Refraction of Light in IB Physics | IB 物理：光的折射考点精讲

📚 Refraction of Light in IB Physics | IB 物理：光的折射考点精讲

Refraction is one of the most fundamental wave phenomena in the IB Physics syllabus. It describes how light changes direction and speed when it travels from one transparent medium into another. A firm grasp of Snell’s law, refractive index, total internal reflection, and dispersion is essential not only for the examination but also for understanding technologies such as optical fibres and lenses. This masterclass unpacks every key point, pairing clear English explanations with precise Chinese translations to help you master the concepts, equations, and typical exam-style questions.

折射是 IB 物理课程中最基本的波动现象之一。它描述了光从一种透明介质进入另一种介质时方向和速度的变化。牢固掌握斯涅尔定律、折射率、全内反射和色散，不仅对考试至关重要，也是理解光纤和透镜等技术的基础。本文精讲每一个考点，用清晰的英文讲解搭配准确的中文翻译，帮助你掌握概念、公式和典型考题。

1. What is Refraction? | 什么是折射？

Refraction is the change in direction of a wave as it passes from one medium to another with a different optical density. This bending occurs because the wave’s speed changes at the boundary. For light, the frequency remains constant, so a change in speed leads to a change in wavelength, which ultimately causes the ray to deviate from its original path unless the incidence is normal.

折射是指波从一种介质进入光学密度不同的另一种介质时方向的改变。这种偏折是由于波在界面上的速度发生变化。对光来说，频率保持不变，因此速度的改变会导致波长的变化，除非垂直入射，否则光线会偏离原来的路径。

The angle between the incident ray and the normal is called the angle of incidence (i), while the angle between the refracted ray and the normal is the angle of refraction (r). When light enters a denser medium (e.g., from air into glass), it slows down and bends towards the normal. Conversely, moving into a less dense medium causes it to speed up and bend away from the normal.

入射光线与法线之间的夹角叫入射角 (i)，折射光线与法线之间的夹角叫折射角 (r)。光进入光密介质时（例如从空气进入玻璃），速度减慢，向法线偏折；反之，进入光疏介质时速度增大，远离法线偏折。

The phenomenon is a direct consequence of the wave nature of light, describable both by Huygens’ principle and by the conservation of the frequency at the interface. Remember: frequency, determined by the source, never changes; only speed and wavelength adjust.

这一现象是光波动性的直接结果，既可以用惠更斯原理解释，亦符合界面处频率保持不变的规律。请牢记：频率由光源决定，永不改变；只有速度和波长进行调节。

2. Snell’s Law | 斯涅尔定律（折射定律）

Snell’s law quantitatively links the angles of incidence and refraction to the refractive indices of the two media. It is expressed as:

斯涅尔定律定量地将入射角和折射角与两种介质的折射率联系起来，公式为：

n₁ sin θ₁ = n₂ sin θ₂

where n₁ and n₂ are the absolute refractive indices of medium 1 and medium 2, and θ₁ and θ₂ are the angles measured from the normal in the respective media. The law arises from the requirement that the phase of the wave must match along the boundary.

式中 n₁ 和 n₂ 分别为介质 1 和介质 2 的绝对折射率，θ₁ 和 θ₂ 是各自介质中与法线的夹角。定律来源于波在界面处相位必须相匹配的条件。

In many exam questions, one medium is air (n ≈ 1.00), so the law simplifies to sin θ₁ = n₂ sin θ₂. This version is often used to find the refractive index of glass or water. It is essential to always identify which side is ‘medium 1’ and which is ‘medium 2’ to avoid sign errors.

在很多考题中，一种介质是空气 (n ≈ 1.00)，因此定律简化为 sin θ₁ = n₂ sin θ₂。这一形式常用于求玻璃或水的折射率。务必始终确认哪一侧是“介质 1”、哪一侧是“介质 2”，以避免符号错误。

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 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 的比值：

n = c / v

Since v is always less than c for any material medium, n is always greater than 1. A higher n means the light travels more slowly and bends more sharply at the interface. Typical values include n ≈ 1.33 for water, n ≈ 1.50 for crown glass, and n ≈ 2.42 for diamond. Refractive index is dimensionless and depends on both the material and the wavelength of light (dispersion).

由于在任何实物介质中 v 总小于 c，所以 n 总大于 1。n 值越大，光速越慢，界面处偏折越显著。常见值包括：水 n ≈ 1.33，冕玻璃 n ≈ 1.50，钻石 n ≈ 2.42。折射率无量纲，且依赖于材料和光的波长（色散）。

IB often asks students to relate the refractive index to wavelength changes: λ_medium = λ_vacuum / n. This is important for explaining why the colour of light does not change inside a medium but its wavelength does. Frequency stays constant, ensuring colour perception remains the same when light exits the medium.

