📚 Light Interference: Key Points for WJEC A-Level Physics | A-Level WJEC 物理：光的干涉 考点精讲
Interference of light is a cornerstone of wave physics at A-Level, revealing the hidden wave nature of light through overlapping beams. For WJEC candidates, mastering this topic means understanding how coherent waves combine, predicting fringe patterns, and applying a few key equations. This guide breaks down every essential concept from Young's double‑slit to diffraction gratings, with clear bilingual explanations and practical exam tips.
光的干涉是 A-Level 波动物理的基石，通过光束的叠加揭示了光隐藏的波动本性。对于 WJEC 考生而言，掌握这一主题意味着理解相干波如何组合、预测条纹图样，并灵活运用几个关键方程。本指南从杨氏双缝到衍射光栅逐一拆解所有核心概念，提供清晰的双语解释和实用的应试技巧。
1. Coherence and the Condition for Interference | 相干性与干涉条件
For a stable interference pattern to form, the two light sources must be coherent — they must emit waves with the same frequency and a constant phase difference. Ordinary light bulbs are incoherent because their atoms radiate independently and randomly. Laser light is inherently coherent, while in Young's classic experiment coherence is achieved by splitting a single wavefront using a narrow single slit before the double slit.
要形成稳定的干涉图样，两个光源必须相干 — 它们必须发出频率相同且相位差恒定的波。普通灯泡是非相干的，因为其原子独立且随机地辐射。激光本质上是相干的，而在杨氏经典实验中，通过使用双缝前的一条窄单缝来分割单一波前，从而获得相干光。
- Coherent sources: same frequency, constant phase difference / 相干光源：频率相同，相位差恒定
- Methods to achieve coherence: laser directly; single slit + double slit; thin‑film division of amplitude / 获得相干的方法：直接使用激光；单缝+双缝；薄膜分振幅
2. Path Difference and Phase Difference | 光程差与相位差
e of the wavelength (nλ), the waves arrive in phase and constructive interference occurs. If the path difference is a half‑ hase and destructive interference results. Phase difference Δφ = (2π/λ) × path difference.
干涉效应由到达某点的两条光线之间的光程差（Δx 或 δ）决定。若光程差是波长的整数倍（nλ），波同相到达，产生相长干涉。若光程差是半整数倍（(n+½)λ），波完全反相，产生相消干涉。相位差 Δφ = (2π/λ) × 光程差。
Constructive: δ = nλ, Destructive: δ = (n + ½)λ / 相长：δ = nλ，相消：δ = (n + ½)λ
3. Young's Double‑Slit Experiment (WJEC Focus) | 杨氏双缝实验（WJEC 考点）
The classic demonstration of light interference uses a coherent source (laser or filtered lamp plus a single slit) to illuminate two parallel narrow slits separated by distance a. On a screen placed at distance D, a pattern of equally spaced bright and dark fringes appears. The central bright fringe corresponds to zero path difference; the first‑order bright fringes occur where the path difference is λ.
经典的光干涉演示使用相干光源（激光或经滤光的灯加单缝）照射间距为 a 的两条平行窄缝。在距离为 D 的屏幕上，出现等间距的明暗相间条纹。中央明纹对应零光程差；一级明纹出现在光程差为 λ 处。
- Central bright fringe: zero order, highest intensity / 中央明纹：零级，强度最高
- Symmetrical fringes on either side / 两侧条纹对称
- With white light: central white fringe, coloured fringes on sides (red on the outer edges, blue/violet inside) / 用白光：中央白色条纹，两侧彩色条纹（红光在外，蓝/紫在内）
4. Deriving the Fringe Spacing Formula | 条纹间距公式推导
D, where y is the distance from the central maximum to a fringe on the screen. For the nth‑ (distance between adjacent bright fringes) Δy = λD / a. This formula is only valid when D ≫ imation holds. WJEC typically provides this formula but expects you to use it confidently.
