Diffraction of Light | 光的衍射考点精讲

📚 Diffraction of Light | 光的衍射考点精讲

Light travels in straight lines when it passes through a large opening or travels in a uniform medium, but when it encounters a narrow slit or an obstacle with a size comparable to its wavelength, it bends and spreads out. This phenomenon is called diffraction, and it provides strong evidence for the wave nature of light. In the WJEC GCSE Physics specification, understanding diffraction is crucial for explaining how light behaves at edges and how patterns of bright and dark fringes form on a screen.

光在通过较大开口或者在均匀介质中传播时沿直线行进，但当它遇到一个宽度与波长相当的狭缝或障碍物时，就会发生弯曲并扩散开来。这种现象称为衍射，它为光的波动性提供了有力证据。在 WJEC GCSE 物理考纲中，理解衍射对于解释光在边缘处的行为以及明暗条纹图样如何在屏幕上形成至关重要。

1. What Is Diffraction? | 什么是衍射？

Diffraction is the bending and spreading of waves as they pass through a narrow gap or around an obstacle. For light, this effect is most noticeable when the size of the gap or obstacle is similar to the wavelength of the light. Diffraction occurs with all types of waves, including sound and water waves, but light diffraction requires very small slits because visible light wavelengths are extremely small (around 400–700 nanometres).

衍射是波在通过狭缝或绕过障碍物时发生弯曲和扩散的现象。对于光来说，当缝隙或障碍物的尺寸与光的波长相近时，这种效应最为明显。衍射适用于所有类型的波，包括声波和水波，但光的衍射需要非常窄的狭缝，因为可见光的波长极小（大约 400–700 纳米）。

When a wavefront passes through a narrow gap, each point on the wavefront acts as a source of secondary wavelets that spread out in all directions. This is explained by Huygens’ principle, which underpins the wave model of light. The resulting bending allows light to reach regions that would be in shadow if light travelled only in straight lines.

当波前通过窄缝时，波前上的每一点都成为向外扩散的次波源，这可以用惠更斯原理来解释，该原理是光的波动模型的基础。由此产生的弯曲使光能够到达如果光只沿直线传播就会处于阴影中的区域。

2. Conditions for Noticeable Diffraction | 显著衍射的条件

For diffraction of light to be clearly observed, the width of the slit must be comparable to the wavelength of the light used. If the slit is much wider than the wavelength, light passes through without significant spreading and produces a sharp image of the slit on a screen. As the slit narrows, the amount of diffraction increases—the light spreads out more and the central bright region becomes wider.

要清晰地观察到光的衍射，狭缝的宽度必须与所用光的波长相当。如果狭缝远宽于波长，光通过时不会发生明显的扩散，而是在屏幕上形成清晰的狭缝像。随着狭缝变窄，衍射程度增加——光扩散得更开，中央亮区变得更宽。

In the WJEC practical context, students often use a laser and a single slit of adjustable width. By reducing the slit width, they can watch the central maximum broaden and see more fringes appearing on either side. Monochromatic light is preferred because it gives a well-defined pattern without colour blurring.

在 WJEC 的实验背景下，学生经常使用激光和可调宽度的单缝。通过减小狭缝宽度，他们可以观察到中央亮纹变宽，并在两侧出现更多条纹。单色光更受欢迎，因为它能给出清晰定义的图样，没有彩色模糊。

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

When monochromatic light passes through a single narrow slit, a characteristic pattern appears on a distant screen. The pattern consists of a broad, very bright central maximum flanked by alternating dark and bright fringes that become progressively dimmer and narrower. The central maximum is roughly twice as wide as the subsidiary maxima.

当单色光通过一个窄缝时，在远处的屏幕上会出现特征的图样。该图样由一个宽阔且非常明亮的中央亮纹和两侧交替出现的暗纹与亮纹组成，这些次亮纹逐渐变暗、变窄。中央亮纹的宽度大约是次级亮纹的两倍。

The dark fringes occur at angles where light waves from different parts of the slit arrive out of phase and cancel each other out. For a single slit of width a, the condition for the first dark fringe is a sinθ = λ, where θ is the angle from the centre. The second dark fringe satisfies a sinθ = 2λ, and so on. These positions define the boundaries between bright and dark regions.