IB 考试常要求学生联系折射率与波长的变化：λ_介质 = λ_真空 / n。这一点对于解释为何介质内光的颜色不变而波长变化很重要。频率恒定，保证了光离开介质时人眼感知的颜色不变。

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

A medium is described as optically denser if its refractive index is higher than that of the medium it is being compared with. For example, glass (n ≈ 1.5) is optically denser than water (n ≈ 1.33). The term ‘denser’ refers to optical density, not necessarily physical density; it specifically means light travels slower in that medium.

如果一种介质的折射率高于与之比较的介质，则称之为光密介质。例如玻璃 (n ≈ 1.5) 比水 (n ≈ 1.33) 光密。“密”指的是光密度，并非物理密度；它特指光在该介质中行进较慢。

When light travels from a rarer to a denser medium, it bends towards the normal (θ₂ < θ₁). Conversely, going from denser to rarer, it bends away from the normal (θ₂ > θ₁). This directionality is critical when predicting the path of a refracted ray using Snell’s law and is the foundation for total internal reflection.

光从光疏介质进入光密介质时，向法线偏折 (θ₂ < θ₁)；反之，从光密到光疏则远离法线偏折 (θ₂ > θ₁)。在利用斯涅尔定律预测折射光线路径时，这种方向性至关重要，也是全内反射的基础。

5. Total Internal Reflection and Critical Angle | 全内反射与临界角

Total internal reflection (TIR) occurs when light travelling in a denser medium strikes the boundary with a rarer medium at an angle of incidence greater than a specific critical angle θc. At the critical angle, the angle of refraction is exactly 90°, giving Snell’s law the form:

全内反射 (TIR) 发生在光从光密介质射向光疏介质，且入射角大于特定的临界角 θc 时。在临界角处，折射角恰好为 90°，斯涅尔定律化为：

n₁ sin θc = n₂ sin 90° → sin θc = n₂ / n₁

where n₁ > n₂. For angles greater than θc, no refraction occurs; all light is reflected back into the denser medium. TIR is a highly efficient process – almost 100% of the light energy is reflected, unlike ordinary mirror reflection which always involves some absorption.

其中 n₁ > n₂。当入射角大于 θc 时，不会发生折射；所有光都被反射回光密介质。全内反射效率极高——几乎 100% 的光能被反射，这与普通镜面反射总会伴随吸收不同。

Two conditions must be met for TIR: (1) light must travel from a denser to a rarer medium, and (2) the angle of incidence must exceed the critical angle. Exam questions frequently test these conditions, often by asking whether TIR will occur in a given scenario.

全内反射必须满足两个条件：(1) 光必须从光密介质射向光疏介质；(2) 入射角必须大于临界角。试题经常考查这些条件，例如问在给定情景中是否会发生全内反射。

6. Applications of Total Internal Reflection: Optical Fibres | 全内反射的应用：光纤

Optical fibres make use of TIR to transmit light signals over long distances with very little loss. A typical fibre consists of a high-refractive-index core surrounded by a cladding with a slightly lower refractive index. Light entering the core at a suitable angle undergoes repeated TIR at the core-cladding interface, staying confined within the core as it propagates.

光纤利用全内反射实现光信号的长距离低损耗传输。典型光纤由高折射率的纤芯和折射率稍低的包层组成。光以合适角度进入纤芯后，在纤芯-包层界面反复发生全内反射，被束缚在纤芯内向前传播。

The acceptance angle for an optical fibre is the maximum angle at which light can enter the fibre and still be guided. This is related to the numerical aperture, a concept sometimes explored in higher-level IB questions. Optical fibres are crucial in telecommunications, medical endoscopes, and high-speed internet.

光纤的接受角是光能进入光纤并依然被导引的最大角度。这与数值孔径有关，有时会在 IB 高阶题中出现。光纤在通信、医用内窥镜和高速互联网中至关重要。

7. Dispersion of Light | 光的色散

Dispersion is the phenomenon in which the refractive index of a medium varies with the wavelength (or colour) of light. Shorter wavelengths (violet/blue) travel more slowly in glass and therefore are refracted more than longer wavelengths (red). When white light passes through a prism, the different colours are spread out into a spectrum – violet is deviated most, red the least.

色散是介质的折射率随光的波长（或颜色）变化而变化的现象。短波长光（紫/蓝）在玻璃中传播更慢，因此比长波长光（红）偏折更厉害。当白光通过三棱镜时，不同颜色的光被展开成光谱——紫光偏折最大，红光最小。

This dependence of n on wavelength explains rainbows, chromatic aberration in lenses, and why diamond sparkles with so many colours. In IB Physics, you may be asked to explain how a prism produces a spectrum or to sketch the path of red and violet rays through a triangular prism, showing clearly that violet bends more.

折射率对波长的这种依赖关系解释了彩虹、透镜的色差以及钻石为何闪烁出多种色彩。在 IB 物理中，你可能会被要求解释棱镜如何产生光谱，或画出红光和紫光通过三棱镜的路径，清楚地表明紫光偏折更大。

8. Measuring Refractive Index – Practical Investigation | 测定折射率 – 实验探究

A classic IB experiment involves tracing light rays through a transparent rectangular block or a semicircular dish. By measuring the angles of incidence and refraction using pins and a protractor, students can determine the refractive index of the material. The half-circle dish method is often preferred because the ray enters and leaves along the radius, eliminating a second refraction at the exit point, which simplifies analysis.

