IB Physics: Interference of Light – Key Points | IB 物理：光的干涉考点精讲

📚 IB Physics: Interference of Light – Key Points | IB 物理：光的干涉考点精讲

Light interference is a wave phenomenon that arises when two or more coherent light waves superpose. In IB Physics, mastering interference is essential for explaining Young’s double-slit pattern, thin-film colours, and diffraction gratings. This article brings together the key concepts, crucial equations, and common exam pitfalls to help you tackle any interference question with confidence.

光的干涉是一种波动现象，由两列或多列相干光波叠加而成。在 IB 物理中，掌握干涉知识是解释杨氏双缝图样、薄膜色彩和衍射光栅的基础。本文梳理核心概念、关键公式和常见考试陷阱，让你从容面对任何干涉考题。

1. Interference and Coherence | 干涉与相干条件

Interference occurs when waves from two sources overlap and superpose. To produce a stable interference pattern with light, the sources must be coherent – they must have the same frequency and a constant phase difference. Ordinary light bulbs emit many short, uncorrelated wave trains, so splitting a single wavefront (division of wavefront) or dividing amplitude (division of amplitude) is used to achieve coherence artificially.

当两列波相遇并叠加时就发生干涉。要用光产生稳定的干涉图样，光源必须是相干的——有相同的频率和恒定的相位差。普通灯泡发出的波列短且无关联，因此常通过分割同一波前（分波前法）或分割振幅（分振幅法）来人工获得相干光。

A laser provides highly coherent light because photons are emitted in phase and with a very narrow frequency spread. In Young’s double-slit experiment, a single narrow slit before the double slits acts as a spatial filter, making the light waves reaching the two slits coherent even from a non-laser source.

激光是一种高度相干的光源，因为光子同相位发射且频率范围极窄。在杨氏双缝实验中，双缝前放置一个窄单缝起到空间滤波作用，即使使用非激光光源，也能使到达双缝的光波彼此相干。

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

In Young’s iconic experiment, coherent light illuminates two narrow, parallel slits separated by a distance d. The two emerging wavefronts overlap on a distant screen, producing a pattern of evenly spaced bright and dark fringes. The geometry relies on a large screen distance L, so that the paths to a point P at a displacement y from the centre are nearly parallel.

在杨氏经典的实验中，相干光照射两条相距为 d 的平行狭缝。从双缝出来的两列波前在远处的屏幕上交叠，产生等间距的明暗条纹。装置中屏幕距离 L 很大，因此到达偏离中心 y 处 P 点的两条光线近乎平行。

The path difference Δx between light from the two slits to point P is approximately d sin θ, where θ is the angle from the central axis. For small angles (θ in radians), sin θ ≈ tan θ = y/L, giving a convenient expression Δx ≈ d y/L. This approximation is central to deriving fringe positions in exams.

从双缝到 P 点的光程差 Δx 近似为 d sin θ，其中 θ 是相对于中心轴的角位置。在小角度下（θ 以弧度计），sin θ ≈ tan θ = y/L，因此 Δx ≈ d y/L。这一近似是考试中推导条纹位置的核心。

3. Path Difference and Phase Difference | 光程差与相位差

The phase difference Δφ between two coherent waves is directly proportional to the path difference: Δφ = (2π/λ) Δx. A path difference of one wavelength λ creates a phase change of 2π rad, which means the waves arrive in step and reinforce each other.

两列相干波之间的相位差 Δφ 与光程差成正比：Δφ = (2π/λ) Δx。一个波长 λ 的光程差对应 2π rad 的相位变化，这意味着两列波同时到达波峰并相互加强。

In some situations, such as reflection from a denser medium, an additional phase change of π (half-wavelength loss) occurs. This must be added to the path difference when writing interference conditions for thin films or air wedges.

在某些情形下，比如从光密介质反射时，会产生额外的 π 相位跳变（半波损失）。在书写薄膜或空气劈尖的干涉条件时，必须将这一额外的相位差考虑进去。

4. Conditions for Bright and Dark Fringes | 明暗条纹条件

Constructive interference (bright fringe) occurs when the waves meet in phase, i.e. the path difference is an integer multiple of the wavelength: Δx = mλ, where m = 0, ±1, ±2, … . Destructive interference (dark fringe) happens when the waves meet exactly out of phase: Δx = (m + ½)λ.

