📚 Edexcel Physics: Refraction of Light | Edexcel 物理：光的折射 考点精讲
Refraction is one of the core topics in the Edexcel IAL and GCE Physics specifications. Understanding how light bends when it enters a different medium is essential for tackling questions on lenses, optical fibres, and wave behaviour. This article provides a structured revision guide covering Snell’s law, refractive index, critical angle, total internal reflection, and common applications, with paired English–Chinese explanations throughout.
折射是 Edexcel IAL 和 GCE 物理大纲的核心内容之一。理解光进入不同介质时如何弯折，对于解答透镜、光纤和波动行为的题目至关重要。本文提供结构化的复习指南，涵盖斯涅尔定律、折射率、临界角、全内反射及常见应用，通篇采用中英对照讲解。
1. What is Refraction? | 什么是折射？
Refraction is the change in direction of a wave when it passes from one medium to another due to a change in its speed. In optics, we usually consider light travelling between transparent materials such as air, water, glass, or plastic. If the light hits the boundary at an angle other than 90°, its path bends. The bending occurs because the wavefronts slow down or speed up asymmetrically.
折射是指波从一种介质进入另一种介质时，因速度改变而引起方向变化的现象。在光学中，我们通常研究光在空气、水、玻璃或塑料等透明材料之间的传播。如果光以非90°的角度照射边界，其传播路径会发生弯折。这种弯折是由于波前减速或加速的不对称所引起的。
Refraction explains everyday phenomena such as a drinking straw appearing bent in a glass of water, or the apparent depth of a swimming pool being shallower than its real depth. In the Edexcel specification, you are expected to explain these effects using wave theory and ray diagrams.
折射可解释日常现象，例如水杯中的吸管看起来是弯的，或游泳池的视在深度比实际深度浅。在 Edexcel 大纲中，要求你用波动理论和光线图解释这些效果。
2. Snell’s Law | 斯涅尔定律
Snell’s law quantifies the relationship between the angles of incidence and refraction. For light passing from medium 1 to medium 2, the law is written as:
斯涅尔定律定量描述了入射角和折射角之间的关系。当光从介质1进入介质2时，该定律写作：
n₁ sin θ₁ = n₂ sin θ₂
Here n₁ and n₂ are the absolute refractive indices of the two media, θ₁ is the angle of incidence in medium 1, and θ₂ is the angle of refraction in medium 2. All angles are measured from the normal to the boundary.
其中 n₁ 和 n₂ 分别是两种介质的绝对折射率，θ₁ 是介质1中的入射角，θ₂ 是介质2中的折射角。所有角度均从法线量起。
Often, one of the media is a vacuum or air, which has a refractive index of approximately 1. In that case, Snell’s law simplifies to n sin θ = constant, and n = sin i / sin r, where i is the angle in air/vacuum and r is the angle in the other medium. This simplified form is frequently used in Edexcel exam calculations.
通常，其中一种介质是真空或空气，其折射率近似为1。此时斯涅尔定律简化为 n sin θ = 常数，及 n = sin i / sin r，其中 i 为空气/真空中的角度，r 为另一介质中的角度。Edexcel 考试计算中常使用这种简化形式。
3. Absolute Refractive Index | 绝对折射率
The absolute refractive index n of a medium is defined as the ratio of the speed of light in a vacuum c to the speed of light in the medium v:
介质的绝对折射率 n 定义为真空中光速 c 与介质中光速 v 之比：
n = c / v
Since v is always less than c, the refractive index is always greater than 1. A higher refractive index means light travels more slowly in that medium. Typical values include approximately 1.00 for vacuum, 1.0003 for air, 1.33 for water, about 1.50 for crown glass, and 2.42 for diamond.
由于 v 总是小于 c，折射率总是大于1。折射率越高，光在该介质中的传播速度越慢。典型值包括：真空约1.00，空气约1.0003，水1.33，冕牌玻璃约1.50，金刚石2.42。
Edexcel questions may ask you to calculate v given n and c, or to compare the optical density of materials. Remember that optical density is not the same as physical mass density; it refers to the slowing effect on light.