经典的 IB 实验包括用透明矩形块或半圆形碟传递光线。通过大头针和量角器测量入射角和折射角，学生可以测定材料的折射率。半圆形碟法常被优先选用，因为光线沿半径方向入射和出射，消除了出射点的第二次折射，简化了分析。

Data processing typically involves constructing a graph of sin θ₁ against sin θ₂. The gradient of the best-fit straight line through the origin equals the refractive index of the second medium relative to the first. Uncertainty analysis, error bars, and the use of a line of worst fit are common components that align with IB’s emphasis on practical skills.

数据处理通常需要绘制 sin θ₁ 对 sin θ₂ 的图。通过原点的一条最佳拟合直线的斜率等于第二介质相对第一介质的折射率。不确定度分析、误差棒以及最劣拟合线的使用是常见要素，与 IB 对实验技能的强调相一致。

Measured Quantity (测量量)	Instrument (仪器)	Typical Uncertainty (典型不确定度)
Angle of incidence (入射角)	Protractor (量角器)	±1°
Angle of refraction (折射角)	Protractor (量角器)	±1°
Position of pins (大头针位置)	Ruler (直尺)	±1 mm

9. Worked Example 1 – Using Snell’s Law | 示例 1 – 斯涅尔定律的应用

A ray of light travels from air into a glass block with refractive index 1.50. If the angle of incidence is 30°, calculate the angle of refraction inside the glass.

一束光从空气射入折射率为 1.50 的玻璃块。若入射角为 30°，计算玻璃内的折射角。

Solution: Using n₁ sin θ₁ = n₂ sin θ₂, with n₁ = 1.00, θ₁ = 30°, n₂ = 1.50. So sin θ₂ = (1.00 × sin 30°) / 1.50 = (0.5) / 1.50 = 0.3333. Therefore θ₂ = arcsin(0.3333) ≈ 19.5°.

解：应用 n₁ sin θ₁ = n₂ sin θ₂，n₁ = 1.00, θ₁ = 30°, n₂ = 1.50。得 sin θ₂ = (1.00 × sin 30°) / 1.50 = 0.5 / 1.50 = 0.3333。因此 θ₂ = arcsin(0.3333) ≈ 19.5°。

Notice that the angle is less than the angle of incidence, consistent with a ray bending towards the normal in the denser medium.

注意该角小于入射角，符合光密介质中向法线偏折的规律。

10. Worked Example 2 – Critical Angle for TIR | 示例 2 – 全内反射的临界角

An underwater light source is placed in a swimming pool. What is the critical angle for light travelling from water (n = 1.33) into air? Will a diver looking up at the surface see the entire outside world, or only a limited cone?

游泳池水下有一个光源。光从水 (n = 1.33) 进入空气的临界角是多少？潜水员抬头看水面时，是看到整个外部世界还是仅看到一个有限的锥形视野？

Solution: sin θc = n_air / n_water = 1.00 / 1.33 ≈ 0.7519. Hence θc ≈ 48.8°. Light incident at angles greater than this is totally internally reflected. Thus the diver sees a circular window of the sky bounded by angles up to about 49° from the vertical; beyond that, only reflected images of the pool interior appear.

解：sin θc = n_空气 / n_水 = 1.00 / 1.33 ≈ 0.7519，因此 θc ≈ 48.8°。入射角大于该值的光被全内反射。因此潜水员看到的天空是一个圆形窗口，从垂直方向算起约 49° 以内；超出该角度，只能看到池内景物反射的倒影。

11. Common Misconceptions and Pitfalls | 常见误区与陷阱

One common error is to assume the refracted ray always deviates away from the normal when entering a new medium. Please remember: it depends on whether the second medium is denser or rarer. Always compare refractive indices before deciding the direction of bending.

一个常见错误是以为折射光线进入新介质时总会远离法线。请记住：偏折方向取决于第二介质是光密还是光疏。务必先比较折射率，再判断偏折方向。

Another misconception is that the frequency of light changes during refraction. The correct statement is: frequency is invariant; speed and wavelength change. This explains why the colour of light remains the same even though the wave properties adjust.

另一误区是认为折射时光的频率改变。正确表述是：频率不变；速度和波长变化。这解释了为什么光即使波动特性调整，颜色仍保持不变。

Students also sometimes forget that Snell’s law uses angles measured from the normal, not from the surface. Drawing a normal line on diagrams and labelling angles clearly can prevent this mistake.

学生有时忘记斯涅尔定律使用的是与法线的夹角，而非与界面的夹角。在图上画法线并清晰标出角度，可避免此类错误。

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Refraction of Light in IB Physics | IB 物理：光的折射 考点精讲