Young's Double-Slit Experiment | 杨氏双缝干涉实验讲解

📚 Young’s Double-Slit Experiment | 杨氏双缝干涉实验讲解

Young’s double-slit experiment, first performed by Thomas Young in 1801, stands as one of the most elegant demonstrations of the wave nature of light. By splitting a single wavefront into two coherent sources and allowing them to overlap, the experiment produces a stable interference pattern of bright and dark fringes on a screen. This classical investigation not only confirmed the wave theory of light but also provided a reliable method for measuring the wavelength of light, a technique that remains central in A-Level Physics syllabuses.

杨氏双缝干涉实验由托马斯·杨于1801年首次完成，是证明光具有波动性最精妙的实验之一。通过将一个波前分成两个相干光源并使它们重叠，实验在屏幕上产生了明暗相间的稳定干涉条纹。这项经典研究不仅证实了光的波动说，还为测量光的波长提供了可靠方法，这一方法至今仍是A-Level物理课程的核心内容。

1. Introduction to the Experiment | 实验简介

The experiment uses a monochromatic light source, such as a sodium lamp or a laser, to illuminate a single narrow slit, which then acts as a point source to illuminate two closely spaced parallel slits. The light waves emerging from these two slits are coherent because they originate from the same wavefront. When these waves overlap on a distant screen, they interfere constructively or destructively depending on the path difference, yielding a series of equally spaced bright and dark bands called fringes.

实验使用单色光源（如钠灯或激光）照射一条狭窄的单缝，单缝作为点光源再照亮两条紧密排列的平行双缝。从双缝射出的光波来自同一波前，因此是相干的。当这些波在远处的屏幕上重叠时，根据光程差发生相长或相消干涉，形成一系列等间距的明暗条纹，称为干涉条纹。

Unlike the single-slit diffraction pattern, the double-slit interference pattern has fringes of nearly equal intensity (when slit widths are very small), which makes it ideal for precise measurements. Historically, this experiment settled the long-standing dispute between Newton’s corpuscular theory and Huygens’ wave theory.

与单缝衍射图样不同，双缝干涉图样（当缝宽极小时）的条纹强度几乎相等，因此非常适合精密测量。历史上，这项实验平息了牛顿微粒说与惠更斯波动说之间的长期争论。

2. Experimental Setup and Requirements | 实验装置与条件

A typical A-Level laboratory arrangement consists of a laser, a double-slit slide (with slit separation d typically 0.1–0.5 mm), a screen (distance D usually 1–3 m), and a darkened room. The laser beam directly illuminates the double slit, bypassing the single slit, because laser light is already highly monochromatic and spatially coherent.

典型的A-Level实验室布置包括一台激光器、一个双缝片（缝间距 d 通常为0.1–0.5 mm）、一块屏幕（距离 D 通常1–3 m）以及暗室环境。激光束直接照射双缝，无需单缝，因为激光本身具有高度的单色性和空间相干性。

If a non-laser source is used, a colour filter and a single slit must be placed before the double slit to ensure approximate temporal and spatial coherence. The screen should be perpendicular to the optical axis, and the distance D should be measured carefully from the double slit to the screen using a metre rule or a measuring tape.

若使用非激光光源，则必须在双缝前放置滤光片和单缝，以确保近似的时间和空间相干性。屏幕应垂直于光轴，距离 D 须用米尺或卷尺从双缝处仔细测量至屏幕。

Key requirements for obtaining clear fringes are: a narrow, intense source; monochromatic light; small slit separation d compared with D; and a stable, vibration-free setup.

获得清晰条纹的关键条件包括：狭窄且亮度高的光源、单色光、与 D 相比很小的缝间距 d，以及稳定无振动的装置。

3. Principle of Superposition and Interference | 叠加与干涉原理

When two or more waves of the same type overlap in space, the resultant displacement at any point is the vector sum of the individual displacements. This is the principle of superposition. For light waves, the electric field vectors add together.

当两列或更多同类型的波在空间中重叠时，任一点的合位移是各列波位移的矢量和。这就是叠加原理。对于光波，电场矢量相互叠加。

If the two waves arrive at a point in phase (crest meets crest, trough meets trough), they reinforce each other, leading to a bright fringe – this is constructive interference. If they arrive exactly out of phase (crest meets trough), they cancel each other, producing a dark fringe – destructive interference.

如果两列波在某点同相到达（波峰遇波峰，波谷遇波谷），它们相互加强，产生明纹——这就是相长干涉。如果它们恰好反相到达（波峰遇波谷），它们相互抵消，产生暗纹——相消干涉。

The phase relationship between the two waves at a point on the screen depends entirely on the path difference, that is, the difference in the distances travelled by the waves from the two slits to that point.

