📚 Refraction of Light in IB Edexcel Physics: Key Points | IB Edexcel 物理：光的折射 考点精讲
Understanding how light bends as it passes from one medium to another is fundamental to both IB and Edexcel Physics. This article covers the essential principles, Snell’s law, refractive index, total internal reflection, and real‑world applications such as optical fibres, directly aligned with your syllabus requirements.
理解光从一种介质进入另一种介质时如何发生弯曲，是 IB 与 Edexcel 物理课程的基础。本文涵盖基本原理、斯涅尔定律、折射率、全内反射以及光纤等实际应用，紧密贴合考纲要求。
1. The Nature of Refraction | 折射的本质
Refraction is the change in direction of a wave when it passes from one medium to another due to a change in its speed. For light, this happens at the boundary between two transparent materials of different optical densities.
折射是波在穿过不同介质时，因其传播速度改变而导致传播方向发生变化的現象。对于光来说，这发生在两种不同光密度的透明材料之间的界面处。
When light enters a denser medium (higher refractive index), it bends towards the normal. Conversely, when it enters a less dense medium (lower refractive index), it bends away from the normal. If the incident ray hits the boundary exactly along the normal, no bending occurs; the ray continues straight on.
当光进入光密介质（折射率较大）时，它會靠近法线偏折。相反，进入光疏介质（折射率较小）时，则会偏离法线。如果入射光线恰好沿着法线方向射入界面，则不会发生偏折，光线继续沿直线传播。
The wave model explains refraction perfectly: frequency remains constant, but wavelength and speed change. The reduction in speed causes the wavefronts to tilt, producing the observed change in direction.
波动模型完美地解释了折射现象：频率保持不变，但波长和速度发生改变。速度的减小导致波前倾斜，从而产生观察到的方向变化。
2. Refractive Index and Optical Density | 折射率与光密度
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 that medium, v:
介质的绝对折射率 n 定义为真空中光速 c 与该介质中光速 v 之比：
n = c / v
Since v is always less than c, the refractive index is always greater than 1. For air, n ≈ 1.00, for water n ≈ 1.33, and for typical glass n ≈ 1.5.
由于介质中的光速 v 始终小于 c，因此折射率总是大于 1。空气的折射率 n ≈ 1.00，水 n ≈ 1.33，普通玻璃 n ≈ 1.5。
Optical density is not the same as mass density. A material with a higher refractive index is said to be optically denser. Light travels slower in optically denser media.
光密度与质量密度并不等同。折射率较高的材料被认为是光密介质。光在光密介质中传播较慢。
3. Snell’s Law: The Quantitative Relationship | 斯涅尔定律：定量关系
Snell’s law relates the angles of incidence and refraction to the refractive indices of the two media. The formula is:
斯涅尔定律将入射角和折射角与两种介质的折射率联系起来。公式如下：
n₁ sin θ₁ = n₂ sin θ₂
Here, θ₁ is the angle in medium 1 and θ₂ is the angle in medium 2, both measured from the normal. This law applies for any pair of transparent media, as long as the normal is used as the reference direction.
其中 θ₁ 是介质 1 中的光线与法线的夹角，θ₂ 是介质 2 中的光线与法线的夹角，两者均从法线量起。该定律适用于任何一对透明介质，只要以法线为参考方向。
In examinations, you must be comfortable finding unknown angles or refractive indices using this relation. A typical problem gives three of the four quantities and asks you to solve for the fourth.
在考试中，你必须能够熟练运用该关系求解未知角度或折射率。典型题目會给出四个量中的三个，要求你解出第四个。
Remember to set your calculator to degree mode and use inverse sine when needed. Also, note that the formula can be rearranged to n₁ / n₂ = sin θ₂ / sin θ₁.
请记住将计算器设置为角度模式，并在需要时使用反正弦函数。同时注意，该公式可以变形为 n₁ / n₂ = sin θ₂ / sin θ₁。
4. Experimental Determination of Refractive Index | 折射率的实验测定
A classic IB and Edexcel practical involves tracing rays through a rectangular glass block. By plotting sin θ₁ against sin θ₂ (or sin i vs sin r), the gradient gives the refractive index of the glass.
IB 与 Edexcel 的经典实验是通过矩形玻璃块追踪光线。以 sin θ₁ 对 sin θ₂（或 sin i 与 sin r）作图，斜率即為玻璃的折射率。
The procedure: shine a narrow ray of light at the glass block, mark incident and emergent rays, remove the block and draw in the refracted ray inside. Measure angles with a protractor. Repeat for various angles of incidence, then calculate sines and draw a line of best fit.
实验步骤：将一束细光线射入玻璃块，标记入射光线和出射光线，移走玻璃块并画出内部的折射光线。使用量角器测量角度。对不同入射角重复实验，计算正弦值并画出最佳拟合线。
Common errors include parallax when marking rays, inaccurate protractor alignment, and rays not being truly narrow. These can be minimised by using fine pencil lines and taking multiple readings.
