Diffraction of Light: IB WJEC Physics Key Points | 光的衍射：IB WJEC物理考点精讲

📚 Diffraction of Light: IB WJEC Physics Key Points | 光的衍射：IB WJEC物理考点精讲

Diffraction is a fundamental wave phenomenon that provides compelling evidence for the wave nature of light. In IB and WJEC Physics, understanding single‑slit diffraction, diffraction gratings, and the associated equations is essential for tackling both theoretical problems and practical examination questions. This revision guide breaks down every critical concept you need to master, from Huygens’ Principle to the Rayleigh criterion, ensuring you are fully prepared for your exam.

衍射是一种基本的波动现象，为光的波动性提供了令人信服的证据。在 IB 和 WJEC 物理课程中，理解单缝衍射、衍射光栅以及相关方程，对于解决理论问题和实际考试题目都至关重要。本复习指南将逐一剖析你需要掌握的所有关键概念，从惠更斯原理到瑞利判据，确保你为考试做好充分准备。

1. What is Diffraction? | 什么是衍射？

Diffraction is the bending and spreading of waves when they encounter an obstacle or pass through a narrow opening. The amount of spreading depends on the ratio of the wavelength λ to the size of the aperture or obstacle a. When the aperture is comparable to the wavelength, the effect is most pronounced.

衍射是波遇到障碍物或穿过窄缝时发生的弯曲和扩展现象。扩展的程度取决于波长 λ 与孔径或障碍物大小 a 的比值。当孔径与波长可比拟时，衍射效应最为显著。

For light, diffraction explains why shadows are not perfectly sharp and why we can observe interference patterns behind single slits and gratings. It is a direct consequence of the wave model; geometric optics alone cannot account for these observations.

对于光而言，衍射解释了为什么影子并非完全清晰，以及为什么在单缝和光栅之后能观察到干涉图样。这是波动模型的直接结果；仅靠几何光学无法解释这些现象。

In the IB and WJEC syllabuses, diffraction is often demonstrated using a laser and a single slit or a diffraction grating, linking it to measurements of wavelength and the analysis of spectra.

在 IB 和 WJEC 教学大纲中，衍射通常通过激光与单缝或衍射光栅进行演示，从而与波长的测量和光谱分析联系起来。

2. Huygens’ Principle and Diffraction | 惠更斯原理与衍射

Huygens’ Principle states that every point on a wavefront acts as a source of secondary spherical wavelets. The new wavefront at a later time is the envelope of these wavelets. This principle elegantly explains how diffraction occurs: when part of a wavefront is obstructed by a barrier, the secondary wavelets from the unobstructed portion spread into the geometric shadow region.

惠更斯原理指出，波前上的每一点都可以视为次级球面子波的波源。后续时刻的新波前就是这些子波的包络面。该原理优雅地解释了衍射如何发生：当波前的一部分被障碍物阻挡时，未被阻挡部分的次级子波会扩展到几何阴影区域中。

In the context of a single slit, each point across the slit width acts as a source of secondary wavelets. The superposition of these wavelets at a distant screen gives rise to the characteristic diffraction pattern with a broad central maximum and progressively fainter secondary maxima.

在单缝的情形中，缝宽上每一点都充当次级子波的波源。这些子波在远处屏幕上的叠加，就产生了具有宽阔中央亮纹和逐渐变弱的次级亮纹的特征衍射图样。

This principle is fundamental to understanding not only diffraction but also interference, and it is a key concept WJEC and IB examiners love to link to wave propagation.

这一原理不仅是理解衍射的基础，也是理解干涉的基础，它是 WJEC 和 IB 考官都喜欢与波的传播联系起来考查的关键概念。

3. Single-Slit Diffraction Pattern | 单缝衍射图样

When monochromatic light passes through a narrow single slit of width a, a diffraction pattern is formed on a distant screen. The pattern consists of a very bright, wide central maximum flanked on either side by a series of narrower, less intense secondary maxima separated by completely dark minima.

当单色光通过一个宽度为 a 的窄单缝时，在远处屏幕上会形成衍射图样。该图样由一个非常明亮、宽阔的中央亮纹以及两侧一系列较窄、强度较弱的次级亮纹组成，亮纹之间是完全暗的极小位置。

The central maximum covers an angular width of 2θ₁, where θ₁ corresponds to the first minimum. The intensity drops rapidly after the central peak; the secondary maxima are much fainter, and their intensity decreases with increasing order.