暗纹出现在来自狭缝不同部分的光波以反相到达并相互抵消的角度。对于宽度为 a 的单缝，第一暗纹的条件是 a sinθ = λ，其中 θ 是偏离中心的角度。第二暗纹满足 a sinθ = 2λ，依此类推。这些位置定义了亮区和暗区之间的边界。

A table can help summarise the pattern:

Feature	Description
Central maximum	Very bright, width approx. 2λL/a (L = distance to screen)
First dark fringe	a sinθ = λ
Subsidiary maxima	Much dimmer, located between higher-order dark fringes

下表可以帮助总结图样特征：中央亮纹非常明亮，宽度约为 2λL/a（L 为到屏幕的距离）；第一暗纹满足 a sinθ = λ；次级亮纹暗淡得多，位于高阶暗纹之间。

4. Effect of Slit Width on Diffraction | 狭缝宽度对衍射的影响

Changing the width of the single slit has a direct impact on the diffraction pattern. As the slit becomes narrower (a decreases), the angle of the first dark fringe increases because sinθ = λ/a, so θ = sin⁻¹(λ/a). A smaller denominator gives a larger angle, making the central maximum spread out more. The overall pattern becomes wider but also dimmer because less light passes through the slit.

改变单缝的宽度会直接影响衍射图样。当狭缝变窄（a 减小）时，由于 sinθ = λ/a，第一暗纹的角度增大，因为分母变小导致角度变大，中央亮纹扩散得更开。整个图样变得更宽，但也更暗，因为通过狭缝的光减少。

Conversely, widening the slit results in a narrower central maximum and smaller diffraction effects. When the slit is very wide compared to the wavelength, the pattern resembles a simple image of the slit with little noticeable bending. This relationship is a key demonstration of the wave nature of light.

相反，加宽狭缝会导致中央亮纹变窄，衍射效应减小。当狭缝远宽于波长时，图样接近于简单的狭缝像，几乎没有明显的弯曲。这种关系是光波动性的重要证明。

5. Effect of Wavelength on Diffraction | 波长对衍射的影响

The wavelength of light used also determines the extent of diffraction. Longer wavelengths produce larger angles for diffraction minima because sinθ = λ/a, so the pattern spreads out more. If white light is used instead of monochromatic light, the central maximum appears white, but the fringes on either side show a spectrum with red (longer λ) on the outside and blue/violet (shorter λ) on the inside. This is because each colour diffracts by a different amount.

所用光的波长也决定衍射的程度。较长的波长产生更大的衍射暗纹角度，因为 sinθ = λ/a，因此图样扩散得更开。如果使用白光代替单色光，中央亮纹呈现白色，但两侧的条纹呈现光谱，红（波长较长）在外侧，蓝/紫（波长较短）在内侧。这是因为每种颜色衍射量不同。

In the laboratory, this can be shown by passing white light through a narrow slit and observing the rainbow-like fringes. Comparing a red laser and a blue laser through the same slit highlights the wavelength dependence: red light gives a more spread-out pattern.

在实验室中，将白光通过窄缝并观察彩虹般的条纹可以展示这一点。比较红光激光和蓝光激光通过同一狭缝，可以突出波长依赖性：红光产生更扩散的图样。

6. Diffraction Gratings | 衍射光栅

A diffraction grating consists of a large number of parallel, equally spaced slits (or grooves). When monochromatic light shines on a grating, each slit acts as a coherent source of light waves, and the transmitted waves interfere. The resulting pattern on a screen shows very sharp, intense maxima at specific angles, separated by wide dark regions. These are much sharper than single-slit patterns because the interference of many beams produces very narrow bright lines.

