小）无相位变化。因此，两束反射光之间存在 180° 的净相位差，这会使干涉条件反转。

This concept is frequently tested: given a film with specific refractive indices, you must determine whether the central point is bright or dark based on thickness, wavelength, and phase changes. Practice with diagrams to get comfortable.

这一概念经常出现在考试中：给定具有特定折射率的薄膜，你必须根据厚度、波长和相位变化来判断中心点是亮还是暗。多做图表练习，以便熟练掌握。

10. Applications and Exam Tips | 应用与考试技巧

Optical applications of interference include anti-reflection coatings on lenses, where a thin film of appropriate thickness and refractive index causes destructive interference for a chosen wavelength, reducing reflections. Interference is also used in interferometers to measure tiny displacements or refractive index changes.

干涉的光学应用包括镜头的增透膜，通过具有适当厚度和折射率的薄膜，对特定波长产生相消干涉，从而减少反射。干涉还用于干涉仪，以测量微小位移或折射率变化。

Common exam pitfalls: confusing D and d, incorrect units (often need metres), forgetting that Δx can be measured over several fringes to improve accuracy, and misapplying phase change rules. In thin-film problems, always draw the film, label refractive indices, and count phase changes systematically.

常见考试陷阱：混淆 D 和 d，单位错误（通常需要米），忘记可以通过测量多条条纹的间距来提高精度，以及错误应用相位变化规则。在薄膜问题中，一定要画出薄膜，标注折射率，并系统地计算相位变化。

Memorise the key equations and use them confidently. When measuring fringe spacing in the lab, measure the distance across multiple fringes and divide by the number of gaps. And always check that your final answer for λ is reasonable — visible light is around 400–700 nm.

记住关键公式，并自信地运用它们。在实验室测量条纹间距时，测量多个条纹的总距离，再除以间隔数。最后务必检查求出的 λ 是否合理——可见光约为 400–700 nm。

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Interference of Light for IB WJEC Physics | IB WJEC 物理：光的干涉 考点精讲