Refraction of Light | 光的折射考点精讲

📚 Refraction of Light | 光的折射考点精讲

Refraction is the change in direction of a wave passing from one medium to another caused by its change in speed. In IGCSE CCEA Physics, understanding how light bends at boundaries between different materials is essential. This article breaks down the key concepts of refraction, Snell’s law, critical angle, total internal reflection, and practical applications — all aligned with the CCEA specification.

折射是指波从一种介质进入另一种介质时，由于速度改变而发生的方向变化。在 IGCSE CCEA 物理中，理解光在不同材料边界处如何弯曲至关重要。本文拆解折射、斯涅尔定律、临界角、全反射及其实际应用等核心概念，紧密贴合 CCEA 考纲要求。

1. What is Refraction? | 什么是折射？

When a light ray travels from one transparent medium to another (e.g., air to glass), its speed changes. This speed change causes the ray to change direction, unless it hits the boundary at exactly 90°. The bending of light at the interface of two media is called refraction.

当光线从一种透明介质进入另一种透明介质（如从空气到玻璃）时，其速度会发生变化。除非光线以恰好 90° 入射到界面，否则速度的改变会导致光线方向改变。光在两种介质界面处的弯曲现象称为折射。

The speed of light in a vacuum is approximately 3.00 × 10⁸ m/s. In other materials, light always travels slower. This slowing down is responsible for the bending effect. If light enters a denser medium at an angle, it bends towards the normal line — an imaginary line perpendicular to the surface at the point of incidence.

光在真空中的速度约 3.00 × 10⁸ m/s。在其他材料中，光总是速度较慢。这种减速导致了弯曲效应。若光以一定角度进入光密介质，它会向法线偏折 —— 法线是在入射点垂直于界面的一条假想线。

2. Key Terms in Refraction | 折射中的关键术语

English: To describe refraction precisely, we use several important terms:

Incident ray: the incoming light ray.
Refracted ray: the ray that has changed direction after passing into the new medium.
Normal: a line drawn at 90° to the surface at the point of incidence.
Angle of incidence (i): angle between the incident ray and the normal.
Angle of refraction (r): angle between the refracted ray and the normal.
Optical density: a measure of how much a medium slows down light; unrelated to mass density.

中文： 为精确描述折射，我们使用几个重要术语：

入射光线： 进入新介质前的光线。
折射光线： 进入新介质后方向改变的光线。
法线： 在入射点垂直于界面的一条假想线。
入射角 (i)： 入射光线与法线的夹角。
折射角 (r)： 折射光线与法线的夹角。
光密度： 衡量介质使光减速程度的量；与质量密度无关。

Always measure angles from the normal, never from the surface. This is a common source of error in ray diagrams and calculations.

始终从法线开始测量角度，而不是从界面。这是光线图与计算中常见的错误来源。

3. Snell’s Law | 斯涅尔定律

Snell’s law gives the mathematical relationship between the angles of incidence and refraction when light passes from one medium to another. It is expressed as:

n₁ sin θ₁ = n₂ sin θ₂

斯涅尔定律给出了光线从一种介质传播到另一种介质时入射角与折射角之间的数学关系。其表达式为：

n₁ sin θ₁ = n₂ sin θ₂

Where n₁ and n₂ are the absolute refractive indices of the first and second media, and θ₁ (or i) and θ₂ (or r) are the angles measured from the normal. In many IGCSE problems, one medium is air (n ≈ 1.00), so the formula simplifies to:

n = sin i / sin r

其中 n₁ 和 n₂ 分别是第一种和第二种介质的绝对折射率，θ₁（或 i）和 θ₂（或 r）是从法线测量的角度。在许多 IGCSE 问题中，一种介质是空气（n ≈ 1.00），因此公式简化为：

n = sin i / sin r

This simplified form is used when light travels from air into a denser medium. Remember, i is in air, r is in the denser medium. If light goes from denser to rarer, swap the indices appropriately.

当光从空气进入光密介质时使用此简化形式。记住，i 在空气中，r 在光密介质中。若光从光密到光疏，应适当交换折射率。

4. Refractive Index and Speed of Light | 折射率与光速

The absolute refractive index (n) of a medium is defined as the ratio of the speed of light in vacuum (c) to the speed of light in that medium (v):

n = c / v

介质的绝对折射率 (n) 定义为光在真空中的速度 (c) 与光在该介质中的速度 (v) 之比：

n = c / v

For example, the refractive index of water is about 1.33, meaning light travels 1.33 times slower in water than in vacuum. The following table lists typical refractive indices for IGCSE:

Medium / 介质	Refractive Index (n) / 折射率	Speed of light (×10⁸ m/s) / 光速
Vacuum / 真空	1.00	3.00
Air / 空气	≈ 1.00	≈ 3.00
Water / 水	1.33	2.26
Perspex / 有机玻璃	1.50	2.00
Glass (crown) / 玻璃（冕牌）	1.50–1.55	1.94–2.00
Diamond / 钻石	2.42	1.24

When light passes from one medium to another, its frequency remains constant, but its wavelength changes. This follows from wave equation v = fλ; because v decreases in a denser medium and f is fixed, λ must also decrease.

