📚 Refraction of Light: Key Points for IB & OCR Physics | 光的折射：IB与OCR物理考点精讲
Refraction is one of the most fundamental wave behaviours you will encounter in both IB and OCR A-level Physics. When a wave passes from one medium to another, its speed changes, and unless it strikes the boundary head-on, its direction also changes. This bending of light not only explains everyday phenomena such as the apparent depth of a swimming pool but also underpins critical technologies like optical fibres and lenses. A solid grasp of Snell’s law, refractive index, critical angle and total internal reflection is essential for top marks in both coursework and written examinations. In this revision guide, we will walk through every key concept, provide paired explanations in English and Chinese, and highlight typical pitfalls so that you can approach any refraction problem with confidence.
折射是最基本的波行为之一，在IB和OCR A-Level物理中都是一个核心考点。当波从一种介质进入另一种介质时，它的速度会发生变化，并且除非垂直入射，否则传播方向也会改变。光的折射不仅解释了游泳池看起来变浅等日常现象，也是光纤、透镜等重要技术的基础。牢固掌握斯涅尔定律、折射率、临界角和全内反射，对于拿下实验报告和笔试高分至关重要。在本篇考点精讲中，我们将梳理每一个关键知识点，提供英中对照讲解，并提示常见误区，帮助你自信应对任何折射题目。
1. Introduction to Refraction | 折射现象简介
Refraction is the change in direction of a wave as it passes from one transparent medium into another with a different optical density. This occurs because the wave’s speed changes while its frequency remains constant. The ray bends towards the normal (an imaginary line perpendicular to the boundary) if it enters a medium where it travels more slowly, and away from the normal if it enters a medium where it travels faster. The angles of incidence i and refraction r are always measured relative to the normal.
折射是指波从一种透明介质进入另一种光密程度不同的介质时发生的方向改变。这是因为波速改变而频率保持不变。如果波进入波速更慢的介质，光线会偏向法线（虚构的垂直于界面的线）；如果进入波速更快的介质，则光线会偏离法线。入射角 i 和折射角 r 总是相对于法线测量。
The concept of the ‘normal’ is crucial: it is a construction line drawn at a right angle to the surface at the point of incidence. On ray diagrams, all angles must be shown from the normal, never from the surface itself.
法线的概念至关重要：它是在入射点处与界面成直角的一条辅助线。在光路图中，所有角度都应以法线为基准，绝对不要以界面本身为基准。
In IB and OCR assessments, you are often asked to sketch or interpret ray diagrams showing refraction at a plane boundary. Always label the normal, the incident ray, the refracted ray, and the corresponding angles.
在IB和OCR的考核中，常常要求你绘制或分析光线在平面界面上发生折射的光路图。一定要标注法线、入射光线、折射光线及相应的角度。
2. Snell’s Law | 斯涅尔定律
Snell’s law provides the quantitative relationship between the angles of incidence and refraction and the refractive indices of the two media. It is usually written as:
斯涅尔定律给出了入射角、折射角与两种介质折射率之间的定量关系。通常表达为：
n₁ sin θ₁ = n₂ sin θ₂
Here n₁ and n₂ are the absolute refractive indices of medium 1 and medium 2 respectively, θ₁ is the angle of incidence, and θ₂ is the angle of refraction. The law tells us that the product n sin θ remains constant across the interface.
这里 n₁ 和 n₂ 分别是介质1和介质2的绝对折射率，θ₁ 是入射角，θ₂ 是折射角。这一定律表明，n sin θ 的乘积在界面两边保持不变。
Snell’s law assumes that the media are isotropic and that the wavelength of light is small compared to any irregularities at the boundary. It is derived from the conservation of the wave’s frequency and the continuity of wavefronts. In examinations, you will often be given three of the four quantities and asked to calculate the unknown.
斯涅尔定律假设介质是各向同性的，且光波长远小于界面上的任何不规则尺寸。它可以由波的频率守恒和波前连续性推导得到。在考试中，经常给出四个物理量中的三个，要求计算未知的那个。
Be careful with the order of subscripts: the ‘1’ side typically refers to the incident medium and the ‘2’ side to the refractive medium. However, you can label the media in any order as long as you are consistent.
