📚 Refraction of Light & Refractive Index (Edexcel IGCSE Science 3.8.2) | 光的折射与折射率 (Edexcel IGCSE 科学 3.8.2)
Refraction is a fundamental wave phenomenon that occurs when light passes from one transparent medium to another, changing speed and direction. In Edexcel IGCSE Science (Physics component, specification point 3.8.2), understanding refraction and the refractive index is essential for explaining how lenses work, why a swimming pool looks shallower, and how optical fibres transmit data. This article covers the laws of refraction, the refractive index (n), Snell’s law, total internal reflection, critical angle, and key experimental methods, providing a thorough revision resource.
折射是一种基本的波动现象：当光从一种透明介质斜射入另一种透明介质时，由于传播速度改变，光线会发生偏折。在 Edexcel IGCSE 科学（物理部分，考纲 3.8.2）中，理解折射和折射率对于解释透镜成像、游泳池变浅的原因以及光纤如何传输数据至关重要。本文将涵盖折射定律、折射率 (n)、斯涅尔定律、全反射、临界角以及关键实验方法，为一篇完整的复习资料。
1. What is Refraction? | 什么是折射？
Refraction is the bending of light rays when they travel obliquely from one transparent medium to another with a different optical density. When light enters a denser medium, such as from air into glass or water, its speed decreases and it bends towards the normal (the imaginary line perpendicular to the boundary). Conversely, when light moves into a less dense medium, it speeds up and bends away from the normal. If the incident ray strikes the boundary along the normal, no bending occurs—only a change in speed.
折射是指光线从一种透明介质斜射入另一种光密度不同的介质时发生的弯曲现象。当光进入光密介质（例如从空气进入玻璃或水）时，速度减小，光线向法线（垂直于界面的假想线）靠拢。反之，当光进入光疏介质时，速度增大，光线偏离法线。如果入射光线沿法线方向射入界面，则不会发生弯曲，仅速度改变。
2. The Laws of Refraction | 折射定律
Edexcel IGCSE requires you to recall two laws of refraction. First, the incident ray, the refracted ray and the normal at the point of incidence all lie in the same plane. Second, for a given pair of media, the ratio of the sine of the angle of incidence (i) to the sine of the angle of refraction (r) is a constant. This constant is called the refractive index (n) of the second medium with respect to the first. These two statements form the foundation for all quantitative work on refraction.
Edexcel IGCSE 要求你记住两条折射定律。第一，入射光线、折射光线和入射点处的法线位于同一平面内。第二，对于给定的一对介质，入射角 (i) 的正弦与折射角 (r) 的正弦之比是一个常数。这个常数称为第二种介质相对于第一种介质的折射率 (n)。这两个陈述构成了所有折射定量计算的基础。
3. Understanding Refractive Index | 理解折射率
t in a vacuum, n is always greater than 1 for any material. A higher refractive index indicates that light travels more slowly in the medium and bends more strongly. Table 1 shows typical values.
折射率 (n) 衡量介质使光速减慢的程度，定义为真空中的光速 (c) 与介质中的光速 (v) 之比：n = c/v。由于光在真空中速度最快，任何材料的折射率都大于 1。折射率越高，表示光在介质中传播越慢，弯曲也就越剧烈。表 1 列出了常见的折射率值。
| Medium | Refractive index (n) |
|---|---|
| Vacuum | 1.00 |
| Air (at sea level) | ≈1.00 |
| Water | 1.33 |
| Perspex / acrylic | 1.49 |
| Crown glass | 1.50 |
| Flint glass | 1.60–1.90 |
| Diamond | 2.42 |
4. Snell’s Law: n = sin i / sin r | 斯涅尔定律：n = sin i / sin r
When light travels from a vacuum (or air) into another medium, Snell’s law is written as:
n = sin i / sin r
m n = sin i / sin r. Always ensure i and r are measured from the normal, not the boundary.
当光从真空（或空气）进入另一种介质时，斯涅尔定律写作：
n = sin i / sin r
其中 i 为真空/空气中的入射角，r 为介质中的折射角，n 是该介质的绝对折射率。如果光在两种非真空介质之间传播，关系式变为 n₁ sin θ₁ = n₂ sin θ₂。在 IGCSE 阶段，计算主要集中在简化形式 n = sin i / sin r。务必记住 i 和 r 是从法线量起，而非从界面量起。
5. Measuring Refractive Index Experimentally | 实验测定折射率
in i / sin r for several angles and find an average value. Repeating for different angles improves accuracy. Alternatively, a semicircular block can be used so that the ray enters along the radius and leaves without further deviation, simplifying angle measurement.
