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

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

Light changes speed and direction when it passes from one transparent medium to another. This phenomenon, called refraction, is a cornerstone of wave optics and appears frequently in IB and AQA Physics exams. Understanding Snell’s law, refractive index, total internal reflection, and their practical applications is essential for solving quantitative problems and explaining natural optical effects.

光从一种透明介质进入另一种介质时，速度与方向都会发生变化。这种现象称为折射，是波动光学的基石，在 IB 和 AQA 物理考试中出现频率极高。掌握斯涅尔定律、折射率、全内反射及其实际应用，对于解决定量问题和解释自然光学现象至关重要。

1. What Is Refraction? | 什么是折射？

Refraction is the bending of a light ray as it crosses the boundary between two media with different optical densities. The change in direction occurs because the speed of light differs in each medium: it travels fastest in a vacuum (c = 3.00 × 10⁸ m s⁻¹) and slows down in materials like glass or water.

折射是光线穿过两种光学密度不同的介质界面时发生的弯曲。方向改变是由于光在不同介质中的速度不同：在真空中最快（c = 3.00 × 10⁸ m s⁻¹），在玻璃或水等材料中变慢。

The incident ray, refracted ray, and the normal at the point of incidence all lie in the same plane. When light enters a denser medium (e.g., from air to glass), it bends towards the normal. Conversely, going into a less dense medium bends the ray away from the normal.

入射光线、折射光线和入射点处的法线都位于同一平面。当光进入更密的介质（例如从空气到玻璃），它会折向法线。反之，进入更疏的介质时，光线会偏离法线。

A key concept is that the frequency of light remains constant across the boundary; only its speed and wavelength change. This explains why the colour of light does not alter during refraction, although its wavelength shortens in a denser medium.

一个关键概念是：光的频率在界面两侧保持不变，只有速度和波长改变。这解释了为什么光在折射时颜色不变，尽管其波长在更密介质中会变短。

2. Snell’s Law – The Refraction Equation | 斯涅尔定律——折射方程

Snell’s law quantitatively links the angles of incidence and refraction with 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。其表达式为：

n₁ sin θ₁ = n₂ sin θ₂

Here n₁ and n₂ are the absolute refractive indices of medium 1 and medium 2, while θ₁ is the angle of incidence and θ₂ is the angle of refraction, both measured from the normal.

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，两者都从法线量起。

If light travels from vacuum (or air, n ≈ 1) into a medium of refractive index n, the law simplifies to sin θ₁ = n sin θ₂. This form is often used when one medium is air. Always ensure your calculator is in degree mode, and check the geometry of the ray diagram carefully.

如果光从真空（或空气，n ≈ 1）进入折射率为 n 的介质，定律可简化为 sin θ₁ = n sin θ₂。当一种介质是空气时常用此形式。务必确保计算器处于角度模式，并仔细核对光线图中的几何关系。

A common exam pitfall is misidentifying the angles. Remember: θ is always the angle between the ray and the normal, not the angle with the surface. Drawing a clear normal line on diagrams prevents this mistake.

考试中常见的陷阱是角度的错误辨识。记住：θ 始终是光线与法线之间的夹角，而不是与界面的夹角。在图上画出清晰的法线可避免这一错误。

3. 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:

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 light travels slower in any material than in vacuum, n is always greater than 1. For example, the refractive index of water is about 1.33, meaning light travels at roughly 2.26 × 10⁸ m s⁻¹ in water.

因为光在任何材料中的传播速度都比真空中慢，所以 n 总是大于 1。例如，水的折射率约为 1.33，意味着光在水中的传播速度约为 2.26 × 10⁸ m s⁻¹。

The refractive index also depends on the wavelength of light. This dependence is called dispersion and is responsible for the splitting of white light into a spectrum by a prism. Shorter wavelengths (violet) generally experience a higher refractive index than longer wavelengths (red) in glass, so they bend more.

折射率还取决于光的波长。这种依赖性称为色散，是棱镜将白光分解为光谱的原因。在玻璃中，短波长（紫光）的折射率通常高于长波长（红光），因此弯曲程度更大。

When comparing two media, the relative refractive index n₂₁ = n₂ / n₁ = v₁ / v₂ = sin θ₁ / sin θ₂ describes how light bends at the interface. This concept is tested when a ray passes from water to glass, for instance.

比较两种介质时，相对折射率 n₂₁ = n₂ / n₁ = v₁ / v₂ = sin θ₁ / sin θ₂ 描述了光在界面处的弯曲规律。例如，光线从水射入玻璃时，这一概念就会受到考查。

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

When light travels from a denser medium to a less dense medium (n₁ > n₂), the refracted ray bends away from the normal. As the angle of incidence increases, the angle of refraction approaches 90°. The incidence angle at which θ₂ = 90° is called the critical angle θc.

当光从光密介质射向光疏介质（n₁ > n₂）时，折射光线偏离法线。随着入射角的增大，折射角趋近于 90°。使 θ₂ = 90° 的入射角称为临界角 θc。

For any incidence angle greater than the critical angle, Snell’s law would require sin θ₂ > 1, which is impossible. In this regime, refraction ceases and the entire boundary acts like a perfect mirror – total internal reflection (TIR) occurs.