注意下标的顺序：下标1通常代表入射介质，下标2代表折射介质。不过，只要前后一致，介质顺序也可以灵活标注。
3. Refractive Index | 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 that medium v:
介质的绝对折射率 n 定义为真空中的光速 c 与该介质中的光速 v 之比：
n = c / v
Since light always travels more slowly in a material than in a vacuum, n is always greater than 1. For example, air has n ≈ 1.0003, water has n ≈ 1.33, and typical crown glass has n ≈ 1.50. A higher refractive index indicates a greater ‘optical density’ and a slower wave speed.
因为光在任何材料中的速度都小于真空中的速度，所以 n 总是大于 1。例如，空气的 n 约为 1.0003，水的 n 约为 1.33，典型冕牌玻璃的 n 约为 1.50。折射率越大，表示光密程度越高，波速越慢。
| Medium | Refractive index n |
| Vacuum | 1 (exactly) |
| Air | 1.0003 ≈ 1 |
| Water | 1.33 |
| Crown glass | 1.50 – 1.54 |
| Diamond | 2.42 |
Another useful quantity is the relative refractive index, ₁n₂ = n₂/n₁ = v₁/v₂. This appears when light passes between two materials that are not vacuum. For IB and OCR, it is often simpler to apply Snell’s law directly using absolute refractive indices.
还有一个有用的量是相对折射率，₁n₂ = n₂/n₁ = v₁/v₂。当光在非真空的两种介质之间传播时，可以用到这一概念。对于IB和OCR考试，使用绝对折射率直接套用斯涅尔定律通常更简单。
Remember: the frequency of the wave does not change during refraction because it is determined by the source. The wavelength λ changes proportionally to the wave speed (v = fλ). Therefore, when light enters a medium of higher n, its wavelength decreases, which will be important when we discuss dispersion.
记住：波的频率在折射过程中保持不变，因为它由波源决定。波长 λ 会随波速成比例变化（v = fλ）。因此，光进入折射率更高的介质时，波长变短，这一点在讨论色散时很重要。
4. Refraction from a Rarer to a Denser Medium | 光疏到光密介质的折射
When light travels from an optically less dense (rarer) medium to an optically denser one, its speed decreases. According to Snell’s law, the ray bends towards the normal. This means the angle of refraction r is smaller than the angle of incidence i.
当光从光疏介质进入光密介质时，速度减小。根据斯涅尔定律，光线偏向法线，即折射角 r 小于入射角 i。
Consider light moving from air (n₁ ≈ 1) into glass (n₂ = 1.50). If the angle of incidence is 30°, applying n₁ sin i = n₂ sin r gives sin r = (1 × sin 30°)/1.50 ≈ 0.333, so r ≈ 19.5°. The bending towards the normal is clearly illustrated.
考虑光从空气（n₁ ≈ 1）进入玻璃（n₂ = 1.50）。如果入射角为30°，代入 n₁ sin i = n₂ sin r 得到 sin r = (1 × sin 30°)/1.50 ≈ 0.333，因此 r ≈ 19.5°。这清晰地展示了光线向法线靠拢。
A common exam question asks you to explain why a swimming pool appears shallower. This is because light rays from the bottom of the pool are refracted away from the normal as they leave the water, making the virtual image of the bottom higher than its actual position. Refraction from a denser to a rarer medium will be explored next.
一个常见的考题是解释为什么游泳池看起来更浅。这是因为从池底发出的光线离开水面时偏离法线折射，使得池底的虚像上移，看起来比实际位置更浅。我们接下来探讨光从光密介质到光疏介质的折射。
5. Refraction from a Denser to a Rarer Medium & Critical Angle | 光密到光疏介质与临界角
When light travels from a denser medium (higher n) into a rarer medium (lower n), it speeds up and bends away from the normal. Here, the angle of refraction r is always larger than the angle of incidence i.
当光从光密介质（折射率更高）进入光疏介质（折射率更低）时，速度加快并偏离法线。在这种情况下，折射角 r 总是大于入射角 i。
As i increases, r increases even faster. At a specific incident angle, r will reach exactly 90°. This incident angle is called the critical angle, θc. Its value can be found by setting r = 90° in Snell’s law:
随着 i 增大，r 增大得更快。在某一个入射角下，r 会恰好达到90°。这个入射角称为临界角，记作 θc。将 r = 90° 代入斯涅尔定律即可求得临界角：
sin θc = n₂ / n₁ (where n₁ > n₂)
For a ray leaving glass (n₁ = 1.50) and entering air (n₂ ≈ 1.00), sin θc = 1.00 / 1.50 = 0.667, so θc ≈ 41.8°. Many optical devices, such as right-angled prisms in periscopes, rely on the fact that 45° is greater than the critical angle for glass.