中央亮纹的角宽度为 2θ₁，其中 θ₁ 对应于第一极小。中央峰之后强度迅速下降；次级亮纹要暗得多，且随着级数增加强度递减。

This pattern differs fundamentally from an interference pattern produced by two slits: in a single-slit diffraction pattern, the central band is twice as wide as the outer bands, and the intensity variation is governed purely by diffraction.

这种图样与双缝产生的干涉图样有本质区别：在单缝衍射图样中，中央亮带宽度是外侧亮带宽度的两倍，并且强度变化完全由衍射决定。

4. Intensity Distribution and Minima Condition | 单缝强度分布与极小条件

For single‑slit diffraction, the positions of the dark fringes (minima) are given by the condition:

a sin θ = nλ (n = 1, 2, 3, …)

其中 a is the slit width, θ is the angle measured from the centre to the n‑th minimum, λ is the wavelength of the light, and n is a positive integer. There is no central minimum at n = 0.

对于单缝衍射，暗纹（极小）的位置由以下条件给出：

a sin θ = nλ (n = 1, 2, 3, …)

其中 a 是缝宽，θ 是从中心到第 n 级暗纹的角度，λ 是光的波长，n 为正整数。在 n = 0 处没有暗纹。

The angular half‑width of the central maximum is therefore θ₁ = arcsin(λ/a). For small angles, sin θ ≈ θ in radians, and the half‑width is approximately λ/a. This shows that a narrower slit produces a wider diffraction pattern.

因此，中央亮纹的半角宽度为 θ₁ = arcsin(λ/a)。对于小角度，以弧度为单位的 sin θ ≈ θ，半角宽度约为 λ/a。这表明缝越窄，衍射图样越宽。

Light reaching the screen at angles where the path difference between wavelets from the top and centre of the slit is λ/2 leads to destructive interference; this generalises to the condition a sin θ = nλ for complete darkness. The intensity variation can be expressed as I = I₀(sin β/β)², where β = (πa sin θ)/λ. This is provided for deeper understanding but not always required for basic calculations.

当从缝顶和缝中心发出的子波之间的光程差为 λ/2 时，到达屏幕的光发生相消干涉；这推广到完全暗纹的条件 a sin θ = nλ。强度变化可以表示为 I = I₀(sin β/β)²，其中 β = (πa sin θ)/λ。这用于加深理解，但基础计算中不总是需要。

5. Diffraction Grating Basics | 衍射光栅基础

A diffraction grating consists of a large number of equally spaced, identical parallel slits. When monochromatic light passes through a grating, the combined effects of diffraction and interference produce a pattern of very sharp, bright principal maxima at specific angles.

衍射光栅由大量等间距、完全相同的平行狭缝组成。当单色光通过光栅时，衍射和干涉的综合效应会在特定角度产生非常锐利、明亮的主极大。

Gratings are characterised by their slit separation d (the distance between the centres of adjacent slits), which is often expressed as the reciprocal of the number of lines per unit length, e.g. 1/N for N lines per metre. Typical transmission gratings have 300 to 1200 lines per millimetre.

光栅的特征参数是缝间距 d（相邻狭缝中心之间的距离），通常表示为单位长度线数的倒数，例如每米 N 条线时 d = 1/N。典型的透射光栅每毫米有 300 至 1200 条线。

Because a grating involves many slits, the maxima are much narrower and brighter than those produced by a double slit, making gratings excellent tools for spectroscopy and precise wavelength measurements.

由于光栅包含许多狭缝，其亮纹比双缝产生的亮纹窄得多、也亮得多，使得光栅成为光谱学和精确波长测量的绝佳工具。

6. The Grating Equation | 光栅方程

For a diffraction grating, constructive interference occurs when the path difference between waves from adjacent slits is an integer multiple of the wavelength. This gives the famous grating equation:

d sin θ = nλ (n = 0, 1, 2, 3, …)

其中 d is the slit separation, θ is the angle of the n‑th order maximum measured from the central (zero‑order) maximum, and n is the order number.

对于衍射光栅，当相邻狭缝发出的波之间的光程差为波长的整数倍时，发生相长干涉。这就得到了著名的光栅方程：

d sin θ = nλ (n = 0, 1, 2, 3, …)

其中 d 是缝间距，θ 是从中央（零级）亮纹测得的第 n 级亮纹的角度，n 是级数。

The zero‑order maximum (n = 0) is always at θ = 0 and is the brightest. Higher‑order maxima appear symmetrically on both sides. The number of observable orders is limited by the fact that sin θ cannot exceed 1, so n ≤ d/λ. This is a common examination point: if d is smaller or λ is larger, fewer orders are visible.