当光从一种介质进入另一种介质时，频率保持不变，但波长改变。由波速方程 v = fλ 可知，由于在光密介质中 v 减小而 f 不变，λ 必定减小。

5. Optically Denser and Rarer Media | 光密介质与光疏介质

A medium with a higher refractive index is said to be optically denser. One with a lower refractive index is optically rarer. Note: optical density has nothing to do with mass density. For example, oil has a higher refractive index than water, yet floats on water.

折射率较高的介质称为光密介质，折射率较低的称为光疏介质。注意：光密度与质量密度无关。例如，油的折射率高于水，却能浮在水面上。

When light goes from a rarer to a denser medium, it bends towards the normal (angle of refraction < angle of incidence). Conversely, when light goes from a denser to a rarer medium, it bends away from the normal (angle of refraction > angle of incidence). This can be remembered by the phrase: “Rarer to Denser – towards the Normal.”

当光从光疏介质射向光密介质时，光线向法线偏折（折射角 < 入射角）。反之，当光从光密介质射向光疏介质时，光线远离法线偏折（折射角 > 入射角）。可通过口诀记忆：“疏入密，向法偏”。

This directional change is easily worked out using Snell’s law: if n₂ > n₁, sin θ₂ must be smaller than sin θ₁, so θ₂ < θ₁.

此方向变化可用斯涅尔定律轻松计算：若 n₂ > n₁，则 sin θ₂ 必须小于 sin θ₁，因此 θ₂ < θ₁。

6. Total Internal Reflection (TIR) | 全反射

When light travels from a denser medium to a rarer medium, it bends away from the normal. As the angle of incidence increases, the refracted angle approaches 90°. At a particular incident angle, called the critical angle (c), the refracted ray is at 90° to the normal, travelling along the boundary.

当光从光密介质射向光疏介质时，光线远离法线偏折。随着入射角增大，折射角逐渐接近 90°。在一个特定的入射角——称为临界角 (c)——处，折射光线与法线成 90°，沿界面传播。

If the angle of incidence is increased beyond the critical angle, all the light is reflected back into the denser medium. This phenomenon is called total internal reflection (TIR). No light passes into the rarer medium.

若入射角增大到超过临界角，所有光线都会反射回光密介质中。这一现象称为全反射 (TIR)。没有光线会进入光疏介质。

Two conditions must be met for TIR to occur:

The light must be travelling from a denser medium to a rarer medium.
The angle of incidence must be greater than the critical angle for that interface.

全反射必须满足两个条件：

光线必须从光密介质射向光疏介质。
入射角必须大于该界面的临界角。

7. Critical Angle and Its Calculation | 临界角及其计算

Using Snell’s law, the critical angle c can be calculated when light goes from a medium of refractive index n into air (n = 1). At the critical angle, the refracted angle is 90°, so sin r = sin 90° = 1. Substituting into n = sin i / sin r (with i = c, r = 90°):

n = sin c / sin 90° => n = sin c / 1 => sin c = 1/n

利用斯涅尔定律，当光从折射率为 n 的介质进入空气（ n = 1 ）时，可计算临界角 c 。在临界角下，折射角为 90°，因此 sin r = sin 90° = 1。代入 n = sin i / sin r （其中 i = c, r = 90°）：

n = sin c / sin 90° => n = sin c / 1 => sin c = 1/n

Thus, the critical angle depends only on the refractive index of the denser medium. For example, for glass with n = 1.50, sin c = 1/1.50 = 0.667, so c ≈ 41.8°. For water (n = 1.33), c ≈ 48.8°. A higher refractive index gives a smaller critical angle, making TIR occur more easily.

因此，临界角仅取决于光密介质的折射率。例如，对于折射率 n = 1.50 的玻璃， sin c = 1/1.50 = 0.667，c ≈ 41.8°。对于水（ n = 1.33 ），c ≈ 48.8°。折射率越高，临界角越小，越容易发生全反射。

8. Dispersion of White Light | 白光的色散

When white light passes through a prism, it is split into a spectrum of colours (red, orange, yellow, green, blue, indigo, violet). This effect, called dispersion, occurs because different colours of light have slightly different refractive indices in glass — violet light slows down more and bends more than red light.

当白光通过棱镜时，被分解成彩色光谱（红、橙、黄、绿、蓝、靛、紫）。这种效应叫做色散，原因在于不同颜色的光在玻璃中的折射率略有不同 —— 紫光比红光减慢的程度更大，弯曲也更明显。

In a prism, a rainbow pattern emerges: red is deviated the least, violet the most. This is why a prism can produce a visible spectrum. Remember: the frequency of light does not change during refraction; only speed and wavelength change. Red light has the longest wavelength in the visible spectrum and is refracted the least.

在棱镜中，会出现彩虹图案：红光偏折最小，紫光偏折最大。这就是棱镜能产生可见光谱的原因。记住：折射过程中光的频率不变；只有速度和波长改变。红光在可见光谱中波长最长，折射最小。

9. Real-World Applications of Refraction | 折射的实际应用

Refraction explains many everyday phenomena. For example, a swimming pool appears shallower than it really is because light rays from the bottom bend away from the normal when they leave the water. The brain interprets the rays as having travelled in straight lines, so the object appears raised.