对于从玻璃（n₁ = 1.50）进入空气（n₂ ≈ 1.00）的光线，sin θc = 1.00 / 1.50 = 0.667，θc ≈ 41.8°。许多光学器件，如潜望镜中的直角棱镜，正是利用了45°大于玻璃临界角这一事实。
The critical angle is only defined when light initially travels in the denser medium. If the rarer medium is air (n₂ ≈ 1), the formula simplifies to sin θc = 1 / n. This special case is extremely common in IB and OCR calculations.
临界角只有在光最初在光密介质中传播时才有意义。如果光疏介质是空气（n₂ ≈ 1），公式简化为 sin θc = 1 / n。这种特例在IB和OCR计算题中非常常见。
6. Total Internal Reflection | 全内反射
When the angle of incidence exceeds the critical angle for a denser-to-rarer transition, the ray of light is completely reflected back into the denser medium. No refraction occurs; the boundary behaves like a perfect mirror. This phenomenon is called total internal reflection (TIR).
当入射角大于从光密到光疏介质的临界角时，光线被完全反射回光密介质中。没有折射发生，界面表现得像一面完美的镜子。这种现象称为全内反射（TIR）。
For TIR to take place, two conditions must be satisfied simultaneously:
发生全内反射必须同时满足两个条件：
- The light must be travelling from an optically denser medium to a less dense one.
- 光必须从光密介质射向光疏介质。
- The angle of incidence must be greater than the critical angle.
- 入射角必须大于临界角。
In ray diagrams, the reflected ray obeys the law of reflection: the angle of incidence equals the angle of reflection, both measured from the normal. Total internal reflection is more efficient than reflection from metallic mirrors because very little energy is absorbed.
在光路图中，反射光线遵守反射定律：入射角等于反射角，都以法线为基准。全内反射比金属镜面反射效率更高，因为几乎没有能量被吸收。
This principle is exploited in fibre optics, diamond brilliance, and even in mirages. The high refractive index of diamond (n = 2.42) gives a small critical angle (about 24.4°), so light entering the gem undergoes multiple TIRs and emerges sparkling.
这一原理被用于光纤、钻石的璀璨，甚至海市蜃楼。钻石的高折射率（n = 2.42）使临界角极小（约24.4°），进入宝石的光线会经历多次全内反射，最终璀璨夺目。
7. Applications: Optical Fibres | 应用：光纤
An optical fibre consists of a central core made of high-purity glass or plastic, surrounded by a cladding of slightly lower refractive index. Light entering one end of the core at an appropriate angle undergoes repeated total internal reflection at the core–cladding boundary, guiding the light along the fibre with minimal loss.
光纤由高纯度玻璃或塑料构成的中央纤芯以及折射率稍低的包层组成。光以适当角度进入纤芯一端后，会在纤芯与包层的界面上反复发生全内反射，从而沿光纤传导，损耗极小。
The cladding serves two main purposes: it protects the core surface from scratches and contamination, and because its refractive index is only slightly lower than that of the core, it ensures that only rays with very small entry angles are guided, reducing modal dispersion. A typical step-index fibre might have a core of n₁ = 1.50 and cladding of n₂ = 1.48, yielding a critical angle of about 81° at the core-cladding interface.
包层有两大作用：保护纤芯表面免受划伤和污染，以及由于其折射率只比纤芯略低，确保只有入射角度极小的光线才能被传导，从而减少模间色散。典型的阶跃折射率光纤可能采用 n₁ = 1.50 的纤芯和 n₂ = 1.48 的包层，纤芯-包层界面的临界角约为81°。
In exam questions, you may be asked to calculate the maximum acceptance angle for a fibre, or to explain why signals can be transmitted over long distances using TIR. Always link your explanation to the critical angle and Snell’s law.
在考试中，你可能需要计算光纤的最大接收角，或解释为什么利用全内反射可以长距离传输信号。一定要将解释与临界角和斯涅尔定律联系起来。
8. Dispersion of Light | 光的色散
Dispersion is the splitting of white light into its constituent colours because the refractive index of a material depends on the wavelength (or frequency) of light. In most transparent media, the refractive index decreases with increasing wavelength; this is called normal dispersion. Therefore, violet light (shorter wavelength) is refracted more than red light (longer wavelength).