IGCSE 的一项标准实验是追踪光线穿过矩形玻璃块或有机玻璃块。学生让一束窄光以一定角度射向一个面，标记出入射光线和出射光线，然后画出在块内传播的折射光线。用角度量角器测量 i 和 r，对不同角度计算 n = sin i / sin r 并求出平均值。多次重复不同角度可提高准确性。也可以用半圆形玻璃块，使光线沿半径方向射入，出射时不发生进一步偏折，从而简化角度测量。
6. Total Internal Reflection | 全反射
Total internal reflection (TIR) occurs when light travelling in a denser medium strikes a boundary with a less dense medium at an angle of incidence greater than the critical angle (c). Under these conditions, all the light reflects back into the denser medium, and no refraction takes place. TIR is a very efficient way to guide light, as almost no energy is lost. Two essential conditions must be met: the light must move from a higher refractive index material to a lower one, and the angle of incidence must exceed the critical angle.
全反射 (TIR) 发生在光从光密介质射向光疏介质的界面上，且入射角大于临界角 (c) 时。在这种情况下，所有光线都被反射回光密介质，不发生折射。全反射是导引光的高效方式，几乎无能量损失。必须满足两个条件：光必须从折射率较高的材料射向折射率较低的材料，且入射角必须大于临界角。
7. Critical Angle and Its Calculation | 临界角及其计算
less dense medium. From Snell’s law, when r = 90°, sin r = 1, so n = 1 / sin c. Therefore:
sin c = 1 / n
its high refractive index, causing a brilliant sparkle from multiple internal reflections.
临界角 (c) 是光密介质中的入射角，它使光疏介质中的折射角恰好等于 90°。根据斯涅尔定律，当 r = 90° 时，sin r = 1，因此 n = 1 / sin c。于是有：
sin c = 1 / n
该公式假定光从光密介质射入空气（或真空）。例如，水 (n = 1.33) 的 sin c = 1/1.33 ≈ 0.75，c ≈ 49°；玻璃 (n = 1.50) 时 c ≈ 42°。值得注意的是，钻石因其高折射率而具有极小的临界角 (c ≈ 24°)，多次内反射使其璀璨耀眼。
8. Optical Fibres and Prisms | 光纤和棱镜
Optical fibres exploit total internal reflection to transmit light signals over long distances with minimal loss. The core of a fibre has a higher refractive index than the outer cladding, ensuring that light entering at a suitable angle repeatedly undergoes TIR and stays within the core. This technology underpins high-speed internet and medical endoscopes. Prisms in periscopes and binoculars also use TIR at 45° to reflect light efficiently without the need for silvered mirrors.
光纤利用全反射原理，以极低的损耗长距离传输光信号。光纤纤芯的折射率高于外包层，确保以适当角度进入的光线反复发生全反射，始终留在纤芯内。该技术支撑着高速互联网和医用内窥镜。潜望镜和双筒望远镜中的棱镜也利用 45° 全反射高效反射光线，无需镀银镜面。
9. Real and Apparent Depth | 实深与视深
Refraction makes objects submerged in water appear closer to the surface than they really are. When viewing vertically from air into water, the apparent depth (dapp) is less than the real depth (dreal). For small angles of incidence, the refractive index can be approximated as:
n ≈ real depth / apparent depth
This explains why a swimming pool looks shallower than its true depth, and why a straight stick appears bent at the water’s surface. Understanding this effect is important for safety when judging water depth.
折射使浸没在水中的物体看起来比实际更接近水面。当从空气垂直向下观察水中物体时，视深 (dapp) 小于实深 (dreal)。对于小入射角，折射率可近似为：
n ≈ 实深 / 视深
这解释了游泳池看起来比实际浅的原因，也解释了为何直棍在水中交界处看似弯折。理解该效应对判断水深、保障安全非常重要。
10. Key Points Summary | 重点总结
Here are the essential takeaways for Edexcel IGCSE Science 3.8.2:
- Refraction occurs due to a change in wave speed at a boundary between two media of different optical densities.
- The incident and refracted rays and the normal are coplanar; n = sin i / sin r (Snell's law).
- Refractive index n = c/v and is always ≥ 1.
- Total internal reflection occurs when light travelling from a denser to a less dense medium has an angle of incidence greater than the critical angle c.
- Critical angle: sin c = 1/n (where the second medium is air).
- Applications include optical fibres, prisms and the real/apparent depth relationship.
以下是 Edexcel IGCSE 科学 3.8.2 的核心要点：
- 折射是由于波在不同光密度介质界面处的速度变化而引起的。
- 入射光线、折射光线和法线共面；n = sin i / sin r（斯涅尔定律）。
- 折射率 n = c/v，始终 ≥ 1。
- 当光从光密介质射向光疏介质，且入射角大于临界角 c 时，发生全反射。
- 临界角公式：sin c = 1/n（假设另一介质为空气）。
- 应用包括光纤、棱镜以及实深/视深关系。
Published by TutorHao | Science Revision Series | aleveler.com
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