屏幕上某点两列波之间的相位关系完全取决于光程差，即从两条缝到该点光波所传播的距离之差。

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

Consider a point P on the screen at a distance x from the central axis. If S₁ and S₂ are the two slits separated by a distance d, the path difference Δ is given by S₂P – S₁P. For small angles, where D is much larger than d and x, the geometry approximates two nearly parallel rays making an angle θ with the axis. The path difference is then d sin θ.

考虑屏幕上离中心轴距离为 x 的一点 P。设 S₁ 和 S₂ 为间距为 d 的两条缝，光程差 Δ 由 S₂P – S₁P 给出。对于小角度，当 D 远大于 d 和 x 时，几何上可近似为两条近乎平行的光线与轴线成 θ 角。光程差则为 d sin θ。

Using the right-angled triangle formed by the axial line and the screen, sin θ can be approximated by tan θ = x / D for small angles, since sin θ ≈ θ and tan θ ≈ θ in radians. Hence, the path difference Δ = d sin θ ≈ d (x / D).

利用轴线与屏幕构成的直角三角形，在小角度下 sin θ 可近似为 tan θ = x / D，因为在弧度制下 sin θ ≈ θ 且 tan θ ≈ θ。因此，光程差 Δ = d sin θ ≈ d (x / D)。

The phase difference δ between the two waves is related to the path difference by δ = (2π / λ) × path difference. So δ = (2π / λ) d sin θ, or approximately δ = (2π d x) / (λ D).

两列波之间的相位差 δ 与光程差的关系为 δ = (2π / λ) × 光程差。因此 δ = (2π / λ) d sin θ，或近似为 δ = (2π d x) / (λ D)。

5. Conditions for Constructive and Destructive Interference | 明纹与暗纹条件

Constructive interference (bright fringe) occurs when the path difference is an integer multiple of the wavelength, i.e., Δ = nλ, where n = 0, 1, 2, … The phase difference is thus 2nπ, meaning the waves are in phase.

当光程差为波长的整数倍时发生相长干涉（明纹），即 Δ = nλ，其中 n = 0, 1, 2, … 此时相位差为 2nπ，意味着波同相。

Destructive interference (dark fringe) occurs when the path difference is an odd multiple of half wavelengths: Δ = (n + ½)λ, where n = 0, 1, 2, … The phase difference is (2n+1)π, so the waves arrive completely out of phase.

当光程差为半波长的奇数倍时发生相消干涉（暗纹）：Δ = (n + ½)λ，其中 n = 0, 1, 2, … 相位差为 (2n+1)π，因此波完全反相到达。

Expressed in terms of the angle θ, bright fringes satisfy d sin θ = nλ, and dark fringes satisfy d sin θ = (n + ½)λ. On the screen, the position x_n of the n‑th bright fringe (n = 0 at central maximum) is given by x_n = nλD / d, provided the small-angle approximation is valid.

用角度 θ 表达，明纹满足 d sin θ = nλ，暗纹满足 d sin θ = (n + ½)λ。在屏幕上，第 n 级明纹（中心极大处 n = 0）的位置 x_n 由 x_n = nλD / d 给出，前提是小角度近似成立。

6. Derivation of Fringe Spacing Formula | 条纹间距公式推导

The fringe spacing (fringe width) Δx is the distance between two consecutive bright fringes (or two consecutive dark fringes). Using the bright fringe condition x_n = nλD / d, the separation between the (n+1)-th and n‑th bright fringe is:

条纹间距（条纹宽度）Δx 是两个相邻明纹（或暗纹）之间的距离。利用明纹条件 x_n = nλD / d，第 (n+1) 级与第 n 级明纹的间距为：

Δx = x_{n+1} – x_n = (n+1)λD/d – nλD/d = λD / d

Notably, Δx is independent of n, which means the fringes are equally spaced. This is a key characteristic of double-slit interference (as opposed to single-slit diffraction where the central maximum is twice as wide). The formula is valid only when the small-angle approximation holds, typically when x ≪ D and d ≪ D.

值得注意的是，Δx 与 n 无关，这意味着条纹是等间距的。这是双缝干涉的一个关键特征（与单缝衍射中中央极大宽度加倍不同）。该公式仅在小角度近似成立时有效，通常当 x ≪ D 且 d ≪ D 时成立。

To measure the slit separation d experimentally, one can rearrange the formula: d = λD / Δx. Similarly, the wavelength λ = d Δx / D. These relationships form the basis of practical wavelength measurements.