Edexcel 题目可能会要求你根据 n 和 c 计算 v，或比较材料的光密度。记住光密度与物理质量密度不同，它指的是对光速的减缓作用。
4. Change in Speed and Wavelength | 速度与波长的变化
When monochromatic light passes from one medium to another, its frequency remains constant, but its speed and wavelength change. The relationship is:
当单色光从一种介质进入另一种介质时，其频率保持不变，但速度和波长会改变。关系式为：
v = f λ
Since f is constant, λ ∝ v. In medium 2, the wavelength λ₂ becomes λ₁ / n_rel, where n_rel is the relative refractive index n₂/n₁. This explains why the colour of light does not change in refraction (frequency determines colour), but the direction and wave pattern do.
由于 f 恒定，λ ∝ v。在介质2中，波长 λ₂ 变为 λ₁ / n_rel，其中 n_rel 为相对折射率 n₂/n₁。这就解释了为什么折射时光的颜色不变（频率决定颜色），而方向和波形却发生变化。
In exam diagrams, you may be asked to sketch wavefronts entering a different medium. The wavelength becomes shorter in a denser medium, and the wavefronts tilt accordingly. Use this concept to show how the direction change arises from the speed difference across the boundary.
在考试图示中，你可能被要求画出波前进入不同介质的草图。在更密的介质中波长变短，波前相应倾斜。利用这一概念，可以说明方向变化如何由于边界处的速度差而产生。
5. Critical Angle | 临界角
The critical angle C occurs when light travels from a denser medium into a less dense medium (e.g., from glass to air) and the angle of refraction becomes 90°. The critical angle is defined only for n₁ > n₂.
临界角 C 发生在光从光密介质射向光疏介质（如从玻璃到空气）且折射角为90°时。临界角仅在 n₁ > n₂ 时定义。
Applying Snell’s law at the critical condition: n₁ sin C = n₂ sin 90°. Since sin 90° = 1, we get:
在临界条件下应用斯涅尔定律：n₁ sin C = n₂ sin 90°。因为 sin 90° = 1，可得：
sin C = n₂ / n₁ = 1 / n (if n₂ = 1 for air)
For a glass–air boundary with n = 1.50, sin C = 1/1.50 = 0.667, therefore C ≈ 42°. This value appears frequently in prism and optical fibre questions.
对于折射率 n=1.50 的玻璃-空气边界，sin C = 1/1.50 = 0.667，因此 C ≈ 42°。这个数值经常出现在棱镜和光纤的题目中。
6. Total Internal Reflection | 全内反射
When the angle of incidence inside the denser medium exceeds the critical angle, no refraction occurs; instead, all light is reflected back into the denser medium. This phenomenon is called total internal reflection (TIR).
当光密介质内的入射角大于临界角时，不会发生折射；相反，所有光都被反射回光密介质。这一现象称为全内反射（TIR）。
For TIR to happen, two conditions must be met: (1) light must be travelling from a medium of higher refractive index to one of lower refractive index; (2) the angle of incidence must be greater than the critical angle. If either condition is not met, some light will refract out.
发生全内反射必须满足两个条件：（1）光必须从折射率较高的介质射向折射率较低的介质；（2）入射角必须大于临界角。若不满足任一条件，部分光将折射出去。
TIR is highly efficient because almost 100% of the light energy is reflected, unlike metallic mirrors that absorb some energy. This makes it ideal for optical fibres and prismatic reflectors in binoculars and periscopes.
全内反射效率极高，因为几乎100%的光能被反射，不像金属镜会吸收部分能量。这使其成为光纤以及双筒望远镜和潜望镜中棱镜反射器的理想选择。
7. Applications: Optical Fibres | 应用：光纤
Optical fibres rely on total internal reflection to transmit light signals over long distances with minimal loss. A fibre consists of a core with a higher refractive index surrounded by a cladding with a slightly lower refractive index.
光纤利用全内反射以极低的损耗远距离传输光信号。光纤由折射率较高的纤芯和折射率略低的包层组成。
Because the core has a higher n than the cladding, light entering at an angle greater than the critical angle is continuously reflected along the fibre. The cladding also protects the core and prevents signal leakage. Step-index and graded-index fibres are mentioned in specifications; the key point is that the critical angle between core and cladding determines the acceptance angle.