对于任何大于临界角的入射角，斯涅尔定律将要求 sin θ₂ > 1，这是不可能实现的。在这个区间，折射消失，整个界面相当于一个完美的反射镜——发生全内反射（TIR）。

The critical angle can be found by setting θ₂ = 90° in Snell’s law: n₁ sin θc = n₂ sin 90°. Since sin 90° = 1, we obtain:

临界角可以通过在斯涅尔定律中令 θ₂ = 90° 求得：n₁ sin θc = n₂ sin 90°。由于 sin 90° = 1，我们得到：

sin θc = n₂ / n₁

If the less dense medium is air (n₂ ≈ 1), the formula simplifies to sin θc = 1 / n₁. For glass with n = 1.5, the critical angle is approximately 41.8°. Two conditions must be met for TIR: the light must travel from a denser medium to a less dense one, and the angle of incidence must exceed the critical angle.

如果光疏介质是空气（n₂ ≈ 1），公式简化为 sin θc = 1 / n₁。对于 n = 1.5 的玻璃，临界角约为 41.8°。要发生全内反射必须满足两个条件：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。

5. Optical Fibres and Their Working Principle | 光纤及其工作原理

Optical fibres are thin strands of glass or plastic that exploit total internal reflection to transmit light signals over long distances with minimal loss. A fibre consists of a core with a higher refractive index surrounded by cladding with a slightly lower refractive index.

光纤是由玻璃或塑料制成的细丝，利用全内反射以极小的损耗长距离传输光信号。光纤由折射率较高的纤芯和折射率略低的包层组成。

Light entering the core at an angle greater than the critical angle for the core–cladding boundary undergoes repeated TIR and propagates along the fibre, even if the fibre is bent. This principle underpins modern telecommunications, endoscopy, and high-speed internet.

光以大于纤芯-包层界面临界角的角度进入纤芯后，会经历多次全内反射，并沿光纤传播，即使光纤发生弯曲也是如此。这一原理支撑着现代电信、内窥镜和高速互联网。

Exam questions may ask you to calculate the critical angle at the core–cladding interface, discuss why cladding is necessary (it protects the core, reduces loss, and allows a larger acceptance angle), or explain signal degradation due to modal and material dispersion.

考试题可能要求计算纤芯-包层界面的临界角，讨论包层为何必不可少（保护纤芯、减少损耗、允许更大的接受角），或解释由于模式色散和材料色散引起的信号衰减。

Acceptance angle is the maximum angle at which light can enter the fibre and still be guided by TIR. It is related to the numerical aperture of the fibre and can be derived using Snell’s law at the air-core interface and the critical angle inside.

接受角是指光进入光纤后仍能通过全内反射传导的最大角度。它与光纤的数值孔径相关，可利用空气-纤芯界面的斯涅尔定律和内部的临界角进行推导。

6. Dispersion and the Prism | 色散与棱镜

Dispersion occurs because the refractive index of a material varies with wavelength. In a triangular glass prism, white light enters and leaves through non-parallel faces, causing different colours to refract by different amounts. Violet light is refracted most, red light least, producing a continuous spectrum.

色散的产生是因为材料的折射率随波长而变化。在三角玻璃棱镜中，白光通过非平行面入射和出射，导致不同颜色的光折射程度不同。紫光折射最大，红光最小，产生连续光谱。

The angle of deviation (δ) for a ray passing through a prism depends on the prism’s apex angle (A), the refractive index, and the angle of incidence. The minimum deviation condition yields a useful formula: n = sin((A + δₘ)/2) / sin(A/2), which can be used to measure n experimentally.

光线通过棱镜的偏向角（δ）取决于棱镜的顶角（A）、折射率和入射角。最小偏向条件提供了一个实用公式：n = sin((A + δₘ)/2) / sin(A/2)，可用于实验测量折射率。

In nature, dispersion is responsible for rainbows. Water droplets act as tiny refractors and reflectors, dispersing sunlight into its constituent colours. A primary rainbow forms when light undergoes one internal reflection inside a droplet; a secondary rainbow appears at a wider angle with two reflections.

在自然界中，色散现象造就了彩虹。小水滴充当微小折射体和反射体，将太阳光分解成其组成颜色。主虹是光在水滴内部经历一次内反射形成的；副虹则以更宽的角度出现，经历两次反射。

7. Apparent Depth and Refraction in Everyday Life | 视深与日常生活中的折射

A straight stick appears bent at the water surface, and a swimming pool looks shallower than it really is. These illusions are explained by refraction. Light rays from an underwater object bend away from the normal as they leave the water, making the object appear at a shallower depth – the apparent depth.

直棍在水面处看起来是弯的，游泳池底部看起来比实际更浅。这些错觉都可以用折射解释。来自水下物体的光线离开水面时偏离法线，使物体看起来位于较浅的位置——即视深。

For near-normal viewing, the relationship between real depth (d_real) and apparent depth (d_app) is:

在接近正上方观察时，实际深度（d_real）与视深（d_app）之间的关系为：

n = d_real / d_app

This approximation holds only for small angles. For a water surface (n = 1.33), an object 2.0 m deep appears to be only about 1.5 m deep. This concept is straightforward to test experimentally with a beaker, a pin, and a ruler.

