Light Diffraction for GCSE CIE Physics | GCSE CIE 物理：光的衍射考点精讲

📚 Light Diffraction for GCSE CIE Physics | GCSE CIE 物理：光的衍射考点精讲

Diffraction is a fundamental wave phenomenon that is essential in understanding how light behaves when it encounters obstacles or narrow openings. In the GCSE CIE Physics syllabus, you are expected to explain what diffraction is, describe the diffraction of light using a single slit and a diffraction grating, and apply the grating equation to determine the wavelength of light. Mastering these concepts will help you tackle exam questions confidently, especially those involving the measurement of light’s wavelength and the analysis of interference patterns.

衍射是波的一种基本现象，对于理解光遇到障碍物或狭缝时的行为至关重要。在 GCSE CIE 物理考纲中，你需要解释什么是衍射，描述单缝和衍射光栅对光的衍射，并运用光栅方程测定光的波长。掌握这些概念将帮助你自信地应对考试题目，特别是那些涉及测量光波长和分析干涉图样的考题。

1. What is Diffraction? | 什么是衍射？

Diffraction is the spreading out of waves when they pass through a narrow gap or around an obstacle. This effect occurs for all types of waves, including light, sound, and water waves. The amount of diffraction depends on the size of the gap relative to the wavelength: significant diffraction happens when the gap width is similar to the wavelength of the wave.

衍射是波通过狭窄缝隙或绕过障碍物时发生的扩散现象。所有类型的波都可以发生衍射，包括光波、声波和水波。衍射的程度取决于缝隙宽度与波长的相对大小：当缝隙宽度与波长相近时，衍射现象最为明显。

For light, the wavelength is extremely small (about 4×10⁻⁷ m to 7×10⁻⁷ m for visible light), so diffraction is only noticeable when light passes through very tiny openings, such as a thin slit or a diffraction grating.

对于光来说，波长极小（可见光约 4×10⁻⁷ m 至 7×10⁻⁷ m），因此只有在光穿过非常微小的开口（如细缝或衍射光栅）时，才能观察到明显的衍射现象。

2. Diffraction of Light through a Single Slit | 单缝光衍射

When monochromatic light (light of a single wavelength) passes through a narrow single slit, it produces a diffraction pattern on a screen placed some distance away. The pattern consists of a broad, bright central maximum, with dimmer and narrower maxima on either side. Dark regions (minima) separate these bright fringes.

当单色光（单一波长的光）通过一个狭窄的单缝时，会在远处的屏幕上产生衍射图样。图样包含一个宽且明亮的中央极大，两侧有较暗且较窄的次级极大，亮纹之间由暗区（极小）隔开。

The central maximum is approximately twice as wide as the secondary maxima. This is because light waves from different parts of the slit interfere constructively and destructively, giving the characteristic pattern.

中央极大的宽度大约是次级极大的两倍。这是因为来自缝隙不同部分的光波发生相长干涉和相消干涉，形成了这种特征图样。

3. Effect of Slit Width on Diffraction Pattern | 缝宽对衍射图样的影响

If the slit width is decreased, the amount of diffraction increases. This makes the central maximum become wider, and the fringes spread out more. Conversely, if the slit becomes wider, the diffraction effect decreases and the fringes become narrower and closer together.

如果减小缝宽，衍射程度增大，中央极大变宽，条纹展开得更多。反之，如果缝宽增大，衍射效应减弱，条纹变窄且更靠近。

When the slit width is much larger than the wavelength, virtually no diffraction is observed – light travels in nearly straight lines, producing a sharp image of the slit. This matches the idea that diffraction is pronounced only when the gap size is comparable to the wavelength.

当缝宽远大于波长时，几乎观察不到衍射——光近乎直线传播，形成缝隙的清晰像。这正对应了只有当缝隙尺寸与波长相当时，衍射才明显的原理。

4. Effect of Wavelength on Single-Slit Diffraction | 波长对单缝衍射的影响

Longer wavelengths of light produce greater diffraction. For a fixed slit width, red light (longer wavelength, ~700 nm) produces a wider central maximum than blue light (shorter wavelength, ~450 nm). This means the fringe spacing increases with wavelength.

波长越长，衍射效应越明显。对于固定的缝宽，红光（波长较长，约 700 nm）产生的中央极大比蓝光（波长较短，约 450 nm）的更宽。这意味着条纹间距随波长增大而增大。

This principle is key in understanding white light diffraction: when white light passes through a single slit, the different colours spread out by different amounts, creating a coloured diffraction pattern.

这一原理是理解白光衍射的关键：当白光通过单缝时，不同颜色的光产生不同程度的衍射，形成彩色的衍射图样。

5. Introduction to the Diffraction Grating | 衍射光栅简介

A diffraction grating consists of a large number of equally spaced parallel slits (or lines) etched on a glass or metal surface. A typical grating used in the lab has hundreds of lines per millimetre. When light passes through or reflects off a grating, each slit acts as a source of diffracted waves that interfere with each other to produce a pattern of sharp, bright maxima.