由于纤芯的折射率高于包层，以大于临界角的角度进入的光会沿光纤不断反射。包层也保护纤芯并防止信号泄漏。大纲中提及阶跃折射率和渐变折射率光纤；关键是纤芯与包层间的临界角决定了接收角。
Exam questions often ask why the cladding is necessary (protection, reduces dispersion, keeps signals inside) and why a very narrow fibre core reduces modal dispersion, allowing higher data rates. Be prepared to draw ray paths showing TIR inside the core.
考试题目常问包层为何必要（保护、减小色散、保持信号在内），以及为何极细的纤芯可以降低模式色散，从而提高数据传输速率。准备好画出显示纤芯内全内反射的光线路径。
8. Applications: Prisms and Lenses | 应用：棱镜和透镜
Glass prisms with 45°–45°–90° angles utilise TIR to reflect light by 90° or 180°. Because the critical angle for crown glass is about 42°, a 45° incident angle inside the prism guarantees TIR. This makes prisms ideal for reflecting light in periscopes and binoculars without metallic coatings.
45°–45°–90°的玻璃棱镜利用全内反射将光反射90°或180°。由于冕牌玻璃的临界角约为42°，棱镜内部45°的入射角可保证全内反射。这使得棱镜非常适合在潜望镜和双筒望远镜中无需金属镀膜即可反射光线。
Lenses, on the other hand, use refraction to converge or diverge light. A converging (convex) lens brings parallel rays to a focus because the curved surfaces refract rays towards the principal axis. The focal length depends on the curvature and refractive index of the lens material. The lens maker’s formula is not required for all Edexcel units, but you should understand how refraction at the two surfaces determines the behaviour.
另一方面，透镜利用折射来会聚或发散光线。会聚（凸）透镜将平行光线聚焦，因为弯曲的表面将光线向主光轴折射。焦距取决于透镜材料的曲率和折射率。虽然不是所有 Edexcel 单元都要求透镜制造者公式，但你应理解两个表面的折射如何决定其行为。
9. Dispersion of White Light | 白光的色散
When white light passes through a triangular prism, it splits into its constituent colours—a spectrum from red to violet. This dispersion occurs because the refractive index of glass varies slightly with wavelength: violet light slows down more and is refracted most, while red light is refracted least.
白光通过三棱镜时会分解成其组成颜色——从红到紫的光谱。这种色散的产生是由于玻璃的折射率随波长略有变化：紫光减速更多，折射最大，而红光折射最小。
Dispersion is responsible for chromatic aberration in simple lenses and the formation of rainbows in nature. In Edexcel physics, you should be able to describe why different colours follow different paths and identify which colour deviates most.
色散导致简单透镜产生色差，也造成自然界中的彩虹。在 Edexcel 物理中，你应能描述为何不同颜色遵循不同路径，并辨别哪种颜色偏折最大。
A common misconception is that frequency changes during refraction. Emphasise that frequency is invariant; only speed and wavelength change. Dispersion arises because n = c/v depends on wavelength in a dispersive medium.
常见的误解是频率在折射中改变。要强调频率不变，只有速度和波长变化。色散的产生是因为在色散介质中 n = c/v 随波长变化。
10. Experimental Measurement of Refractive Index | 折射率的实验测量
You are expected to know a standard method to determine the refractive index of a glass block or a liquid. For a rectangular glass block, use an optical pin method: measure the angles of incidence i and refraction r for several rays, then plot sin i against sin r. The gradient of the straight line gives n.
你需要知道测定玻璃块或液体折射率的标准方法。对于矩形玻璃块，可用光学针法：测量多条光线的入射角 i 和折射角 r，然后绘制 sin i 对 sin r 的图像。直线的斜率即为 n。
For a liquid, a semicircular dish is often used so that the ray always enters at the centre and passes normally to the curved surface, avoiding further refraction at that face. This allows direct measurement of the refracted angle in air. The critical angle method can also be used for liquids: find C then apply n = 1 / sin C.