色散是指白光被分解为各色光，原因是材料的折射率与光的波长（或频率）有关。在大多数透明介质中，折射率随波长增大而减小，这称为正常色散。因此，紫光（波长较短）比红光（波长较长）偏折得更多。
When a narrow beam of white light passes through a triangular glass prism, it is refracted twice—once upon entry and once upon exit. The different colours are deviated by different amounts, spreading out into a visible spectrum from red to violet. Red light suffers the least deviation, violet the most.
当一束窄带白光通过三棱镜时，它会发生两次折射——一次在入射时，一次在出射时。不同颜色被偏折的程度不同，从而展开成从红到紫的可见光谱。红光的偏折最小，紫光的偏折最大。
Dispersion is responsible for rainbows, chromatic aberration in lenses, and the design of spectrometers. In the IB and OCR specifications, you are not required to quote Cauchy’s equation, but you should be able to sketch the dispersion of white light by a prism and explain the order of colours.
色散是彩虹、透镜的色差以及光谱仪设计的原因。在IB和OCR大纲中，你不需要引用柯西方程，但应能画出白光通过棱镜发生色散的示意图，并解释颜色排列的顺序。
9. Practical: Measuring the Refractive Index | 实验：测量折射率
A classic experiment for both IB internal assessment and OCR practical skills is to determine the refractive index of a glass block or a semicircular perspex slab. The method involves directing a narrow ray of light at the flat face of the block, marking the incident and emergent rays, and then measuring the angles of incidence i and refraction r.
无论是IB内部评估还是OCR实验技能考查，一个经典的实验是用玻璃块或半圆形有机玻璃板测量折射率。方法是用一束窄光照射方块的平面，标记入射和出射光线的路径，然后测量入射角 i 和折射角 r。
The refractive index n is calculated using Snell’s law rearranged as n = sin i / sin r (assuming the block is surrounded by air). A graph of sin i against sin r yields a straight line through the origin, and its gradient equals the refractive index. Alternatively, you can use a semicircular block and measure the critical angle directly, then compute n = 1 / sin θc.
折射率 n 可以通过转换斯涅尔定律 n = sin i / sin r 来计算（假设玻璃块周围是空气）。绘制 sin i 对 sin r 的图像应得到一条通过原点的直线，其斜率即为折射率。另一种方法是使用半圆形块直接测量临界角，然后用 n = 1 / sin θc 计算。
Sources of error include imprecise ray tracing, difficulty in aligning the normal, and the beam width. Repeating the measurements for several angles, plotting a graph, and using a sharp pencil can all help reduce uncertainty. Always cite the graph’s goodness of fit when discussing reliability.
误差来源包括光线描迹不够精确、法线对齐困难和光束宽度。对不同角度重复测量、绘制图像并使用尖铅笔都有助于减小不确定度。在讨论可靠性时，一定要提到图像的拟合优度。
10. Common Misconceptions | 常见误解
Misconception 1: ‘Light speeds up in a denser medium.’ In fact, light travels slower in a denser (higher n) medium. The term ‘optically dense’ does not mean mechanically dense; it simply means a higher refractive index.
误解一：“光在更密介质中更快。”实际上，光在线度更密（n 更高）的介质中走得更慢。“光密”不是指力学上的密度，只是指折射率更高。
Misconception 2: ‘Refractive index can be less than 1.’ Since n = c/v and v ≤ c, the absolute refractive index is always ≥ 1. Relative refractive indices can be less than 1, but an absolute n < 1 would imply faster-than-light travel, which is impossible.
误解二：“折射率可以小于1。”因为 n = c/v 且 v ≤ c，绝对折射率总是 ≥ 1。相对折射率可以小于1，但绝对 n < 1 意味着超光速，这是不可能的。
Misconception 3: ‘Frequency changes during refraction.’ Frequency is determined solely by the source and remains constant. It is the speed and wavelength that change at the boundary.
误解三：“折射时频率会发生改变。”频率只由波源决定，在折射过程中保持不变。改变的是波速和波长。
Misconception 4: ‘Total internal reflection can happen when light goes from rarer to denser.’ TIR only occurs when light attempts to leave a denser medium for a rarer one at an angle greater than the critical angle.
误解四：“光从光疏射向光密时可能发生全内反射。”全内反射只发生在光试图以大于临界角的角度离开光密介质进入光疏介质时。
11. Key Equations & Summary | 关键公式与总结
To wrap up, here are the indispensable relationships you must be able to recall and apply in any refraction problem:
最后，这里列出你必须能回忆起并能应用的必不可少的折射关系式：
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