Edexcel Physics: Diffraction of Light – Key Points | Edexcel 物理：光的衍射考点精讲

📚 Edexcel Physics: Diffraction of Light – Key Points | Edexcel 物理：光的衍射考点精讲

Light, as a wave, bends around obstacles and spreads into regions that would otherwise be shadowed. In the Edexcel A Level Physics specification, diffraction of light is a core component of the ‘Waves and Particle Nature of Light’ topic. Understanding how a single slit, a double slit, and a diffraction grating produce characteristic patterns is essential for both theoretical explanations and practical examinations. This revision guide systematically covers the key concepts, formulas, experimental setups, and common pitfalls students encounter when studying light diffraction.

光作为一种波，在遇到障碍物时会发生弯曲并传播到几何阴影区。在 Edexcel A Level 物理大纲中，光的衍射是“波与光的粒子性”主题的核心内容。理解单缝、双缝和衍射光栅如何产生特征图样，对于理论解释和实验考试都至关重要。本复习指南系统地梳理了学生在学习光的衍射时需要掌握的关键概念、公式、实验装置以及常见易错点。

1. What Is Diffraction? | 什么是衍射？

Diffraction is the spreading of a wave as it passes through an aperture or moves past an obstacle. The amount of spreading depends on the size of the aperture relative to the wavelength. Noticeable diffraction occurs when the aperture width is comparable to, or smaller than, the wavelength of the incident wave.

衍射是波在穿过缝隙或绕过障碍物时发生扩散的现象。扩散的程度取决于缝隙宽度与波长的相对大小。当缝隙宽度与入射波的波长相近或更小时，衍射现象最为显著。

In geometrical optics, light travels in straight lines and would produce a sharp shadow. However, diffraction explains why we see fringes of light and dark regions near the edge of an object, even when the source is coherent. This confirms the wave nature of light.

在几何光学中，光沿直线传播并会产生清晰的阴影。然而，衍射解释了为什么即使光源是相干的，在物体边缘附近仍能观察到明暗相间的条纹。这证实了光的波动性。

2. Huygens’ Principle – Why Diffraction Occurs | 惠更斯原理——衍射为何发生

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 all these wavelets. When a wavefront encounters a slit, the points across the slit width emit wavelets, which then interfere with each other, producing a diffraction pattern.

惠更斯原理指出，波前上的每一点都可以看作是一个次级球面子波的波源。下一时刻的新波前是所有这些子波的包络面。当波前到达狭缝时，狭缝上的各点都会发射子波，这些子波相互干涉，从而形成衍射图样。

If the slit is much wider than the wavelength, the wavelets from the centre and the edges largely cancel in the shadow region, resulting in a narrow beam. If the slit is narrow, the wavelets spread out significantly into the shadow region, demonstrating pronounced diffraction.

如果狭缝宽度远大于波长，来自中心和边缘的子波在阴影区域几乎完全抵消，从而形成窄光束。如果狭缝很窄，子波会大幅扩散到阴影区域，展现出明显的衍射。

3. Single-Slit Diffraction – The Experiment | 单缝衍射实验

A typical single-slit diffraction experiment uses a monochromatic laser directed at a narrow vertical slit. A screen is placed several metres away. The resulting pattern consists of a broad, bright central maximum flanked by alternating dark and bright fringes of decreasing intensity.

典型的单缝衍射实验使用单色激光照射一个竖直的窄缝。屏幕放置在几米之外。产生的图样由一个宽阔明亮的中央明纹和两侧强度递减的明暗相间条纹组成。

The central maximum is twice as wide as the secondary maxima and is the brightest. Dark fringes (minima) occur where destructive interference is complete. The intensity distribution can be predicted using phasor addition of wavelets from points across the slit.

中央明纹的宽度是次级明纹的两倍，也是最亮的。暗条纹（极小）出现在完全相消干涉的位置。强度分布可以通过狭缝上各点发出的子波的相量加法进行预测。

4. Dark Fringe Condition for Single Slit a sinθ = nλ | 单缝暗纹条件 a sinθ = nλ

For a single slit of width a, illuminated by light of wavelength λ, destructive interference occurs at angles θ satisfying the equation:

a sinθ = nλ

where n = ±1, ±2, ±3, … (n is the order of the dark fringe). The central maximum lies between n = -1 and n = +1.

对于宽度为 a 的单缝，以波长为 λ 的光照射时，在满足以下方程的角度 θ 处发生相消干涉：a sinθ = nλ，其中 n = ±1, ±2, ±3, …（n 是暗纹的级次）。中央明纹位于 n = -1 和 n = +1 之间。

This formula is derived by dividing the slit into two halves and requiring the path difference between a wavelet from the top of the slit and one from the midpoint to be λ/2. The same principle extends to higher orders by dividing the slit into an even number of equal segments.