衍射光栅由大量平行、等间距的狭缝（或刻槽）组成。当单色光照射光栅时，每条狭缝都作为相干光源，透射波发生干涉。在屏幕上产生的图样显示出在特定角度非常锐利、强度大的极大值，之间是宽阔的暗区。这些亮线比单缝图样锐利得多，因为许多光束的干涉产生了非常窄的亮线。

Gratings are used in spectrometers to separate light into its component wavelengths and to measure wavelengths very precisely. The grating equation is fundamental to understanding how diffraction gratings work.

光栅用于光谱仪中，将光分解为其组成波长，并非常精确地测量波长。光栅方程是理解衍射光栅工作原理的基础。

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

For a diffraction grating with slit separation d (the distance between adjacent slits), the angle θ at which a bright order n occurs is given by the equation:

d sinθ = nλ

where λ is the wavelength of the light, and n is an integer (0, ±1, ±2, …) called the order of the maximum. n = 0 corresponds to the central maximum, n = 1 to the first-order maxima on either side, and so on.

对于狭缝间距为 d（相邻狭缝中心之间的距离）的衍射光栅，亮纹级次 n 出现的角度 θ 由下式给出：d sinθ = nλ，其中 λ 是光的波长，n 是整数（0, ±1, ±2, …），称为极大值的级次。n = 0 对应中央亮纹，n = 1 对应两侧的第一级亮纹，依此类推。

This equation shows that longer wavelengths give larger diffraction angles for the same order, and that the maximum observable order is limited because sinθ cannot exceed 1 (nλ/d ≤ 1). The number of slits per metre, N = 1/d, is often quoted on gratings (e.g., 300 lines per mm means d = 1/300 mm).

该方程表明，在同一级次下，较长的波长产生较大的衍射角度，并且最大可观察级次受到限制，因为 sinθ 不能超过 1（nλ/d ≤ 1）。光栅上通常标有每米的刻线数 N = 1/d（例如，每毫米 300 线意味着 d = 1/300 mm）。

In the WJEC exam, students are expected to use this equation to calculate wavelength, slit spacing, or the angle of a given order. They must also be able to convert units appropriately (e.g., mm to m) and handle very small numbers using standard form.

在 WJEC 考试中，学生要能够使用该公式计算波长、狭缝间距或给定级次的角度。他们还必须能够正确换算单位（例如 mm 转 m），并使用标准形式处理很小的数字。

8. Deriving the Grating Equation Using Path Difference | 利用光程差推导光栅方程

To understand why d sinθ = nλ, consider two adjacent slits on a grating. When light of wavelength λ reaches the grating, each slit emits wavelets. For a bright fringe to form at an angle θ to the normal, the light from successive slits must arrive in phase. This requires that the path difference between waves from adjacent slits is a whole number of wavelengths, nλ.

要理解为什么 d sinθ = nλ，考虑光栅上的两个相邻狭缝。当波长为 λ 的光到达光栅时，每条狭缝发出次波。要在于法线夹角 θ 处形成亮纹，来自相邻狭缝的光必须同相到达。这就要求相邻狭缝波之间的光程差是波长的整数倍 nλ。

From the geometry, this extra distance is the length of the small side of a right-angled triangle where the hypotenuse is the slit separation d and the angle is θ. Thus, path difference = d sinθ. Setting this equal to nλ gives the condition for constructive interference: d sinθ = nλ.

根据几何关系，这个额外距离是一个直角三角形的短直角边，斜边为狭缝间距 d，夹角为 θ。因此，光程差 = d sinθ。令其等于 nλ 即得到相长干涉的条件：d sinθ = nλ。

When this condition is met, all slits contribute waves that reinforce each other, producing a very bright fringe. Between these orders, waves from many slits cancel out, resulting in darkness. The greater the number of slits, the sharper and brighter the maxima.