常见误差包括标记光线时的视差、量角器未对准以及光线不够细。可通过使用细铅笔线和多次读数来减少这些误差。
5. Total Internal Reflection and the Critical Angle | 全内反射与临界角
When light travels from a denser to a less dense medium, at a particular angle of incidence called the critical angle, θc, the angle of refraction becomes 90°. For any angle of incidence greater than the critical angle, total internal reflection (TIR) occurs: all light is reflected back into the denser medium.
当光从光密介质射向光疏介质时，在某个特定入射角——临界角 θc 下，折射角变为 90°。对于任何大于临界角的入射角，都会发生全内反射（TIR）：所有光线都被反射回光密介质中。
The critical angle is derived from Snell’s law by setting θ₂ = 90°. Thus:
临界角通过斯涅尔定律令 θ₂ = 90° 推导得出：
n₁ sin θc = n₂ sin 90° = n₂
And since sin 90° = 1, we get:
又因为 sin 90° = 1，可得：
sin θc = n₂ / n₁
This formula works only when n₁ > n₂ (i.e., light goes from denser to rarer medium). If n₂ is air (≈ 1), then sin θc = 1 / n₁.
此公式仅在 n₁ > n₂（即光从光密到光疏）时成立。若 n₂ 为空气（≈1），则 sin θc = 1 / n₁。
6. Calculating Critical Angles: Worked Examples | 临界角计算：典型例题
Find the critical angle for a water–air boundary (water refractive index = 1.33).
求水-空气界面的临界角（水的折射率 = 1.33）。
sin θc = 1 / 1.33 ≈ 0.7519
θc = sin⁻¹(0.7519) ≈ 48.8°
This means a ray inside water striking the surface at an angle greater than about 49° from the normal will be totally internally reflected.
这意味着水中的光线以大于约 49°（与法线夹角）的方向射向水面时，会被全内反射。
For a glass–air boundary (glass n = 1.50):
对于玻璃-空气界面（玻璃 n = 1.50）：
sin θc = 1 / 1.50 = 0.6667 → θc ≈ 41.8°
The relatively small critical angle of glass makes it ideal for prisms in periscopes and binoculars.
玻璃较小的临界角使其成为潜望镜和双筒望远镜中棱镜的理想材料。
7. Applications of Total Internal Reflection | 全内反射的应用
Optical fibres use TIR to transmit data as light pulses over long distances with minimal loss. The fibre consists of a high‑index core surrounded by a low‑index cladding. Light entering at an angle greater than the critical angle for the core–cladding boundary undergoes repeated total internal reflections, staying within the core.
光纤利用全内反射以光脉冲的形式长距离传输数据，损耗极小。光纤由高折射率纤芯和低折射率包层组成。以大于纤芯-包层临界角射入的光线会经历多次全内反射，保持在纤芯内传播。
Advantages of optical fibres over copper cables include higher bandwidth, lower signal attenuation, immunity to electromagnetic interference, and greater security.
光纤相较于铜缆的优势包括更高的带宽、更低的信号衰减、不受电磁干扰以及更高的安全性。
Prismatic reflectors in binoculars and periscopes use 45°‑90°‑45° prisms. Light hits the back face at 45°, which exceeds the critical angle for glass (≈42°), thus TIR occurs and the beam is reflected by 90° or 180° depending on design.
双筒望远镜和潜望镜中的棱镜反射器使用 45°-90°-45° 棱镜。光线以 45° 角射向棱镜背面，由于该角度大于玻璃的临界角（约 42°），因此发生全内反射，光束根据设计偏转 90° 或 180°。
Diamond’s sparkle is largely due to its high refractive index (≈2.42), giving a very small critical angle (≈24.4°). Light entering the diamond tends to undergo many internal reflections before exiting, spreading into component colours by dispersion.
钻石的闪耀很大程度归因于其高折射率（约 2.42），从而产生很小的临界角（约 24.4°）。进入钻石的光线在射出前往往经历多次内反射，并通过色散分解成各色光。
8. Dispersion of White Light and Prisms | 白光的色散与棱镜
Although refractive index is often quoted as a single value, it actually varies slightly with wavelength. This phenomenon is called dispersion. For most transparent materials, shorter wavelengths (violet/blue) have a slightly higher refractive index than longer wavelengths (red).
尽管折射率通常以一个单一数值给出，但它实际上随波长而略有变化。这一现象称为色散。对于大多数透明材料，短波长（紫光/蓝光）的折射率略高于长波长（红光）。
When white light passes through a prism, it is refracted twice, and dispersion separates the colours into a spectrum. Violet is deviated the most, red the least. This is direct evidence that the refractive index of glass differs for different colours.