该公式的推导是将狭缝分成两半，令狭缝顶部发出的子波与中点发出的子波之间的光程差为 λ/2。通过将狭缝平分成偶数段，同样的原理可以推广到高级次暗纹。

5. Width of the Central Maximum | 中央明纹的宽度

The angular half-width of the central maximum is given by the first minimum: sinθ ≈ θ = λ / a for small angles. The full angular width is therefore 2λ / a. On a screen at distance D from the slit, the linear width of the central bright region is approximately:

Δy ≈ 2λD / a

中央明纹的半角宽度由第一暗纹决定：对于小角度，sinθ ≈ θ = λ / a。因此整个角宽度为 2λ / a。在距离狭缝 D 的屏幕上，中央亮纹的线宽度近似为 Δy ≈ 2λD / a。

This relationship shows that narrowing the slit (smaller a) increases the width of the central maximum, making diffraction more pronounced. It also indicates that longer wavelengths produce wider fringes, which is crucial when observing white light diffraction.

这一关系表明，减小狭缝宽度（a 变小）会使中央明纹变宽，衍射更加显著。它还表明，波长越长条纹越宽，这在使用白光观察衍射时至关重要。

6. Diffraction Gratings – Construction and Principle | 衍射光栅——结构与原理

A diffraction grating consists of a large number of equally spaced parallel slits (or grooves), typically several hundred per millimetre. The distance between adjacent slits is called the grating spacing d. It is the reciprocal of the number of lines per unit length: d = 1 / N (e.g., if N = 300 lines per mm, d = 1×10⁻³ m / 300 = 3.33×10⁻⁶ m).

衍射光栅由大量等间距的平行狭缝（或刻槽）组成，通常每毫米有数百条。相邻狭缝之间的距离称为光栅常数 d，它是单位长度内线条数的倒数：d = 1 / N（例如，若 N = 300 条/毫米，则 d = 1×10⁻³ m / 300 = 3.33×10⁻⁶ m）。

Because there are many slits, the constructive interference peaks are very sharp and bright. The multiple-slit interference pattern is superimposed on the single-slit diffraction envelope, but for a grating with narrow slits, the single-slit effect mainly modulates the intensity of the orders.

由于有许多狭缝，相长干涉的明纹变得非常锐利和明亮。多缝干涉图样叠加在单缝衍射包络上，但对于狭缝很窄的光栅，单缝效应主要调制各级明纹的强度。

7. The Grating Equation d sinθ = nλ | 光栅方程 d sinθ = nλ

For a transmission diffraction grating, the principal maxima occur when the path difference between waves from adjacent slits is an integer multiple of the wavelength. This gives the grating equation:

d sinθ = nλ

where n = 0, ±1, ±2, ±3, … (the order number). The zeroth order (n = 0) is the direct beam; first order (n = 1) appears on either side, and so on.

对于透射式衍射光栅，当相邻狭缝发出的波之间的光程差为波长的整数倍时，出现主极大。由此得出光栅方程：d sinθ = nλ，其中 n = 0, ±1, ±2, ±3, …（级次）。零级（n = 0）是直射光束；一级（n = 1）出现在两侧，依此类推。

This equation is the key tool for measuring the wavelength of light. By finding the angle θ for a given order and using the known grating spacing d, the wavelength λ can be calculated. The maximum possible order is limited by n ≤ d / λ, because sinθ cannot exceed 1.

该方程是测量光波长的关键工具。通过测得某一级次的衍射角 θ 并使用已知的光栅常数 d，即可计算出波长 λ。最高可能级次受限于 n ≤ d / λ，因为 sinθ 不能大于 1。

8. Determining the Wavelength of Light Using a Grating | 利用光栅测定光波长

In a practical, students set up a laser perpendicular to a grating and record the positions of the bright spots on a screen. The angle θ is found by measuring the distance from the central maximum to the nth order bright spot, x, and the grating-to-screen distance D, using tanθ = x / D. If the angle is small, θ ≈ x / D, but for larger angles the full trig calculation is needed.

在实验中，学生将激光垂直照射光栅，并记录屏幕上亮斑的位置。通过测量从中央亮纹到第 n 级亮斑的距离 x，以及光栅到屏幕的距离 D，利用 tanθ = x / D 求得 θ。若角度较小，θ ≈ x / D，但角度较大时需要进行完整的三角函数计算。

Substituting d, θ, and n into d sinθ = nλ gives λ. Common safety precautions include avoiding direct eye exposure to the laser and handling the grating by its edges. The experiment is a standard way to demonstrate the wave nature of light and to verify the relationship between wavelength, grating spacing, and fringe spacing.