要通过实验测量缝间距 d，可重新排列公式：d = λD / Δx。类似地，波长 λ = d Δx / D。这些关系构成了实际波长测量的基础。

7. Measuring Wavelength Using Young’s Slits | 用杨氏双缝测量波长

In a typical A-level experiment, a laser of known (or unknown) wavelength is used. The double-slit slide has a stated separation d (often verified using a travelling microscope). The screen distance D is measured. The fringe spacing Δx is determined by measuring the total distance across several fringes (say 10Δx) and dividing by the number of gaps, which reduces percentage uncertainty. The wavelength λ is then calculated using λ = d Δx / D.

在典型的A-Level实验中，使用已知（或未知）波长的激光器。双缝片有标明的缝间距 d（通常用移测显微镜验证）。测量屏幕距离 D。通过测量多条条纹（如10Δx）的总距离并除以间隔数目来确定条纹间距 Δx，这能减小百分误差。然后用 λ = d Δx / D 计算波长 λ。

Sources of uncertainty include the measurement of D (parallax, metre rule precision), the measurement of the fringe separation (ruler resolution, width of fringes), and any uncertainty in d. Students should estimate and propagate uncertainties to obtain a result like λ = (630 ± 20) nm for red laser light.

不确定性的来源包括 D 的测量（视差、米尺精度）、条纹间距的测量（直尺分辨率、条纹宽度）以及 d 的任何不确定性。学生应估算和传递不确定性，得到类似红光激光 λ = (630 ± 20) nm 的结果。

If a white light source with a filter is used, the experiment becomes more challenging due to low intensity, but it can still be done by averaging over several fringes. Modern apparatus often uses a photodiode or a smartphone sensor to plot intensity against position, giving a more precise estimation of Δx.

若使用带滤光片的白光源，因强度低实验会更具挑战，但仍可通过取多条条纹平均值完成。现代装置常使用光电二极管或智能手机传感器绘制强度-位置图，从而更精确地估算 Δx。

8. Effect of Slit Separation, Distance and Wavelength | 缝间距、屏距与波长的影响

From Δx = λD / d, it is clear that the fringe spacing increases with wavelength λ and distance D, and decreases with slit separation d. This can be demonstrated qualitatively: using red light produces wider fringes than using blue light; moving the screen further away widens the fringes; and a slide with smaller d gives larger separation.

由 Δx = λD / d 可知，条纹间距随波长 λ 和距离 D 的增大而增大，随缝间距 d 的增大而减小。这一点可做定性演示：红光产生的条纹比蓝光宽；将屏幕移远会使条纹变宽；缝间距 d 更小的双缝片会使条纹间距更大。

If the slit separation d becomes too large (comparable to D or x), the small-angle approximation breaks down, and the fringe spacing is no longer constant; the pattern also becomes dimmer and more closely spaced, eventually overlapping. If d is too small, the pattern becomes very broad but faint, making accurate measurement difficult because individual fringes are wide and poorly defined.

如果缝间距 d 过大（可与 D 或 x 相比），小角度近似不再成立，条纹间距不再恒定；图样也会变得更暗且更密，最终重叠。若 d 过小，图样变得非常宽但很暗淡，由于单条条纹宽且边界不清，难以精确测量。

These dependencies explain why, in practice, a slit separation of about 0.1–0.5 mm and a screen distance of 1–3 m work well for visible light (λ ~ 400–700 nm), giving a fringe spacing of a few millimetres – comfortable for a ruler measurement.

这些依赖关系解释了为何实践中缝间距约0.1–0.5 mm、屏距1–3 m 对可见光（λ ~ 400–700 nm）效果良好，条纹间距为数毫米，便于用直尺测量。

9. White Light Interference and Coherence Length | 白光干涉与相干长度

When a white light source is used, the central fringe (n = 0, zero path difference) is white because all wavelengths interfere constructively at the same position. On either side, coloured fringes appear, with blueish inner edges and reddish outer edges, because the fringe spacing is smaller for shorter wavelengths. Only a few orders are visible because the overlapping of spectra from different wavelengths quickly washes out the pattern.

使用白光源时，中央条纹（n = 0，零光程差）呈白色，因为所有波长在该处同时产生相长干涉。两侧出现彩色条纹，内侧偏蓝，外侧偏红，这是因为较短波长的条纹间距更小。由于不同波长的光谱重叠很快使图样模糊，只能看到少数几级条纹。

The concept of coherence length is important here: white light has a very short coherence length (a few microns), so the path difference must be nearly zero to observe interference. Only near the central fringe is the path difference smaller than the coherence length, which explains the rapid fading of colour into uniform illumination.

在此，相干长度的概念很重要：白光的相干长度极短（几微米），因此要观察到干涉，光程差必须接近零。只有在中央条纹附近，光程差才小于相干长度，这解释了为何彩色条纹会迅速褪去变为均匀照明。

In contrast, a laser has a long coherence length (often several metres), allowing many orders of fringes to be clearly visible across the screen, even for large n.