在小角近似下，光程差 δ ≈ (a × y)/D，其中 y 是屏幕上某纹到中央最大的距离。对第 n 级明纹，δ = nλ，因此 a × yₙ / D = nλ。条纹间距（相邻明纹距离）Δy = λD / a。该公式仅在 D ≫ a 时有效，以保证近似成立。WJEC 通常会给出该公式，但期望你熟练运用。
Δy = λD / a / 条纹间距 = λD / a
5. Factors Affecting Fringe Width | 影响条纹宽度的因素
h increases with longer wavelength λ and with larger screen distance D. It decreases with greater slit separation a. Therefore, red light produces wider fringes than blue light, and moving the screen farther away spreads the fringes. In exams, you may be asked to explain how to make fringes more distinct: increasing a improves brightness but reduces fringe width, so a compromise is needed.
由 Δy = λD / a 可知，条纹宽度随波长 λ 增大和屏幕距离 D 增大而增加，随双缝间距 a 增大而减小。因此，红光产生的条纹比蓝光宽，屏幕移远会使条纹扩展。在考试中，可能会要求解释如何使条纹更清晰：增大 a 可提高亮度但减少条纹宽度，因此需要折衷。
- Increase D → wider fringes / 增加 D → 条纹变宽
- Increase a → narrower fringes / 增加 a → 条纹变窄
- Red light (λ ≈ 700 nm) gives wider fringes than blue (λ ≈ 400 nm) / 红光（λ≈700 nm）比蓝光（λ≈400 nm）条纹宽
6. Measuring Wavelength of Light | 测量光的波长
Using a laser of known wavelength, you can verify the formula; conversely, by measuring Δy, D, and a, you can determine an unknown wavelength. Practical tip: measure the distance across multiple fringes (e.g., N fringes) and divide by N to get a more precise Δy. Use a travelling microscope or a ruler with a Vernier scale. WJEC practical tasks often involve this determination.
使用已知波长的激光，你可以验证公式；反之，通过测量 Δy、D 和 a，你可以确定未知波长。实验技巧：测量多条条纹（例如 N 条）的间距，再除以 N 以获得更精确的 Δy。使用移测显微镜或带游标的直尺。WJEC 的实践任务常涉及此测定。
| Quantity | Symbol | Typical measurement tool |
| Slit separation | a | Travelling microscope / graticule |
| Screen distance | D | Metre rule / tape measure |
| Fringe width | Δy | Travelling microscope or ruler (across many fringes) |
中文对照：双缝间距 a 用移测显微镜或分划板测量；屏距 D 用米尺或卷尺；条纹宽度 Δy 用移测显微镜或直尺（跨越多条条纹）测量。
7. Diffraction Gratings: An Extension | 衍射光栅：扩展内容
s d sin θ, where d is the slit spacing (d = 1/N, N = lines per metre). Constructive interference occurs when d sin θ = nλ, which gives the angle of the nth‑ much sharper, brighter maxima than a double slit, allowing precise wavelength measurement.
衍射光栅是一块刻有许多精细平行刻痕的玻璃板（例如每毫米 300 线）。相邻狭缝光线的光程差为 d sin θ，其中 d 是光栅常数（d = 1/N，N 为每米线数）。相长干涉的条件是 d sin θ = nλ，由此得出第 n 级亮纹的角度。光栅产生的亮纹比双缝尖锐得多、亮得多，允许精密测定波长。
d sin θ = nλ / 光栅公式
8. Order Numbers and Maximum Orders | 级数与最高级数
wards to first, second orders, etc. The highest possible order occurs when sin θ = 1, so nmax = d/λ. If λ is large (red light), nmax is smaller. WJEC questions frequently ask for the number of observable orders or the angle of a given order, requiring the grating formula and geometric reasoning.
整数 n 为级数。中央明纹为零级，向外依次为一级、二级等。最高可能级数出现在 sin θ = 1 时，因此 nmax = d/λ。若 λ 较大（红光），nmax 较小。WJEC 题目常要求计算可观察到的级数或给定级数的角度，需运用光栅公式和几何推理。
- For n = 1, first‑order bright image / n = 1 为一级明纹
- Maximum order nmax = d/λ (round down to nearest integer) / 最高级数 nmax = d/λ（向下取整）
- If nmax = 2.3, observable orders are 0, 1, 2 / 若 nmax = 2.3，可观察到的级数为 0、1、2
9. White Light and Spectra | 白光与光谱
When white light passes through a diffraction grating, the zero‑ less, while longer wavelengths (red) appear at larger angles. This produces a full spectrum for n ≥ 1, with violet nearest the centre and red farthest – opposite of dispersion by a prism. WJEC may ask you to compare grating and prism spectra.
