📚 Diffraction of Waves | 波的衍射
When a wave encounters an obstacle or a narrow gap, it does not always travel in a straight line. Instead, the wavefront bends around edges and spreads into the geometric shadow. This spreading of waves is called diffraction, and it is one of the key wave phenomena tested in CIE A-Level Physics.
当波遇到障碍物或狭缝时，并不总是沿直线传播。波前会绕过边缘并扩展进入几何阴影区。这种波的扩展现象称为衍射，是 CIE A-Level 物理中考查的关键波动现象之一。
1. What is Diffraction | 什么是衍射
Diffraction is the spreading of a wave as it passes through a narrow gap or around an obstacle. The effect occurs for all types of waves, including sound, water, light, and radio waves.
衍射是波通过窄缝或绕过障碍物时发生的扩展现象。所有类型的波都会发生衍射，包括声波、水波、光波和无线电波。
The amount of spreading depends on the relative size of the wavelength λ and the gap width a or the obstacle size. If the gap is much larger than λ, spreading is small. If the gap is comparable to λ, spreading is significant.
衍射程度取决于波长 λ 与缝隙宽度 a（或障碍物尺寸）的相对大小。如果缝隙远大于 λ，扩展很小；如果缝隙与 λ 相当，扩展就很明显。
Diffraction also allows wave energy to enter regions that would be in shadow if waves travelled only in straight lines. This is why diffraction is often described as the bending of waves around corners.
衍射还能使波的能量进入直线传播时本应被遮挡的阴影区域。因此，衍射常被描述为波绕过拐角弯曲传播。
2. Huygens’ Principle and Wavefronts | 惠更斯原理与波阵面
Huygens’ principle states that every point on a wavefront acts as a source of secondary wavelets. The new wavefront is the envelope of these secondary wavelets.
惠更斯原理指出，波前上的每一点都可以看作次波的波源。新的波前是这些次波的包络面。
When a plane wavefront reaches a narrow gap, only a small portion of the wavefront passes through. The secondary wavelets from this portion spread out in circular arcs, producing a curved or nearly semicircular wavefront beyond the gap.
当平面波前到达窄缝时，只有一小部分波前通过。这一部分产生的次波以圆弧形式扩展，在缝隙后方形成弯曲或近似半圆形的波前。
This model explains why diffraction is greater when the gap is narrower: fewer secondary sources remain, so the envelope becomes more curved instead of flat.
该模型解释了为什么缝隙越窄衍射越明显：剩余的次波源越少，包络面就越弯曲而不是保持平面。
3. Conditions for Noticeable Diffraction | 明显衍射的条件
Diffraction is most noticeable when the wavelength λ is comparable to or larger than the gap width a. If λ is much smaller than a, the wave passes through with little spreading and produces a sharp shadow.
当波长 λ 与缝隙宽度 a 相当或更大时，衍射最明显。如果 λ 远小于 a，波通过时几乎不扩展，产生清晰的阴影。
Sound waves have wavelengths from a few centimetres to several metres, so they diffract strongly around doorways and corners. Visible light has wavelengths around 400–700 nm, so it only diffracts noticeably through very narrow slits or diffraction gratings.
声波波长从几厘米到几米，因此可以绕过门和墙角发生明显衍射。可见光波长约为 400–700 nm，因此只有通过非常窄的狭缝或衍射光栅时才会明显衍射。
In a ripple tank, if the gap width is narrowed until it is close to the wavelength of the water waves, the diffracted wavefronts become almost circular. If the gap is widened, the wavefronts remain nearly straight.
在水波槽中，如果把缝隙宽度减小到接近水波波长，衍射波前会几乎呈圆形。如果缝隙加宽，波前则几乎保持直线。
4. Diffraction Through a Single Slit | 单缝衍射
When monochromatic light passes through a single narrow slit, a central bright fringe is observed with alternating dark and bright fringes on both sides. The central maximum is much wider and brighter than the side maxima.
当单色光通过单缝时，会观察到中央亮条纹，两侧交替出现暗纹和亮纹。中央主极大的宽度和亮度远大于两侧次极大。
For a single slit of width a, destructive interference gives dark fringes at angles θ satisfying:
对于宽度为 a 的单缝，相消干涉产生的暗纹满足：
a sin θ = mλ, m = ±1, ±2, ±3, …
The angle θ is measured from the centre line to the dark fringe. The first minimum occurs when m = 1, so a sin θ = λ.
角度 θ 是从中心线到暗纹方向测量的。第一级暗纹对应 m = 1，即 a sin θ = λ。
Between the dark fringes are weak secondary maxima. Their intensity decreases rapidly away from the centre.
暗纹之间是较弱的次极大。远离中央时，强度迅速下降。
5. Intensity Pattern of Single-Slit Diffraction | 单缝衍射强度分布
The intensity pattern of single-slit diffraction shows a bright central maximum covering the region between the first minima on either side. The angular half-width of the central maximum is approximately θ ≈ λ / a for small angles.
单缝衍射的强度图样显示明亮的中央主极大，占据两侧第一暗纹之间的区域。中央主极大的半角宽度近似为 θ ≈ λ / a（小角度情况下）。
Secondary maxima have much lower intensity. Their approximate angular positions lie between the dark fringes, but they are not exactly halfway; their intensities are around 4.7%, 1.6%, and 0.8% of the central maximum.
次极大的强度低得多。它们大致位于暗纹之间，但并不恰好在中间；它们的强度约为中央主极大的 4.7%、1.6% 和 0.8%。
If the slit is made narrower, the central maximum becomes wider, which indicates greater diffraction. If the wavelength increases, the pattern also spreads out.
如果狭缝变窄，中央主极大变宽，说明衍射更明显。如果波长增大，图样也会展宽。
6. Diffraction Gratings | 衍射光栅
A diffraction grating consists of many equally spaced parallel slits. It produces very sharp and bright interference maxima because light from many slits combines constructively at well-defined angles.
衍射光栅由许多等间距的平行狭缝组成。由于来自多个狭缝的光在明确角度处相长叠加，会产生非常锐利且明亮的干涉极大。
The slit separation d is called the grating spacing. If there are N lines per metre, then d = 1 / N. For a grating with 300 lines per mm, d = (1/300) mm = 3.33 × 10⁻⁶ m.
缝间距 d 称为光栅常数。如果每米有 N 条刻线，则 d = 1 / N。例如每毫米 300 条刻线的光栅，d = (1/300) mm = 3.33 × 10⁻⁶ m。
| Feature | 特征 | Single slit | 单缝 |
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