折射可解释许多日常现象。例如，游泳池看起来比实际浅，因为从池底射出的光线离开水面时远离法线偏折。大脑解读时认为光线沿直线传播，因而物体看起来被抬高了。

Lenses in glasses, cameras, and microscopes rely on refraction to focus light. Convex lenses converge light rays, while concave lenses diverge them. Additionally, mirages are an optical phenomenon caused by the refraction of light in layers of air at different temperatures — bending the light path so that a distant object appears displaced or a pool of water appears on a hot road.

眼镜、相机和显微镜中的透镜依靠折射来聚焦光线。凸透镜会聚光线，凹透镜发散光线。此外，海市蜃楼是由不同温度空气层中的光线折射引起的光学现象 —— 光线路径弯曲，使远处物体看起来移位，或在酷热的道路上出现“水洼”。

10. Applications of Total Internal Reflection | 全反射的应用

Total internal reflection is used extensively in optical fibres, which carry data as pulses of light. An optical fibre consists of a dense glass core surrounded by a cladding of lower refractive index. Light entering the core at an angle greater than the critical angle is repeatedly totally internally reflected along the fibre, travelling long distances with minimal loss.

全反射广泛应用于光纤中，光纤以光脉冲的形式传输数据。光纤由高折射率的玻璃纤芯和低折射率的包层构成。以大于临界角的角度进入纤芯的光线，在光纤内不断发生全反射，沿长距离传输且损耗极小。

Other applications include endoscopes used in medicine to view inside the body, and prismatic periscopes and binoculars that use right-angled prisms as reflectors. Prisms can achieve 100% reflection via TIR, unlike mirrors which always lose some light. Additionally, the “sparkle” of diamonds is due to TIR caused by their high refractive index and specially cut facets.

其他应用包括医用内窥镜（用于观察体内），以及利用直角棱镜作为反射器的棱镜潜望镜和双筒望远镜。棱镜通过全反射实现 100% 反射，不同于总会损失部分光线的平面镜。此外，钻石的“闪耀”归因于其高折射率和特殊切割刻面导致的全反射。

11. Experiment: Finding the Refractive Index of Glass | 实验：测定玻璃的折射率

A common IGCSE practical involves tracing a ray of light through a rectangular glass block. Using a ray box, pins, and a protractor, you can measure various angles of incidence (i) and corresponding angles of refraction (r). For each pair, calculate sin i and sin r. Plotting sin i (y-axis) against sin r (x-axis) gives a straight-line graph passing through the origin; its gradient equals the refractive index, n.

IGCSE 常考的一个实验是利用矩形玻璃砖追踪光线。借助光线盒、大头针和量角器，你可以测量不同入射角 i 及对应的折射角 r。针对每对数据计算 sin i 和 sin r。以 sin i 为纵轴、 sin r 为横轴作图，得到一条通过原点的直线；该直线的斜率即为折射率 n。

Key precautions: Ensure the block is placed so that the incident ray enters the curved outline? No, for a rectangular block, use the straight edges. Align pins carefully to avoid parallax error. Check that the normal is correctly drawn at the point of incidence, and measure angles with a protractor to 0.5° precision if possible. Repeat measurements and take averages to reduce random errors.

主要注意事项：确保玻璃砖的位置正确，入射光线从一面进入，在另一面射出。仔细对齐大头针以避免视差。检查法线是否在入射点正确画出，尽量使用量角器精确到 0.5°。重复测量并取平均值以减少随机误差。

12. Common Mistakes and Exam Tips | 常见错误与考试提示

Students often confuse the direction of bending: remember, if light goes into a denser medium, it bends towards the normal. In ray diagrams, always label the normal and measure angles from it, not from the surface.

学生常混淆弯曲方向：记住，若光进入光密介质，就向法线偏折。在光线图中，务必标出法线，并从法线测量角度，而非从界面。

When solving TIR problems, check that the ray is travelling from denser to rarer and that the angle of incidence exceeds the critical angle. Additionally, in Snell’s law calculations, ensure your calculator is in degree mode. Some questions ask for the critical angle in a medium – use sin c = 1/n only when the second medium is air (or vacuum).

在解答全反射问题时，要确认光线从光密至光疏，且入射角大于临界角。另外，在斯涅尔定律计算中，确保计算器处于角度模式。某些题目要求求解介质中的临界角 —— 仅当第二种介质是空气（或真空）时才使用 sin c = 1/n。

Finally, in the practical context, be prepared to describe how you would obtain reliable sin i vs sin r data, how to minimise errors, and how to calculate n from the gradient of the graph or directly using n = sin i / sin r. Understanding the underlying physics rather than just memorising the formula leads to higher marks on extended response questions.

最后，在实验情境中，要做好准备描述如何获取可靠的 sin i 对 sin r 数据，如何减小误差，以及如何通过图像斜率或直接使用 n = sin i / sin r 来计算 n。理解背后的物理原理，而不仅仅是死记公式，能在拓展题中获得更高分数。

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Refraction of Light | 光的折射 考点精讲