当白光通过衍射光栅时，零级最大为白色，因为所有波长在 θ = 0 处都相长干涉。对于较高级次，较短波长（紫光）衍射角度较小，较长波长（红光）出现在较大角度。这产生了 n ≥ 1 级的完整光谱，紫光最靠近中心，红光最远 — 与棱镜色散相反。WJEC 可能要求比较光栅光谱和棱镜光谱。
Key comparison: Grating spectra have multiple overlapping orders; prism spectrum has a single continuous band. Grating spectra are more linear, while prism spectra compress the red end. / 关键比较：光栅光谱有多个重叠级次；棱镜光谱为单一连续带。光栅光谱更线性，棱镜光谱红端被压缩。
10. Thin‑Film Interference (Brief) | 薄膜干涉（简介）
Although not always examined in depth in WJEC, thin‑film interference (e.g., soap bubbles, oil on water) involves division of amplitude. Light reflects from the top and bottom surfaces of a thin film; the path difference depends on film thickness t and refractive index n. An extra phase change of π (equivalent to λ/2) occurs if reflection is from a medium of higher refractive index. This gives conditions for constructive (bright bands) and destructive (dark bands) interference. Familiarity with the principle helps with extension questions.
尽管 WJEC 并不总深入考查，但薄膜干涉（如肥皂泡、水面油膜）涉及分振幅干涉。光从薄膜上下表面反射；光程差取决于薄膜厚度 t 和折射率 n。若从较高折射率介质反射，会产生额外的 π 相位突变（相当于 λ/2）。由此得出相长（亮带）和相消（暗带）条件。熟悉原理有助于应对拓展题。
11. Common Misconceptions and Exam Traps | 常见误区与命题陷阱
ways convert using the wavelength relationship. Another trap is forgetting that the double‑slit formula Δy = λD/a applies to fringes on a screen far away, using the small‑ tion fails. Also, remember that intensity decreases away from the centre because of single‑slit diffraction envelope — this is not required for basic calculations but appears in qualitative questions.
学生常混淆光程差与相位差。务必利用波长关系进行转换。另一陷阱是忘记双缝公式 Δy = λD/a 适用于远处屏幕，采用小角近似；若角度较大，近似失效。此外，记住由于单缝衍射包络，远离中心的条纹强度递减 — 基础计算不要求此点，但在定性题中会出现。
- Coherent vs incoherent: no pattern without coherence / 相干与非相干：不具相干性则无干涉图样
- Δy = λD/a only for small θ / Δy = λD/a 仅适用于小 θ
- Brightness pattern from double slit is modulated by single‑slit diffraction / 双缝的亮度分布受到单缝衍射的调制
12. Summary of Key Equations and Final Tips | 核心公式总结与备考建议
Commit to memory the double‑slit fringe spacing and the grating equation. Practice using units: wavelength in metres (nm converted to m), slit spacing in metres, distance in metres. For WJEC papers, show clear working. In practical‑based questions, comment on uncertainties: using multiple fringe measurements reduces percentage error. Finally, always link theory to the wave model of light — interference is definitive proof of the wave nature of light.
熟记双缝条纹间距公式和光栅方程。练习单位使用：波长以米为单位（纳米转换为米），狭缝间距以米为单位，距离以米为单位。对于 WJEC 试卷，需展示清晰的解题步骤。在实验类问题中，评论不确定性：采用多条条纹测量可降低百分误差。最后，始终将理论与光的波动模型联系起来 — 干涉是光具有波动性的确凿证明。
Key: Δy = λD/a ; d sin θ = nλ / 核心公式
Final advice: draw a clear diagram of the double‑slit geometry, label a, D, y, and θ. That visual alone can solve many problems. / 最后建议：清晰绘制双缝几何示意图，标注 a、D、y 和 θ。仅这一图就能解决许多问题。
Published by TutorHao | Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图