当满足该条件时，所有狭缝贡献的波相互加强，产生非常亮的条纹。在这些级次之间，来自许多狭缝的波相互抵消，导致黑暗。狭缝数目越多，极大值越锐利、明亮。

9. Observing Diffraction and Grating Patterns | 观察衍射和光栅图样

In the GCSE laboratory, the simplest way to observe diffraction is by shining a laser through a single slit and onto a white screen. A darkened room helps see the pattern clearly. For a diffraction grating, replace the single slit with a grating and measure the distances from the central maximum to each coloured fringe when using a white light source. Using geometry, tanθ = x/L, the angle can be found, and then the grating equation used to determine λ.

在 GCSE 实验室中，最简单的观察衍射的方法是让激光照射单缝并在白屏上成像。暗室有助于清晰地看到图样。对于衍射光栅，用光栅代替单缝，并在使用白光光源时测量从中央亮纹到每个彩色条纹的距离。利用三角关系 tanθ = x/L，可以求出角度 θ，然后用光栅方程确定 λ。

Safety must be observed: lasers must be Class 2 or lower, and direct viewing of the beam must be avoided. All measurements should be taken with care to minimise parallax errors.

必须遵守安全规定：使用 2 类或更低级别的激光，避免直接目视光束。所有测量都要小心进行，以尽量减少视差误差。

10. Difference Between Diffraction and Interference | 衍射与干涉的区别

Students sometimes confuse diffraction and interference. Diffraction is the bending of waves around obstacles or through gaps; interference is the superposition of two or more waves leading to regions of reinforcement and cancellation. In a single-slit experiment, both effects occur: the waves from different parts of the same slit diffract and then interfere with each other to produce the pattern. In a double-slit experiment, diffraction at each slit distributes the light, and then the two diffracted beams interfere.

学生有时会混淆衍射和干涉。衍射是波绕过障碍物或通过缝隙的弯曲；干涉是两列或多列波的叠加，导致出现加强和抵消的区域。在单缝实验中，两种效应都存在：来自同一缝隙不同部分的波发生衍射，然后相互干涉产生图样。在双缝实验中，光在每个狭缝处发生衍射扩散，然后两束衍射光发生干涉。

A diffraction grating is essentially a multi-slit interference device where diffraction spreads the light from each slit and the overlapping waves interfere. The sharp fringes are a direct result of multiple-beam interference, not just diffraction alone. So, both concepts are intertwined, but remembering that diffraction refers to wave bending while interference refers to superposition clarifies the distinction.

衍射光栅本质上是一种多缝干涉器件，衍射使每个狭缝的光扩散，然后重叠的波发生干涉。锐利条纹是多光束干涉的直接结果，而不仅仅是衍射。因此，两个概念相互交织，但记住衍射指波的弯曲，干涉指波的叠加，可以澄清区别。

11. Applications of Light Diffraction | 光的衍射应用

Diffraction of light has many practical uses. Diffraction gratings are essential components in spectrometers used to analyse the light from stars, identifying elements by their spectral lines. They are also used in telecommunications wavelength-division multiplexing and in the production of holograms. The phenomenon of diffraction limits the resolution of optical instruments like microscopes and telescopes, because light passing through a circular aperture produces a diffraction pattern with a central Airy disc, affecting the ability to distinguish two close objects.

光的衍射有许多实际用途。衍射光栅是光谱仪中的关键部件，用于分析来自恒星的光，通过光谱线识别元素。它们还用于电信中的波分复用以及全息图的制作。衍射现象限制了光学仪器如显微镜和望远镜的分辨率，因为光通过圆形孔径产生具有中央爱里斑的衍射图样，影响分辨两个临近物体的能力。

Understanding diffraction is therefore not only important for GCSE exams but also for grasping how optical technologies work in the real world. It explains why higher resolution telescopes have larger apertures—to reduce the size of the Airy disc relative to the image.

因此，理解衍射不仅对 GCSE 考试很重要，而且对于掌握光学技术在现实世界中的工作原理也很重要。这解释了为什么高分辨率望远镜具有更大的孔径——为了减小爱里斑相对图像的大小。

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Diffraction of Light | 光的衍射 考点精讲