当两列波以同相位相遇（光程差为波长的整数倍）时发生相长干涉，形成亮条纹：Δx = mλ (m = 0, ±1, ±2, …)。当它们以反相位相遇（光程差为半波长的奇数倍）时发生相消干涉，形成暗条纹：Δx = (m + ½)λ。

Substituting the small-angle approximation for the double slit, the bright fringe position y is given by y_m = mλL/d, and the dark fringe position by y_m = (m + ½)λL/d. The central bright fringe (m = 0) is always situated exactly on the axis.

代入双缝的小角度近似，可得亮条纹位置 y_m = mλL/d，暗条纹位置 y_m = (m + ½)λL/d。中央亮纹（m = 0）始终恰好位于中轴线上。

5. Fringe Spacing Formula | 条纹间距公式

The distance between two consecutive bright fringes (or two dark fringes), called fringe spacing Δy, is constant near the centre and given by:

Δy = λL / d

This result is valid when the screen is far from the slits and the angles are small. It shows that the pattern is uniform in the region where the approximation holds.

相邻两条亮纹（或暗纹）间的距离称为条纹间距 Δy，在中心附近保持恒定，计算公式为：Δy = λL / d。当屏幕足够远且角度很小时该公式成立，说明在近似有效的区域条纹是均匀分布的。

The table below summarises how changing each quantity influences the fringe separation:

Factor / 因素	Effect on Δy / 对 Δy 的影响
Wavelength λ / 波长 λ	Larger λ → larger Δy
Slit separation d / 缝距 d	Larger d → smaller Δy
Screen distance L / 屏距 L	Larger L → larger Δy

掌握这些依赖关系可以帮助你快速预测实验变化后的图样，例如使用红光替代蓝光会使条纹变宽。

6. Effect of Changing Wavelength, Slit Separation, and Screen Distance | 改变波长、缝距和屏距的影响

If the entire experiment is immersed in a medium of refractive index n, the wavelength reduces to λ’ = λ/n. Consequently, fringe spacing becomes Δy’ = (λ/n) × L/d, so the fringes move closer together. This explains why interference patterns appear compressed underwater.

若整个实验装置浸没于折射率为 n 的介质中，波长会减小为 λ’ = λ/n。因此条纹间距变为 Δy’ = (λ/n) × L/d，条纹会变密。这也是水下干涉图样看起来更紧凑的原因。

Decreasing slit separation d widens the fringes, improving measurement precision. Increasing the screen distance L also spreads the pattern but reduces brightness. You must be able to design and interpret experiments that vary these parameters.

减小缝距 d 会使条纹展宽，提升测量精度。增大屏幕距离 L 同样扩开图样，但会降低亮度。你必须能够设计和解读那些改变这些参数的实验。

7. White Light Interference | 白光干涉

When white light is used in Young’s double-slit experiment, the central fringe (m = 0) remains white because all wavelengths constructively interfere there. Away from the centre, coloured fringes appear: violet lies closest to the centre (shorter wavelength, smaller Δy) and red is farthest out (longer wavelength, larger Δy). After a few orders the colours overlap and the pattern washes out.

杨氏双缝使用白光时，中央零级条纹依然为白色，因为所有波长在此处均发生相长干涉。偏离中央位置则出现彩色条纹：紫色（短波长，Δy 小）更靠近中心，红色（长波长，Δy 大）位于外侧。几级之后颜色交叠，条纹变得模糊不清。

Exam questions often ask you to identify which colour appears at a certain position or to explain the formation of a white central fringe. Always relate colour order to fringe spacing: Δy ∝ λ.

考题常要求你辨认特定位置出现的颜色或解释白色中央条纹的形成。回答时始终将颜色顺序与条纹间距联系起来：Δy ∝ λ。

8. Thin Film Interference | 薄膜干涉

Thin film interference arises when light reflects from the top and bottom surfaces of a thin, transparent layer (e.g. soap bubble, oil slick). The two reflected waves travel different distances and may undergo phase changes on reflection, leading to colourful patterns in reflected light.

薄膜干涉指的是光在透明薄膜（如肥皂泡、油膜）的上下表面反射后发生干涉。两束反射波经过的光程不同，并可能在反射时发生相位跳变，从而在反射光中形成斑斓的色彩。

For near-normal incidence, the optical path difference introduced by the film is 2 n t, where n is the film’s refractive index and t its thickness. An additional phase shift of π occurs whenever light reflects from a medium of higher refractive index.

