📚 A-Level Physics: Diffraction of Light – Exam-Focused Revision | A-Level 物理：光的衍射 考点精讲
Diffraction is a hallmark of wave behaviour and a cornerstone of A-Level physics. It describes how light bends around obstacles or spreads after passing through a narrow opening, producing characteristic bright and dark fringes. Mastering diffraction means understanding the conditions for observable patterns, applying the single‑slit and grating equations, and recognising how diffraction limits optical instruments such as telescopes. This article unpacks every key idea you need for the exam, from fundamental principles to common pitfalls, with paired English‑Chinese explanations.
衍射是波动学的一个标志性特征，也是 A-Level 物理的核心考点。它描述了光如何绕过障碍物或通过狭缝后发生扩散，形成明暗相间的图样。掌握衍射需要理解明显衍射的条件、熟练运用单缝和光栅方程，并能分析衍射对望远镜等光学仪器的限制。本文逐一拆解考试必需的关键概念，从基本原理到常见易错点，全部采用中英双语对照讲解。
1. What Is Diffraction? | 什么是衍射？
Diffraction is the spreading of a wave when it passes through a gap or around an obstacle. Instead of travelling in straight lines only, the wavefronts bend into the geometrical shadow. This behaviour is shared by all waves – sound, water, and electromagnetic radiation such as light. The observation of diffraction in light experiments was historically critical in establishing its wave nature.
衍射是指波在穿过狭缝或绕过障碍物时发生扩展的现象。波前不再是直线传播，而是会弯入几何阴影区。声波、水波以及包括光在内的电磁波都会产生衍射。在历史上，光衍射现象的观测对于确立光的波动说起到了至关重要的作用。
2. Conditions for Noticeable Diffraction | 明显衍射的条件
For diffraction to be easily observed, the size of the opening or obstacle must be comparable to the wavelength. Visible light has wavelengths roughly between 400 nm and 700 nm, which is tiny on everyday scales. That is why you do not see obvious diffraction when light passes through a wide doorway; the gap is millions of times larger than the wavelength. In the lab we use slits just a fraction of a millimetre wide or diffraction gratings with thousands of lines per centimetre to make the effect visible.
要让衍射现象显著，狭缝或障碍物的尺寸必须与波长相当。可见光的波长大约在 400 nm 至 700 nm 之间，相对于日常尺度非常微小。这就是为什么光通过宽大的门时看不出明显弯曲——缝隙比波长大数百万倍。在实验室中，我们需要使用只有零点几毫米的单缝或每厘米数千条刻线的衍射光栅，才能清楚地看到衍射效应。
3. Single‑Slit Diffraction: Experimental Setup | 单缝衍射的实验装置
A typical A‑Level setup uses a monochromatic laser, a single slit of known width, and a screen placed several metres away. The laser beam illuminates the slit, and the resulting pattern is captured on the screen. Because the laser provides coherent light, the pattern appears steady and sharp without additional conditioning. Measurements of fringe positions allow the slit width or the wavelength to be determined using the single‑slit equation.
典型的 A-Level 实验装置包括单色激光器、已知宽度的单缝和几米远的屏幕。激光束照射到狭缝上，从屏幕上就能观察到衍射图样。由于激光本身就提供相干光，因此无需额外处理即可获得稳定、清晰的条纹。通过测量条纹的位置，可以利用单缝方程求出缝宽或波长。
4. Single‑Slit Diffraction Pattern | 单缝衍射图样
The pattern consists of a broad, bright central maximum flanked by a series of progressively dimmer secondary maxima. Dark fringes (minima) separate these bright bands. The central maximum is roughly twice as wide as the subsidiary maxima, and its intensity is far greater. The continuous variation in brightness is a direct consequence of interference of wavelets from every point across the slit.
单缝衍射图样的中央是一条宽而亮的极大，两侧对称分布着强度逐级递减的次级极大，它们之间由暗纹（极小）隔开。中央亮纹的宽度大约是次级亮纹的两倍，而且强度远高于其它亮纹。这种亮度的连续变化是来自单缝各点发出的子波相互干涉的直接结果。
5. Single‑Slit Minima Equation | 单缝暗纹公式
The positions of the dark fringes obey a simple relationship:
a sinθ = nλ, n = 1, 2, 3, …
where a is the slit width, θ is the angle of the dark fringe measured from the centre, λ is the wavelength, and n is the order number (not zero). The central maximum is bounded by the first minima at n = 1. This formula is crucial for analysing single‑slit experiments and often appears in numerical questions.
暗纹的角位置满足一个简洁的关系：a sinθ = nλ，其中 a 是缝宽，θ 是从中心量起的暗纹角，λ 是波长，n 取 1, 2, 3……（注意 n ≠ 0）。中央极大以两侧 n = 1 的暗纹为界。这个公式是分析单缝实验的核心，经常在计算题中直接考查。
6. Effect of Slit Width and Wavelength | 缝宽与波长的影响
If the slit is made narrower (smaller a), sinθ must increase for a given n, so the dark fringes move further apart – the pattern spreads. The same effect occurs if the wavelength is increased while keeping the slit width constant. This inverse relationship means that red light gives a wider diffraction pattern than blue light when the same slit is used. Exam questions frequently ask you to predict changes in the pattern when a different colour or a slit of altered width is used.