当白光通过棱镜时，它在两次折射中被色散，分解成光谱。紫光偏折最大，红光最小。这直接证明玻璃对不同颜色的光具有不同的折射率。
Note: dispersion is not due to the prism creating colours, but rather separating the colours already present in white light.
注意：色散不是因为棱镜创造了颜色，而是将白光中已存在的各种颜色分离开来。
9. Wavefront Diagrams and the Wave Model | 波前图与波动模型
In the wave model, refraction is illustrated using wavefront diagrams. When plane waves cross into a medium where they travel slower, the wavelength decreases but the frequency stays constant. The change in speed causes the wavefronts to change direction, i.e., refract.
在波动模型中，折射可用波前图示说明。当平面波进入传播速度较慢的介质时，波长减小而频率保持不变。速度变化导致波前改变方向，即发生折射。
At a boundary, one side of a wavefront reaches the new medium first and slows down, while the other side continues at the higher speed until it arrives, causing the whole wavefront to pivot toward the normal. The geometry leads directly to Snell’s law.
在界面上，波前的一侧首先到达新介质并减速，而另一侧继续以较高的速度传播，直到其也到达界面，这导致整个波前向法线方向旋转。由此几何关系可直接导出斯涅尔定律。
This wave‑based explanation is not examinable in great depth at this level, but understanding it can help with conceptual questions about why frequency remains unchanged.
在这一阶段并不要求深入考查基于波动的解释，但理解它有助于回答为何频率保持不变等概念性问题。
10. Common Misconceptions and Exam Tips | 常见误区与应试技巧
Misconception: Refraction occurs because the light ray ‘wants’ to take the shortest path. Truth: It is the change in speed that causes the change in direction.
误区： 折射的发生是因为光线“想”走最短路径。真相： 是速度的变化导致了方向的改变。
Another mistake is confusing the angles: always measure from the normal, not the surface. If a diagram shows the angle to the surface, subtract it from 90° to get the correct angle for Snell’s law.
另一个常见错误是混淆角度：始终从法线开始测量，而非从界面。如果图中给出的是与界面的夹角，需用 90° 减去该值，以获得斯涅尔定律所需的正确角度。
In calculations, ensure you assign n₁ and θ₁ to the same medium, and n₂ and θ₂ to the other medium. Mislabeling can lead to completely erroneous answers.
在计算中，确保 n₁ 和 θ₁ 同属一种介质，n₂ 和 θ₂ 同属另一种介质。标注混亂可能导致完全错误的答案。
For TIR questions, check two conditions: light must travel from denser to rarer medium, and angle of incidence must exceed the critical angle.
对于全内反射类题目，需检查两个条件：光必须从光密介质射向光疏介质，且入射角必须大于临界角。
11. Practice Problem Walkthrough | 典型例题精解
A ray of light travels from water (n=1.33) into air. If the angle of incidence in water is 35°, calculate the angle of refraction in air. Determine whether the ray is bent toward or away from the normal.
一束光从水（n=1.33）射入空气。若水中的入射角为 35°，计算空气中的折射角，并判断光线是靠近还是偏离法线偏折。
Using Snell’s law: 1.33 × sin 35° = 1 × sin θ₂
sin 35° ≈ 0.5736
So 1.33 × 0.5736 = 0.7629 = sin θ₂
θ₂ = sin⁻¹(0.7629) ≈ 49.7°
The ray bends away from the normal because it is entering a less dense medium (air).
该光线因进入光疏介质（空气）而偏离法线偏折。
What is the critical angle for this water‑air boundary?
该水-空气界面的临界角是多少？
sin θc = 1 / 1.33 ≈ 0.7519 → θc ≈ 48.8°
Since the incident angle 35° is less than the critical angle, refraction occurs rather than TIR, consistent with the result above.
由于入射角 35° 小于临界角，发生的是折射而非全内反射，这与上述结果一致。
12. Summary and Links to the Syllabus | 总结与考纲链接
Refraction is a cornerstone topic in waves and optics for both IB Physics (Topic 4.4 and additional higher level) and Edexcel A Level Physics (Topic 5: Waves and Particle Nature of Light). You must be able to define refractive index, apply Snell’s law, understand total internal reflection and its critical angle, and describe practical uses such as optical fibres.
折射是 IB 物理（专题 4.4 及更高层次内容）和 Edexcel A Level 物理（专题 5：波与光的粒子性）中波与光学的基石主题。你必须能够定义折射率、运用斯涅尔定律、理解全内反射及其临界角，并描述光纤等实际应用。
Tables and diagrams are frequently used to test application of Snell’s law. Practice ray tracing and be precise with angle measurement. In exams, show your working step‑by‑step; the formula is provided but substituting correctly is up to you.
考试常通过表格和图表来考查斯涅尔定律的应用。练习光线追踪并精确测量角度。在考试中，逐步展示你的计算过程；公式虽已给出，但正确代入数据仍靠你自己。
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