A2 Physics: Refraction of Light – Key Exam Points | A2 物理：光的折射考点精讲

📚 A2 Physics: Refraction of Light – Key Exam Points | A2 物理：光的折射考点精讲

Refraction is a fundamental wave phenomenon that underpins much of geometrical optics and fibre technology. In A2 Physics, you must be able to apply Snell’s law, calculate critical angles, and relate refractive index to wave speed and wavelength. This article breaks down every essential exam point, from basic definitions to common pitfalls, to help you score full marks on refraction questions.

折射是波动的基础现象，是几何光学与光纤技术的基石。在 A2 物理中，你必须掌握斯涅耳定律的应用，计算临界角，并建立折射率与波速、波长之间的联系。本文逐一拆解所有关键的考点，从基本定义到常见陷阱，帮助你在折射相关题目中拿下满分。

1. Definition of Refraction | 折射的定义

Refraction is the change in direction of a wave as it passes obliquely from one transparent medium to another, caused by a change in its wave speed. The effect is observed with light, sound, and water waves, but in A2 exams it is almost always about light.

折射是波倾斜地从一种透明介质进入另一种介质时，由于波速改变而引起的传播方向的变化。这一现象在光、声波和水波中都能观察到，但在 A2 考试中几乎只涉及光的折射。

When light enters a slower medium (higher refractive index), it bends towards the normal. When it enters a faster medium (lower refractive index), it bends away from the normal. Crucially, if the wave hits the boundary along the normal, no bending occurs – the light merely changes speed and wavelength.

当光进入速度更慢的介质（折射率较高）时，它会向法线偏折。进入速度更快的介质（折射率较低）时，它会偏离法线。关键的一点是：如果波沿法线方向入射，则不会发生弯曲，光只改变速度和波长。

2. Snell’s Law | 斯涅耳定律

The quantitative relationship between the angles of incidence and refraction is given by Snell’s law. For two media with absolute refractive indices n₁ and n₂, the law states:

入射角与折射角之间的定量关系由斯涅耳定律给出。对于绝对折射率分别为 n₁ 和 n₂ 的两种介质，定律表述为：

n₁ sinθ₁ = n₂ sinθ₂

Here θ₁ is the angle in the first medium and θ₂ in the second, both measured from the normal. The angles are always taken inside the medium, at the point of incidence.

这里 θ₁ 是第一介质中的角度，θ₂ 是第二介质中的角度，两者均从法线量起。角度总是在介质内部的入射点处测量。

Snell’s law can be rewritten as sinθ₁ / sinθ₂ = n₂ / n₁ = v₁ / v₂, where v₁ and v₂ are the speeds of light in the two media. This form is especially useful when comparing two known materials.

斯涅耳定律可改写为 sinθ₁ / sinθ₂ = n₂ / n₁ = v₁ / v₂，其中 v₁ 和 v₂ 分别是光在两种介质中的传播速度。这种形式在比较两种已知材料时特别有用。

The incident ray, refracted ray, and normal all lie in the same plane.
入射光线、折射光线和法线位于同一平面内。
Snell’s law works for any wave type, provided the media are isotropic.
斯涅耳定律适用于任何波，只要介质是各向同性的。

3. Refractive Index: Absolute and Relative | 折射率：绝对折射率与相对折射率

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 定义为真空中的光速 c 与介质中的光速 v 之比：

n = c / v

Since v is always less than c, n is always greater than 1 for transparent materials. The refractive index of air is approximately 1.0003, but in most exam calculations it is taken as exactly 1.

由于 v 总小于 c，对于透明材料 n 恒大于 1。空气的折射率约为 1.0003，但在绝大多数考试计算中取为恰好 1。

The relative refractive index from medium A to medium B is given by n_AB = v_A / v_B = n_B / n_A. This quantity determines which way the light bends when going from A to B.