对于液体，常用半圆形器皿，使光线始终射向圆心并垂直于曲面射出，从而避免在该面再次折射。这可以直接测量空气中的折射角。也可用临界角法测液体：找出 C，然后用 n = 1 / sin C 计算。
Uncertainties must be considered. The largest source of error is usually in marking the rays or aligning protractors. Repeating measurements and using a larger number of data points can reduce random errors. Exam practical questions often ask how to improve accuracy.
必须考虑不确定度。最大的误差来源通常是标记光线或对齐量角器。重复测量并使用更多数据点可以减少随机误差。考试中的实验题常问如何提高准确度。
11. Solving Refraction Problems | 解决折射问题
Typical multi-step problems involve calculating angles at multiple boundaries, finding the apparent depth, or determining whether TIR occurs. Follow a systematic approach: (1) Identify the media and their refractive indices; (2) Draw a ray diagram showing normals at each boundary; (3) Apply Snell’s law step by step; (4) Check if any angle exceeds the critical angle.
典型的多步问题涉及计算多个界面处的角度、求视深或判断是否发生全内反射。遵循系统方法：（1）确定各介质及其折射率；（2）画出光线图，标明每个界面处的法线；（3）逐步应用斯涅尔定律；（4）检查是否有角度超过临界角。
Apparent depth d_app is related to real depth d_real for a nearby observer by: d_app = d_real / n (if viewed from above). This relationship is derived from small-angle approximations and explains why pools look shallower. In examinations, you might be asked to calculate real or apparent depth given n.
对于近处观察者，视深 d_app 与实际深度 d_real 的关系为：d_app = d_real / n（从正上方观看时）。此关系由小角度近似导出，解释了水池为何看起来较浅。考试中，你可能需要根据 n 计算实际或视在深度。
Remember that angles in Snell’s law are always with respect to the normal. A common error is using the angle to the surface. Also, when light moves into a denser medium, θ₂ is smaller than θ₁; draw your diagrams accordingly to visualise the bend.
记住斯涅尔定律中的角度始终是相对于法线的。常见错误是使用与表面的夹角。另外，当光进入光密介质时，θ₂ 小于 θ₁；绘图时应据此表现弯折方向。
12. Common Mistakes and Exam Tips | 常见错误与考试技巧
Many students lose marks by confusing the refractive index formula n = sin i / sin r with the wrong assignment of angles. In the standard form, i is always the angle in vacuum/air, and r is the angle in the material. If the ray is travelling the opposite way, swap the sides or use n₁ sin θ₁ = n₂ sin θ₂ to avoid error.
许多学生因混淆折射率公式 n = sin i / sin r 的角度分配而丢分。标准形式中，i 总是真空/空气中的角度，r 是材料中的角度。若光线传播方向相反，可交换两边或用 n₁ sin θ₁ = n₂ sin θ₂ 避免错误。
Another common mistake is stating that the frequency or colour changes when light enters a new medium. Reinforce that colour perception depends on frequency, which does not change. Wavelength and speed adjust to maintain v = f λ.
另一个常见错误是声称光进入新介质时频率或颜色改变。要巩固颜色感知取决于频率，而频率不变。波长和速度会调整以维持 v = f λ。
When drawing ray diagrams for TIR, ensure the reflected ray obeys the law of reflection (angle of incidence equals angle of reflection). If asked to complete a diagram, always include the normal and label angles clearly. Show that the incident angle is greater than the critical angle.
在绘制全内反射的光线图时，确保反射线遵循反射定律（入射角等于反射角）。如果要求补全图形，务必画出法线并清楚地标出角度。要显示入射角大于临界角。
Finally, pay attention to significant figures and units in calculations. Refractive indices are dimensionless. When using the relationship sin C = 1/n, ensure your calculator is in degree mode, and double-check that you have identified the correct medium for n.
最后，注意计算中的有效数字和单位。折射率是无量纲的。在使用 sin C = 1/n 时，确保计算器处于角度模式，并再次确认所用 n 对应的介质是否正确。
Published by TutorHao | Physics Revision Series | aleveler.com
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