零级亮纹（n = 0）总是位于 θ = 0 且最亮。更高级的亮纹对称出现在两侧。可观察到的级数受到 sin θ 不能超过 1 的限制，因此 n ≤ d/λ。这是常见的考点：如果 d 较小或 λ 较大，能看到的级数就更少。

In calculations, it is crucial to use the same units for d and λ, and to remember that the equation applies to each wavelength independently. For a mixed light source, each wavelength produces its own set of maxima.

在计算中，务必将 d 和 λ 使用相同的单位，并记住该方程对每个波长独立适用。对于混合光源，每个波长都会产生自己的一组亮纹。

7. White Light Diffraction and Spectra | 白光衍射与光谱

When white light is incident on a diffraction grating, the central zero‑order maximum is white because all wavelengths overlap at θ = 0. However, for n ≠ 0, the angle θ depends on wavelength, so the grating disperses the light into its constituent colours, producing a continuous spectrum.

当白光照射到衍射光栅上时，中央零级亮纹是白色的，因为所有波长在 θ = 0 处重叠。然而，对于 n ≠ 0，角度 θ 依赖于波长，因此光栅会将光色散成其组成颜色，产生连续光谱。

Since d sin θ = nλ, a longer wavelength (red) is diffracted through a larger angle than a shorter wavelength (violet). Hence, in each order, the spectrum appears with violet closest to the centre and red furthest away. This is reversed relative to dispersion in a prism, where red is deviated least.

由于 d sin θ = nλ，较长波长（红色）的衍射角比较短波长（紫色）的更大。因此，在每一级光谱中，紫色靠近中心，红色在最外侧。这与棱镜中的色散相反，棱镜中红色偏折最小。

Overlapping of higher‑order spectra can occur: for example, the violet end of the third‑order spectrum may overlap with the red end of the second‑order spectrum. This is an important concept in grating spectroscopy that exam questions often test.

较高级次的光谱可能会发生重叠：例如，第三级光谱的紫端可能与第二级光谱的红端重叠。这是光栅光谱学中的一个重要概念，常出现在考题中。

8. Resolving Power and the Rayleigh Criterion | 分辨率与瑞利判据

The ability of a diffraction grating or any optical instrument to separate two closely spaced wavelengths is described by its resolving power R. For a grating, R = λ/Δλ = nN, where N is the total number of lines illuminated and n is the order number. This means a grating with more lines and used in a higher order can distinguish finer differences in wavelength.

衍射光栅或任何光学仪器区分两个相近波长的能力由其分辨率 R 描述。对于光栅，R = λ/Δλ = nN，其中 N 是被照明的总线数，n 是级数。这意味着具有更多线数并在更高级次使用的光栅能够分辨更细微的波长差异。

The Rayleigh criterion defines the limit of resolution: two neighbouring points or spectral lines are just resolved when the central maximum of one diffraction pattern coincides with the first minimum of the other. For a circular aperture of diameter D, the minimum angular separation is θ = 1.22 λ / D. For a single slit of width a, the criterion involves a sin θ ≈ λ.

瑞利判据定义了分辨极限：当一个衍射图样的中央亮纹与另一个的第一暗纹重合时，这两个相邻的点或谱线恰好能被分辨。对于直径为 D 的圆孔，最小角间距为 θ = 1.22 λ / D。对于宽度为 a 的单缝，该判据涉及 a sin θ ≈ λ。

Although the Rayleigh criterion is often associated with telescopes and microscopes, WJEC and IB may examine it in the context of resolving spectral lines with a grating, helping students appreciate the limits of any wave‑based optical system.

尽管瑞利判据常与望远镜和显微镜相关联，WJEC 和 IB 可能会在光栅分辨谱线的背景下考查它，帮助学生理解任何基于波动的光学系统的局限性。

9. Key Experiments and Practical Skills | 关键实验与实验技能

A standard practical in both syllabuses is measuring the wavelength of laser light using a diffraction grating. You direct a laser beam normally through a grating onto a distant screen or wall, measure the distance from the grating to the screen (L) and the distance from the central maximum to the first‑order spot (y). Using tan θ ≈ y/L and the small‑angle approximation sin θ ≈ θ, the wavelength is calculated via λ = (d y)/(nL) for n = 1.