做近垂直入射考虑时，薄膜引入的光程差为 2 n t，其中 n 为薄膜折射率，t 为厚度。当光从低折射率介质射向高折射率介质反射时，总会附加一个 π 相位跳变。

If the film has refractive index greater than the surrounding media (e.g. soap film in air), one reflection undergoes a phase change (air to film) while the other does not (film to air). Hence the effective path difference for reflected light is 2 n t + λ/2. Constructive interference (bright reflection) then satisfies 2 n t = (m – ½)λ, while destructive interference (dark reflection) satisfies 2 n t = mλ. This explains why a very thin soap film appears dark.

若薄膜折射率大于周围介质（例如空气中的肥皂膜），上表面反射（从空气到膜）伴有相位跳变，下表面反射（从膜到空气）则没有。因此反射光的有效光程差为 2 n t + λ/2。相长干涉（反射增强）条件为 2 n t = (m – ½)λ，相消干涉（反射减弱）条件为 2 n t = mλ。这解释了为何极薄的肥皂膜看起来是暗的。

9. Air Wedge and Newton’s Rings | 空气劈尖与牛顿环

An air wedge is formed by two glass plates separated by a thin spacer at one end, creating a wedge-shaped air gap. Monochromatic light reflected from the top and bottom surfaces of this air layer produces straight, equally spaced interference fringes parallel to the line of contact. Each fringe marks a contour of constant air-gap thickness, hence the name ‘equal-thickness fringes’.

空气劈尖由两玻璃板在一端垫薄片形成，构成楔形空气层。单色光在空气层的上下表面反射后产生平行于接触棱的等间距直线干涉条纹。每条条纹对应固定的空气层厚度，因此被称为等厚干涉条纹。

Newton’s rings are concentric circular fringes observed when a plano-convex lens of large radius R is placed on a flat glass plate. The air film thickness increases radially outwards, resulting in rings that become closer together farther from the centre. The centre is dark (in reflected light) because the two reflections experience a relative π phase shift at the point of contact.

牛顿环是将大曲率半径 R 的平凸透镜置于平板玻璃上时观察到的同心圆环。空气膜厚度沿径向向外增加，因此远离中心的环纹越来越密。反射光中，环心为暗斑，因为接触点处两束反射光之间存在 π 的相对相位变化。

10. Anti-reflection and High-reflectance Coatings | 增透膜与增反膜

Anti-reflection coatings on lenses and solar panels exploit destructive interference in a thin film to minimise reflection. A coating with refractive index n_c such that n_air < n_c < n_glass ensures both reflected beams suffer a half-wavelength loss, cancelling the extra phase difference. The film thickness is chosen so that 2 n_c t = λ/2 (for perpendicular incidence), giving t = λ/(4 n_c) as the thinnest layer that eliminates reflection for a specific wavelength.

透镜和太阳能电池板上的增透膜利用薄膜的相消干涉来减少反射。镀膜折射率 n_c 满足 n_air < n_c < n_glass，则两次反射均有半波损失，额外相位差相互抵消。镀膜厚度满足 2 n_c t = λ/2（垂直入射），得到 t = λ/(4 n_c)，这是针对特定波长消反射的最薄涂层。

High-reflectance coatings instead enhance reflection by making the reflections constructively interfere. By stacking layers of alternating refractive indices, multiple reflections add in phase, producing mirrors with reflectance close to 100% for specific spectral ranges. These are used in laser cavities and optical instruments.

增反膜则通过使反射光相长干涉来增强反射。交替镀上不同折射率的多层膜，使多次反射的相位一致叠加，可在特定光谱范围内获得接近 100% 的反射率，广泛应用于激光谐振腔和光学仪器。

11. Diffraction Grating as Multiple-Slit Interference | 衍射光栅与多光束干涉

A diffraction grating consists of many equally spaced slits (ruled lines) and can be treated as a multiple-slit interference device. The condition for principal maxima is the same as for the double slit: d sin θ = nλ, where d is the grating spacing (inverse of lines per metre) and n is the order number. The angles are typically not small, so the exact sine equation is used.

衍射光栅包含大量等间距的狭缝（刻线），可视为多缝干涉器件。主极大的条件与双缝类似：d sin θ = nλ，其中 d 为光栅常数（每米刻线数的倒数），n 为级数。由于光栅角度通常不小，

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IB Physics: Interference of Light – Key Points | IB 物理：光的干涉 考点精讲