衍射光栅由大量等间距的平行狭缝（或刻线）组成，这些狭缝刻在玻璃或金属表面上。实验室常用的光栅每毫米有数百条刻线。当光通过光栅或被其反射时，每条狭缝都作为衍射波的波源，各波源之间相互干涉，形成锐利、明亮的极大图样。

The key advantage of a diffraction grating over a single slit is that the maxima are much sharper and more widely spaced, allowing precise measurements of angles and therefore wavelength.

与单缝相比，衍射光栅的最大优点是极大更锐利且间距更大，从而能够精确测量角度，进而测定波长。

6. The Diffraction Grating Equation | 光栅方程

For a diffraction grating, the angles at which the bright maxima (also called orders) occur are given by the grating equation:

d sinθ = nλ

where d is the distance between adjacent slits (grating spacing), θ is the angle between the zero-order maximum and the nth-order maximum, n is the order number (an integer: 0, 1, 2, …), and λ is the wavelength of the light.

对于衍射光栅，明纹极大（也称作各级极大）出现的角度由光栅方程给出：

d sinθ = nλ

其中 d 是相邻狭缝间的距离（光栅常数），θ 是零级极大与第 n 级极大之间的夹角，n 是级数（整数 0, 1, 2, …），λ 是光的波长。

You must measure d in metres. If a grating has N lines per metre, then d = 1/N. For a grating labelled ‘300 lines per mm’, this means 300,000 lines per metre, so d = 1/300,000 = 3.33 × 10⁻⁶ m.

d 必须以米为单位。如果光栅每米有 N 条刻线，则 d = 1/N。对于标有 ‘300 lines per mm’ 的光栅，即每毫米 300 条刻线，也就是 300,000 条/米，因此 d = 1/300000 = 3.33 × 10⁻⁶ m。

7. Measuring Wavelength Using a Diffraction Grating | 利用衍射光栅测量波长

A common required practical in GCSE CIE Physics involves shining a laser of known wavelength (or using a white light source with a colour filter) through a diffraction grating and measuring the angles of the bright spots. The set-up includes a grating, a screen or a telescope on a rotating mount, and a metre ruler.

GCSE CIE 物理中常见的实验是让已知波长的激光（或使用白光加滤色片）穿过衍射光栅，并测量亮点的角度。实验装置包括光栅、屏幕或带有旋转座的望远镜，以及一把米尺。

Key steps: Set up the laser and grating so that the beam is perpendicular to the grating. Measure the distance (L) from the grating to the screen. For the first-order maximum (n=1), measure the distance (x) from the central spot to the first bright spot. Then tanθ = x/L, from which θ can be found. Finally, use λ = d sinθ / n to calculate the wavelength.

关键步骤：调整激光和光栅使光束垂直于光栅。测量光栅到屏幕的距离 (L)。对于第一级极大 (n=1)，测量中央亮斑到第一级亮点的距离 (x)。利用 tanθ = x/L 求出 θ。最后用 λ = d sinθ / n 计算波长。

To improve accuracy, you can measure the distance between the two first-order spots on either side of the centre, then divide by 2 to get x, reducing alignment errors. Also, measuring higher orders (e.g., n=2) and averaging the results can give a more reliable value.

为了提高精确度，可以测量中央两侧两个第一级亮点之间的距离，再除以 2 得到 x，这样可以减少对准误差。另外，测量更高级次（如 n=2）并取平均值，可以得到更可靠的波长值。

8. Orders of Maxima and Their Spacing | 极大级数与间距

The zero-order maximum (n=0) is the bright spot directly in line with the incident beam. All wavelengths overlap here, producing the same colour as the source. On either side, symmetric first-order (n=1), second-order (n=2), and possibly higher-order maxima appear. The angle θ increases with order number and with wavelength.

零级极大 (n=0) 是与入射光束在同一直线上的亮斑。所有波长的光在此重叠，呈现与光源相同的颜色。在两侧对称地出现第一级 (n=1)、第二级 (n=2)，甚至更高级次的极大。角 θ 随级数和波长增大而增大。

The maximum possible order is limited because sinθ cannot exceed 1. Therefore, nλ/d ≤ 1, which gives n ≤ d/λ. For visible light and a typical grating (d ~ 1.7×10⁻⁶ m for 600 lines/mm), you might only see up to the second or third order.