两个大纲中的标准实验都是使用衍射光栅测量激光的波长。你将激光束垂直照射到光栅上，在远处的屏幕或墙上形成图样，测量光栅到屏幕的距离 (L) 以及从中央亮纹到一级亮点的距离 (y)。利用 tan θ ≈ y/L 和小角度近似 sin θ ≈ θ，对于 n = 1，波长可通过 λ = (d y)/(nL) 计算。

In WJEC practical assessments, safe use of lasers, accurate alignment, and understanding of uncertainties (e.g. measuring y on both sides and halving) are emphasised. IB internal assessments often involve this experiment with detailed error analysis.

在 WJEC 实验评估中，强调激光的安全使用、精确对准以及对不确定度的理解（例如测量两侧的 y 并取平均）。IB 内部评估通常包含这一实验，并进行详细的误差分析。

Another important demonstration is observing white‑light spectra with a grating and explaining the rainbow patterns. Students should be able to sketch the pattern and describe why red is deviated more than blue.

另一个重要的演示是用光栅观察白光光谱并解释彩虹图样。学生应能绘制该图样，并说明为什么红色比蓝色偏折更大。

10. Common Misconceptions and Exam Traps | 常见误解与考试陷阱

Many students confuse the single‑slit equation a sin θ = nλ (for minima) with the grating equation d sin θ = nλ (for maxima). A useful memory aid is that ‘a’ (aperture) is for single‑slit dark fringes, while ‘d’ (distance between slits) is for grating bright fringes. Mixing them up is a classic error.

许多学生将单缝方程 a sin θ = nλ（用于暗纹）与光栅方程 d sin θ = nλ（用于亮纹）混淆。一个有用的记忆方法是“a”（aperture，孔径）用于单缝暗纹，而“d”（distance，缝距）用于光栅亮纹。混淆二者是经典错误。

Another pitfall is forgetting that the formula sin θ = nλ/d only works if d > nλ, otherwise no finite angle exists and that order is not visible. Always check that sin θ is ≤ 1 before calculating an angle.

另一个易错点是忘记公式 sin θ = nλ/d 只有在 d > nλ 时才成立，否则不存在有限的衍射角，该级次不可见。在计算角度之前，务必检查 sin θ ≤ 1。

In qualitative descriptions, students sometimes say ‘diffraction causes light to bend’ without linking it to wavelength or aperture size. Always relate the degree of diffraction to the ratio λ/a: a large wavelength relative to the gap gives significant spreading.

在定性描述中，学生有时会说“衍射导致光弯曲”而不将其与波长或孔径尺寸联系起来。务必将衍射程度与比值 λ/a 关联：相对于缝宽较大的波长会导致显著的扩展。

11. Summary and Revision Checklist | 总结与复习清单

Mastering diffraction for IB and WJEC Physics means you can confidently sketch and label single‑slit and grating patterns, apply the equations a sin θ = nλ and d sin θ = nλ in the correct contexts, explain white‑light spectra, perform calculations with appropriate units, and outline the Rayleigh criterion for resolution.

掌握 IB 和 WJEC 物理中的衍射意味着你能够自信地绘制并标注单缝和光栅图样，在正确的背景下应用方程 a sin θ = nλ 和 d sin θ = nλ，解释白光光谱，使用适当单位进行计算，并概述分辨率的瑞利判据。

Single‑slit minima: a sin θ = nλ (n = 1,2,3…), with a as slit width.
单缝暗纹: a sin θ = nλ (n = 1,2,3…)，a 为缝宽。
Grating maxima: d sin θ = nλ (n = 0,1,2…), with d = 1/N.
光栅亮纹: d sin θ = nλ (n = 0,1,2…)，d = 1/N。
Small‑angle approximations: sin θ ≈ tan θ ≈ θ (in radians) when θ is small.
小角度近似: 当 θ 很小时，sin θ ≈ tan θ ≈ θ（弧度）。
White light: central white, spectra with violet innermost, red outermost.
白光: 中央白色，光谱中紫色最内侧，红色最外侧。
Resolution: Rayleigh criterion; grating resolving power R = nN.
分辨率: 瑞利判据；光栅分辨率 R = nN。

Revisit typical past‑paper questions on determining wavelength, predicting the number of orders, and comparing diffraction with interference. With these fundamentals secured, you will tackle any diffraction question with clarity.

重温历年真题中关于测定波长、预测可见级数以及比较衍射与干涉的题目。掌握这些基础后，你将能清晰地应对任何衍射题目。

Published by TutorHao | Physics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）

Diffraction of Light: IB WJEC Physics Key Points | 光的衍射：IB WJEC物理考点精讲