相反，激光具有较长的相干长度（通常数米），即使在较大 n 值下，也能在屏幕上清晰地看到多级条纹。

10. Safety Precautions and Experimental Technique | 安全注意事项与实验技巧

Lasers used in school laboratories are usually Class 2 (output < 1 mW), but they still pose a retinal hazard if viewed directly. Students must ensure that the beam never points towards anyone’s eyes, and that reflective surfaces (watches, jewellery, polished metal) are removed from the beam path. Laser safety goggles are recommended, though not always mandatory for low-power lasers.

学校实验室使用的激光器通常为2类（输出功率 < 1 mW），但若直视仍有视网膜损伤的危险。学生必须确保光束绝不指向任何人的眼睛，并移开光束路径上的反射表面（手表、首饰、抛光金属）。建议佩戴激光防护镜，尽管对于低功率激光并非总是强制要求。

Practical tips include darkening the room to improve contrast, using a secure optical bench to prevent accidental misalignment, and using a metre rule fixed at the screen to measure fringe positions. Marking the centre of dark fringes with a fine pencil helps to reduce systematic error.

实用技巧包括使房间变暗以提高对比度、使用稳固的光学平台防止意外失调、以及在屏幕处固定米尺测量条纹位置。用细铅笔标出暗纹中心有助于减少系统误差。

To minimise percentage uncertainty, measure the distance across as many fringes as possible (e.g., 10Δx) rather than a single fringe width. Also, align the screen exactly perpendicular to the laser beam; if the screen is tilted, the measured x-positions will be skewed.

为减小百分误差，应尽可能测量多条条纹的总距离（如10Δx）而非单个条纹宽度。此外，要使屏幕与激光束严格垂直；若屏幕倾斜，测得的 x 位置将产生偏差。

11. Modern Applications and Historical Significance | 现代应用与历史意义

Young’s double-slit experiment is more than a classroom classic; its principle underpins interferometric techniques in science and industry. For example, Michelson interferometers, LIGO (Laser Interferometer Gravitational-Wave Observatory), and optical coherence tomography in medical imaging all rely on interference of coherent beams.

杨氏双缝实验不仅仅是课堂经典；其原理为科学和工业中的干涉测量技术奠定了基础。例如，迈克尔逊干涉仪、LIGO（激光干涉引力波天文台）以及医学成像中的光学相干断层扫描，都依赖相干光束的干涉。

The experiment also profoundly influenced quantum mechanics. Modern versions with single photons or electrons show that interference fringes build up one particle at a time, illustrating wave-particle duality and the role of measurement in quantum theory. Thomas Young’s original work thus connects directly to some of the most advanced physics of the 21st century.

该实验还深刻影响了量子力学。使用单光子或电子的现代版本显示，干涉条纹通过单粒子的累积逐渐形成，展示了波粒二象性以及测量在量子理论中的角色。托马斯·杨的原始工作因此直接与21世纪某些最前沿的物理学相联系。

From a curriculum perspective, mastering Young’s fringes provides students with essential skills in data analysis, graphical methods, uncertainty propagation, and the application of wave theory – all of which are vital for higher education in physics and engineering.

从课程角度看，掌握杨氏条纹为学生提供了数据分析、图解法、不确定性传递及波动理论应用的重要技能——这些都是高等教育物理与工程学科所必需的。

12. Summary and Key Points | 总结与关键点

The double-slit experiment demonstrates the interference of light through coherent superposition. The fringe spacing is given by Δx = λD / d, where d is the slit separation, D the slit-to-screen distance, and λ the wavelength. The constructive condition is d sin θ = nλ, and the destructive condition is d sin θ = (n + ½)λ.

双缝实验通过相干叠加展示了光的干涉。条纹间距由 Δx = λD / d 给出，其中 d 为缝间距，D 为缝到屏幕的距离，λ 为波长。相长干涉条件为 d sin θ = nλ，相消干涉条件为 d sin θ = (n + ½)λ。

Remember that the small-angle approximation sin θ ≈ tan θ = x/D is essential for the linear relation, and that the experiment requires temporally and spatially coherent light. The central fringe is always bright and, with white light, it appears white while higher-order fringes show spectral colours.

切记小角度近似 sin θ ≈ tan θ = x/D 对于线性关系至关重要，且实验需要时间和空间相干光。中央条纹始终为明纹，使用白光时呈白色，而高级次条纹则显示光谱颜色。

Finally, always consider safety with lasers, careful measurement techniques, and the historical and modern significance of this elegant proof of the wave nature of light.

最后，始终注意激光安全、细致的测量技术，以及这一优雅证明光波本性的实验的历史和现代意义。

Published by TutorHao | Physics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）

Young’s Double-Slit Experiment | 杨氏双缝干涉实验讲解