将 d、θ 和 n 代入 d sinθ = nλ 即可求得 λ。常见的安全预防措施包括避免激光直射眼睛以及手持光栅边缘。该实验是证明光的波动性并验证波长、光栅常数及条纹间距之间关系的标准方法。

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

When a diffraction grating is illuminated by white light, each wavelength component is diffracted at a slightly different angle. This produces a continuous spectrum for each order (except n = 0). The violet end of the spectrum is closest to the central maximum, while red is deviated the most, because sinθ is proportional to λ.

当用白光照射衍射光栅时，不同波长的光会以略微不同的角度衍射。这导致每个级次（n = 0 除外）都产生一个连续光谱。紫光最靠近中央明纹，红光偏离最大，因为 sinθ 与 λ 成正比。

At higher orders, the spectra may overlap: the blue end of the second order can coincide with the red end of the first order. This overlap can be predicted by comparing the angular positions for different n and λ. The grating acts as a dispersive element, similar to a prism, but with a linear relationship between sinθ and λ rather than a material-dependent dispersion.

在更高级次，光谱可能会重叠：第二级的紫端可能与第一级的红端重合。通过比较不同 n 和 λ 的角度位置可以预测这种重叠。光栅充当了类似于棱镜的色散元件，但其 sinθ 与 λ 呈线性关系，而非依赖于材料的色散。

10. Comparison: Single Slit vs Diffraction Grating | 对比：单缝与衍射光栅

It is important to distinguish the patterns and formulas. A single wide slit produces a broad central maximum and weaker secondary fringes, with minima given by a sinθ = nλ. A grating produces a series of very sharp, equally spaced (in sinθ) principal maxima, with the equation d sinθ = nλ.

区分图样和公式非常重要。单条宽缝产生宽阔的中央明纹和较弱的次级条纹，暗纹条件为 a sinθ = nλ。光栅产生一系列非常锐利、在 sinθ 上等间距分布的主极大，其方程为 d sinθ = nλ。

Key differences:

Single slit: minima condition a sinθ = nλ; central maximum width is 2λD / a.
单缝：暗纹条件 a sinθ = nλ；中央明纹宽度为 2λD / a。
Diffraction grating: maxima condition d sinθ = nλ; angular separation between orders is determined by d.
衍射光栅：明纹条件 d sinθ = nλ；级次之间的角间隔由 d 决定。
Grating fringes are much narrower and brighter, enabling precise wavelength measurements.
光栅条纹更窄更亮，从而能够实现精确的波长测量。
Double slit (Young’s fringes) is an interference pattern with a diffraction envelope; fringe width w = λD / s where s is slit separation.
双缝（杨氏条纹）是带有衍射包络的干涉图样；条纹宽度 w = λD / s，其中 s 为缝间距。

11. Exam Tips and Common Misconceptions | 考试技巧与常见误区

Edexcel exam questions often ask students to calculate the number of lines per mm from a given d, or to find the highest order visible. Always convert distances to metres and recall that d = 1 / N. When calculating d from ‘lines per mm’, remember that 300 lines per mm means 300 000 lines per metre, so d = 1 / 300 000 m.

Edexcel 考题经常要求学生根据给定的 d 计算每毫米的刻线数，或找出可见的最高级次。始终将距离单位转换为米，并牢记 d = 1 / N。当根据“每毫米线数”计算 d 时，记住 300 线/毫米即每米 300 000 线，因此 d = 1 / 300 000 m。

Common pitfalls include confusing a sinθ = nλ with d sinθ = nλ, using the wrong angle (e.g., confusing the angle from the central maximum with the angle between two first-order maxima), and forgetting that the central maximum is twice as wide for single-slit diffraction. Also, in white light questions, be prepared to describe the appearance of overlapping orders.

常见错误包括混淆 a sinθ = nλ 与 d sinθ = nλ，使用了错误的角度（例如将偏离中央明纹的角度误认为两个一级明纹之间的夹角），以及忘记单缝衍射中中央明纹宽度是其他明纹的两倍。此外，在白光问题中，要准备好描述光谱重叠现象。

Always check the unit of wavelength (often nanometres) and ensure your calculator is in degree mode when working with sinθ. For graph questions, plotting sinθ against n gives a straight line with gradient λ / d, from which λ can be found if d is known.

务必检查波长的单位（通常为纳米），并确保在使用 sinθ 时计算器处于角度模式。在图像分析题中，绘制 sinθ 对 n 的图像会得到一条斜率为 λ / d 的直线，若已知 d 则可求得 λ。

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Edexcel Physics: Diffraction of Light – Key Points | Edexcel 物理：光的衍射考点精讲