这个近似仅在小角度下成立。对于水面（n = 1.33），深 2.0 米的物体看起来只有约 1.5 米深。这一概念很容易用烧杯、大头针和尺子进行实验检验。

Mirages on hot roads are another refraction phenomenon, caused by a temperature gradient in the air. The air near the ground is hotter and less dense, with a lower refractive index. Light from the sky bends upwards, creating the illusion of a reflective puddle.

炎热路面上出现的海市蜃楼是另一种折射现象，由空气温度梯度引起。靠近地面的空气较热、密度较低、折射率较小。来自天空的光向上弯曲，造成反射水洼的假象。

8. Experimental Determination of Refractive Index | 折射率的实验测定

The most common experiment involves tracing the path of a light ray through a rectangular glass block. You shine a narrow beam of light at an incident face, mark the emergent ray, and construct the path by joining the points. Measuring the angles with a protractor allows repeated calculations using Snell’s law.

最常见的实验是追踪光线通过矩形玻璃砖的路径。你将一束窄光束照射在一个入射面上，标记出射光线，并通过连接各点构建光路。用量角器测量角度，然后反复运用斯涅尔定律进行计算。

For precision, a graph of sin θ₁ against sin θ₂ should be plotted for various incidence angles. The slope of the best-fit line passing through the origin gives the refractive index of the block. Do not forget to account for systematic errors such as the thickness of the incident ray and possible displacement of the block.

为提高精确度，应针对不同的入射角绘制 sin θ₁ 对 sin θ₂ 的图线。通过原点的最佳拟合线的斜率就是玻璃砖的折射率。别忘了考虑系统误差，例如入射光线的粗细和玻璃砖可能的位移。

An alternative method uses a semicircular block. The ray enters through the curved face along the radius, so it does not refracted at that surface. The straight face then acts as the boundary where all refraction occurs, simplifying measurements and eliminating one source of error.

另一种方法是使用半圆形玻璃砖。光线沿半径方向从曲面入射，因而在该表面不发生折射。平面作为发生所有折射的边界，从而简化了测量并消除了一项误差来源。

9. Common Misconceptions and Exam Tips | 常见误区与应试技巧

One of the biggest misconceptions is that the ray bends because of a change in wavelength alone. Emphasise that refraction is due to the change in speed; the wavelength adjusts to keep the frequency constant. In diagrams, the wavefronts crowd together in the slower medium, illustrating the shorter wavelength.

最大的误区之一是认为光线弯曲仅仅是因为波长发生了变化。要强调折射源于速度的改变；波长调整是为了保持频率不变。在示意图中，波前在较慢的介质中变得密集，显示出较短的波长。

Never confuse total internal reflection with ordinary reflection from a mirror. TIR only occurs at a boundary from denser to less dense medium and requires an angle larger than the critical angle. Also, remember that TIR reflects all incident energy – it is more efficient than metallic mirrors.

千万不要把全内反射与普通镜面反射混淆。全内反射只发生在从光密到光疏介质的界面上，且需要入射角大于临界角。此外，要记住全内反射反射了所有入射能量，比金属镜的效率更高。

When solving numerical problems, first identify the two media, write their refractive indices, and determine whether the ray goes from optically less dense to more dense or vice versa. Always draw a sketch with the normal. Check that your answer physically makes sense – if light enters water from air, the refraction angle should be smaller than the incidence angle.

解数值题时，首先要确定两种介质，写出它们的折射率，并判断光线是从光疏到光密还是相反。务必画出带法线的草图。检查你的答案在物理上是否合理——如果光从空气进入水中，折射角应小于入射角。

10. Summary of Key Points and Formulae | 要点与公式总结

To consolidate your revision, here is a table of key formulae and typical refractive indices you are likely to encounter in the exam.

为巩固复习，下面列出了考试中可能遇到的关键公式和典型折射率。

Quantity	Formula / Value	Notes
Snell’s law	n₁ sin θ₁ = n₂ sin θ₂	Angles measured from normal
Refractive index	n = c / v	Always ≥ 1
Critical angle	sin θc = n₂ / n₁ (n₁ > n₂)	For glass-air: θc ≈ 41.8°
Apparent depth	n = d_real / d_app	Small-angle approximation
Water (n)	1.33	Typical exam value
Crown glass (n)	1.50 – 1.52	Used in many textbook problems
Diamond (n)	2.42	High n, very small critical angle (≈24.4°)

Finally, practise drawing ray diagrams for various scenarios: rectangular block, semicircular block, prisms, and fibres. Being comfortable with the geometry of refraction will give you an edge in both multiple-choice and structured questions.

最后，要多练习各种场景下的光路图绘制：矩形玻璃砖、半圆形玻璃砖、棱镜和光纤。熟练掌握折射的几何关系将使你在选择题和简答题中都更具优势。

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Refraction of Light in IB AQA Physics: Core Exam Points | IB AQA 物理：光的折射 考点精讲