可能出现的最高级次受到限制，因为 sinθ 不能超过 1。因此 nλ/d ≤ 1，得出 n ≤ d/λ。对于可见光和典型光栅 (如 600 lines/mm，d 约 1.7×10⁻⁶ m)，通常只能看到第二或第三级。

9. White Light Diffraction with a Grating | 白光的光栅衍射

When a white light source is used with a diffraction grating, each wavelength produces its own set of maxima at slightly different angles. This separates the colours into a continuous spectrum in each order (except the zero order, which remains white). The result is a series of rainbow-like spectra on either side of the central bright spot.

当使用白光光源与衍射光栅时，每种波长的光都以略微不同的角度产生各自的极大。这样，在每个级次（零级除外，零级保持白色）中，不同颜色会分开形成连续光谱。结果是在中央亮斑两侧出现一系列彩虹样的光谱。

In each order, the violet end of the spectrum appears closest to the centre, and the red end appears farthest away. This is because violet light has a shorter wavelength, so it is diffracted through a smaller angle, whereas red light is diffracted through a larger angle. This arrangement is opposite to that produced by a glass prism, where red is deviated least.

在每一级中，光谱的紫端离中心最近，红端离中心最远。这是因为紫光波长较短，衍射角度较小；而红光波长较长，衍射角度较大。这种排列与玻璃棱镜产生的光谱相反，棱镜中红光偏折最小。

Feature	Prism	Diffraction Grating
Colour most deviated	Violet	Red
Colour least deviated	Red	Violet
Principle	Refraction (dispersion)	Diffraction and interference

10. Applications of Diffraction | 衍射的应用

Diffraction gratings are widely used in spectrometers to analyse the composition of light from stars or laboratory sources. By measuring the angles of spectral lines, scientists can identify elements present in a sample. This is crucial in astronomy and chemistry.

衍射光栅广泛应用于光谱仪中，用来分析恒星或实验室光源的光的成分。通过测量光谱线的角度，科学家可以确定样品中存在的元素。这在天文学和化学中至关重要。

Another application is in CD and DVD technology: the closely spaced tracks on a disc act as a reflection grating, causing the colourful patterns you see when white light shines on the surface. X-ray diffraction is used to study the atomic structure of crystals, as the regular spacing of atoms acts like a grating for X-rays.

另一个应用是在 CD 和 DVD 技术中：光盘上紧密排列的轨道起着反射光栅的作用，当白光照射在表面时，会看到彩色的图样。X 射线衍射用于研究晶体的原子结构，因为原子的规则间距对 X 射线起到了类似光栅的作用。

11. Common Exam Mistakes to Avoid | 应避免的常见考试错误

1. Confusing the patterns from a single slit and a diffraction grating. A single slit gives a broad central maximum and less sharp fringes; a grating produces very sharp, distinct maxima symmetrically arranged.

1. 混淆单缝和衍射光栅的图样。单缝产生宽的中央极大和不甚锐利的条纹；光栅则产生非常锐利、左右对称的明显极大。

2. Forgetting to convert units. Always make sure d is in metres and all lengths are in the same unit system before substituting into the equation d sinθ = nλ.

2. 忘记换算单位。在代入方程 d sinθ = nλ 之前，务必确保 d 以米为单位，且所有长度使用同一单位制。

3. Measuring the angle between the zero order and the second order and dividing by 2 to get θ for n=2. This is correct only because the geometry is symmetric, but students often misapply this idea.

3. 直接测量零级与第二级之间的角度再除以 2 来得到 n=2 的 θ。这种方法因为几何对称是正确的，但学生经常错误地应用。

4. Stating that a larger slit width causes greater diffraction. The opposite is true: narrower slit, more spreading.

4. 误以为更大的缝宽引起更显著的衍射。事实恰恰相反：缝越窄，扩散越明显。

5. Thinking that the central maximum in white light diffraction shows a spectrum. The zero order is white because all wavelengths overlap there without relative path difference.

5. 认为白光衍射的中央极大显示光谱。零级是白色的，因为所有波长的光在此重叠，没有相对程差。

12. Key Points Summary | 要点总结

Diffraction is the spreading of waves around obstacles or through gaps, most obvious when the gap size ≈ wavelength. A single slit produces a broad central bright fringe with dimmer side fringes; a diffraction grating gives sharp maxima governed by d sinθ = nλ. The grating spacing d is found from the number of lines per metre. White light yields a continuous spectrum with violet closest to the centre for each order. This knowledge is directly tested in practical measurement and explanation questions.

衍射是波绕过障碍或穿过缝隙时发生的扩散，当缝隙尺寸约等于波长时最为明显。单缝产生宽中央亮纹和较暗的次级条纹；衍射光栅产生服从 d sinθ = nλ 的锐利极大。光栅间距 d 由每米的刻线数求得。白光产生连续光谱，每一级紫光最靠近中心。这些知识在实验测量和解释题中直接考查。

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Light Diffraction for GCSE CIE Physics | GCSE CIE 物理：光的衍射 考点精讲