从介质 A 到介质 B 的相对折射率为 n_AB = v_A / v_B = n_B / n_A。这个量决定了光从 A 到 B 时的弯曲方向。

4. Relationship with Wave Speed and Wavelength | 与波速和波长的关系

When light passes from one medium to another, its frequency f remains unchanged, but its speed and wavelength alter. Since v = fλ, a reduction in speed leads to a proportional reduction in wavelength:

光从一种介质进入另一种介质时，频率 f 保持不变，但速度和波长会发生改变。由 v = fλ 可知，速度减小会导致波长成比例地减小：

v₁ / v₂ = λ₁ / λ₂ = n₂ / n₁

Therefore, in a medium of refractive index n, the wavelength is λ_medium = λ_vacuum / n. This explains why light maintains its colour when refracted – colour is determined by frequency, not wavelength.

因此，在折射率为 n 的介质中，波长为 λ_介质 = λ_真空 / n。这解释了为什么光在折射后颜色不变——颜色由频率决定，而非波长。

A common exam question asks you to calculate the new wavelength when monochromatic light enters water or glass. Always remember to divide the vacuum wavelength by the refractive index.

一个常见的考题是要求计算单色光进入水或玻璃后的新波长。务必记住：真空波长要除以折射率。

5. Critical Angle and Total Internal Reflection | 临界角与全内反射

When light travels from a denser medium to a rarer medium (n₁ > n₂), at a particular incident angle the refracted ray emerges along the boundary, i.e., θ₂ = 90°. This incident angle is the critical angle θ_c.

当光从光密介质射向光疏介质（n₁ > n₂）时，在某一特定入射角下，折射光线会沿界面射出，即 θ₂ = 90°。这个入射角就称为临界角 θ_c。

Applying Snell’s law with θ₂ = 90° gives:

将 θ₂ = 90° 代入斯涅耳定律得到：

sin θ_c = n₂ / n₁

If the second medium is air (n₂ = 1), this reduces to sin θ_c = 1 / n. Total internal reflection (TIR) occurs when the angle of incidence exceeds the critical angle; the light is completely reflected back into the denser medium.

若第二介质为空气（n₂ = 1），则简化为 sin θ_c = 1 / n。当入射角大于临界角时，就会发生全内反射（TIR）；光全部被反射回光密介质中。

TIR is a very efficient reflection – no light energy escapes across the boundary, which is why it is used in optical fibres.

全内反射是一种高效的反射——没有光能穿过界面损失掉，正因如此它被用在光纤中。

6. Conditions for Total Internal Reflection | 全内反射的条件

For TIR to occur, two strict conditions must be met simultaneously:

要发生全内反射，必须同时严格满足两个条件：

The light must be travelling from an optically denser medium to an optically less dense medium (n₁ > n₂).
光必须从光密介质射向光疏介质（n₁ > n₂）。
The angle of incidence in the denser medium must exceed the critical angle for that pair of media.
在光密介质中的入射角必须大于这对介质的临界角。

Many candidates lose marks by forgetting to state both conditions explicitly. In an exam, always phrase them precisely using the terms ‘optically denser’ and ‘critical angle’.

许多考生因为忘记明确写出这两个条件而失分。在考试中，务必使用“光密介质”和“临界角”的术语精确表述。

Remember that TIR does not happen when light is merely passing from glass to air – the incident angle must be above the critical angle for that glass-air interface.

记住，并非光从玻璃射向空气就会发生全内反射——入射角必须大于该玻璃–空气界面的临界角。

7. Optical Density and the Deviation of Light | 光密介质与光线的偏折

The term ‘optically dense’ refers to the value of the refractive index, not the mass density of the material. A material with a higher refractive index is described as optically denser. Light always bends towards the normal when entering an optically denser medium and away from the normal when entering an optically rarer medium.

“光密”一词指的是折射率的大小，而非材料的质量密度。折射率较高的材料称为光密介质。进入光密介质时光线总是向法线偏折，进入光疏介质时则偏离法线。

This provides a quick mental check: if you are told a ray bends towards the normal, the second medium must have a larger refractive index. The change in direction is a consequence of the change in speed across the interface.