缝宽变窄（a 减小）时，要保持 n 不变则 sinθ 必须增大，于是暗纹向外移动，整个图样变宽。如果保持缝宽不变而增大波长，也会产生同样的扩散效果。这种反比关系意味着使用同一条单缝时，红光的衍射图样比蓝光更宽。考试中经常要求预判更换光源颜色或改变缝宽后图样如何变化。
7. White Light Single‑Slit Diffraction | 白光单缝衍射
When white light is used instead of a laser, each component wavelength produces its own overlapping diffraction pattern. The central maximum remains white because all colours are brought together at θ = 0. On either side, spectra appear with violet on the inner edge and red on the outer edge. This is because red light, having a longer wavelength, diffracts more and is found at a larger angle for each order. Recognising this colour sequence helps in questions on superposition and dispersion.
如果使用白光代替激光，各波长成分会形成各自的衍射图样并相互叠加。中央极大仍为白色，因为在 θ = 0 处所有颜色汇聚一地。两侧则会出现光谱，并且内沿为紫色、外沿为红色。这是因为红光波长较长，衍射角度更大，因此在同级条纹中出现在更外侧。掌握这一彩色序列有助于应对有关叠加和色散的问题。
8. Diffraction Grating: Many Slits | 衍射光栅：多缝的概念
A diffraction grating consists of a large number of equally spaced, identical slits. The spacing between adjacent slits is called the grating constant d, and is often expressed as d = 1/N, where N is the number of lines per metre. Because many coherent sources contribute, the bright maxima are extremely sharp and well separated, making the grating ideal for accurate wavelength measurements.
衍射光栅由大量等间距且完全相同的狭缝构成。相邻狭缝的间距称为光栅常数 d，通常表示为 d = 1/N，其中 N 为每米长度的刻线数。由于大量相干光源的共同贡献，亮纹极为锐利且分离清晰，光栅因此非常适用于精确测量波长。
9. The Grating Equation | 光栅方程
The condition for constructive interference from a grating is:
d sinθ = nλ, n = 0, 1, 2, …
Here d is the slit separation, θ is the angle of the nth‑order bright maximum, and λ is the wavelength. The zeroth order (n = 0) corresponds to the straight‑through beam. Higher orders appear symmetrically either side. This equation assumes that the incident light is normal to the grating, which is the standard exam case.
光栅产生相长干涉的条件为：d sinθ = nλ，其中 d 是狭缝间距，θ 是第 n 级亮纹的角度，λ 是波长。n = 0 对应零级主极大，即直射光束。更高级次的亮纹对称分布在零级两侧。该方程假设光线垂直入射到光栅表面，这是考试的标准设定。
10. Measuring Wavelength with a Grating | 用光栅测量波长
A standard practical investigation involves shining a laser of unknown wavelength onto a grating of known line spacing and measuring the angles of the first‑order (or higher) peaks. Using the equation d sinθ = nλ, the wavelength can be calculated. To improve accuracy, students often measure the angle for the second or third order and divide accordingly. Common error sources include misalignment of the grating and incorrect angle readings from the spectrometer.
标准的实验操作是将波长未知的激光照射到已知刻线间距的光栅上，测量第一级（或更高级）亮纹的角度，再代入 d sinθ = nλ 计算出波长。为提高精度，通常测量第二或第三级的角位置并相应折算。常见误差来源包括光栅未垂直于入射光，以及分光计的角度读数不准确。
11. Maximum Orders and Spectral Overlap | 最大级数与光谱重叠
Since sinθ cannot exceed 1, the maximum possible order nmax is the integer part of d/λ. For a 600 lines per mm grating and green light (λ ≈ 550 nm), d ≈ 1.67 × 10⁻⁶ m, so nmax ≈ 3. Only three orders (0, ±1, ±2, ±3) will be visible. When a white light source is used, spectra from adjacent orders may overlap; for example, the violet end of the third order might overlap with the red end of the second order. Recognising such overlaps is a frequent extension question.
由于 sinθ 不能大于 1，最大可能级次 nmax 即为 d/λ 的整数部分。例如对于 600 线/毫米的光栅和绿光（λ ≈ 550 nm），d ≈ 1.67 × 10⁻⁶ m，nmax ≈ 3，因此只能看到 0、±1、±2、±3 级。若使用白光光源，相邻级次的光谱可能发生重叠，比如第三级的紫端可能与第二级的红端交叠。识别这种光谱重叠是常见的拔高考题。
12. Diffraction Limit and Rayleigh Criterion | 衍射极限与瑞利判据
Diffraction also sets a fundamental limit on the resolving power of optical instruments. The Rayleigh criterion states that two point sources are just resolved when the central maximum of one diffraction pattern falls on the first minimum of the other. For a circular aperture such as a telescope objective, the minimum resolvable angle is approximately θ ≈ 1.22λ/D, where D is the aperture diameter. In a simplified single‑slit analysis, the angular resolution is often given as θ ≈ λ/a. This concept explains why larger telescopes can distinguish finer details and is a common synoptic topic linking waves and optics.
衍射同样限定了光学仪器的分辨能力。瑞利判据指出，当一个衍射图样的中央极大刚好落在另一个的第一暗纹上时，这两个点源恰能分辨。对于望远镜物镜等圆形孔径，最小可分辨角约为 θ ≈ 1.22λ/D（D 为孔径直径）。在简化的单缝模型中，角分辨率常写为 θ ≈ λ/a。这个概念解释了为何更大的望远镜能看清更细微的结构，也是联系波动学和光学的常见综合考点。
Published by TutorHao | Physics Revision Series | aleveler.com
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