这提供了一个快速的心理检验：如果告知光线向法线偏折，那么第二种介质的折射率一定更大。方向的改变是界面两侧速度变化的结果。

In a plane parallel-sided block the emergent ray is parallel to the incident ray but laterally displaced. This displacement increases with the angle of incidence and the thickness of the block. The exam may ask for this displacement or simply to trace the path.

在平行平面透明板中，出射光线与入射光线平行，但发生了侧向位移。这一位移随入射角和板的厚度的增大而增大。考试可能要求计算此位移，或简单地描绘光路。

8. Refraction Through a Prism and Dispersion | 通过棱镜的折射与色散

A glass prism deviates light twice – once at entry and once at exit – giving a net deviation angle. Because the refractive index of glass varies slightly with wavelength (normal dispersion), different colours are deviated by different amounts. This is the principle of the prism spectrum.

玻璃棱镜使光发生两次偏折——一次在入射面，一次在出射面——从而产生一个净偏向角。由于玻璃的折射率随波长略有变化（正常色散），不同颜色的光偏折程度不同。这就是棱镜光谱的原理。

Violet light is slowed more than red light, so it has a higher refractive index in glass and is deviated more. A prism therefore spreads white light into its constituent colours, with red deviated least and violet most.

紫光比红光减速更多，因此在玻璃中的折射率更高，偏折也更大。所以棱镜能将白光分解成其组成的颜色，红光偏折最小，紫光偏折最大。

In a typical A2 question you might be asked to sketch the path of a white light ray through a prism and label the colours, or to explain why dispersion occurs.

在典型的 A2 考题中，你可能被要求画出白光通过棱镜的光路并标注颜色，或解释色散发生的原因。

9. Applications: Optical Fibres | 应用：光纤

Optical fibres rely entirely on total internal reflection to guide light along a thin glass or plastic core surrounded by a cladding of lower refractive index. The core’s refractive index is slightly higher than that of the cladding, ensuring TIR at the core-cladding interface.

光纤完全依赖全内反射来引导光在细玻璃或塑料纤芯中传播，纤芯外面包裹着折射率较低的包层。纤芯的折射率略高于包层，从而确保在芯–包层界面发生全内反射。

Advantages of optical fibres over copper cables include: higher data transmission rate, immunity to electromagnetic interference, lower signal loss, and greater security (light does not leak out easily). Exam questions often ask you to explain these benefits or to calculate the critical angle for the core-cladding boundary.

相比铜缆，光纤的优势包括：数据传输速率更高、不受电磁干扰、信号损耗更低、安全性更好（光不容易泄漏）。试题常要求解释这些优点，或计算芯–包层界面的临界角。

The maximum angle at which light can enter the fibre and still be guided is called the acceptance angle. This depends on the refractive indices of both core and cladding. Numericals based on this principle are common at A2 level.

光能射入光纤并被传导的最大入射角称为接受角。它取决于纤芯和包层的折射率。基于此原理的数值计算在 A2 阶段很常见。

10. Exam Tips and Common Pitfalls | 考试技巧与常见陷阱

Here are the most frequent mistakes made by A2 candidates and how to avoid them:

以下是 A2 考生最常犯的错误及如何避免：

Confusing angles: Always measure angles from the normal, not the surface. If the question gives an angle to the surface, subtract it from 90° first.
混淆角度：务必从法线开始测量角度，而不是界面。若题目给出的是与界面的夹角，先将其从 90° 中减去。
Misapplying the critical angle formula: Use sin θ_c = n_rarer / n_denser only when light is inside the denser medium. Writing 1 / n without checking if the outer medium is air will cost marks.
误用临界角公式：只有当光处于光密介质中时才使用 sin θ_c = n_疏 / n_密。不确认外界是否为空气就直接写 1 / n 会失分。
Forgetting the frequency stays constant: When calculating wavelength in a new medium, use λ’ = λ / n. Never change the frequency.
忘记频率不变：计算在新介质中的波长时，使用 λ’ = λ / n。切勿动频率。
TIR conditions incomplete: In a written question, always state both: denser-to-rarer travel and i > θ_c.
全内反射条件不全：在文字题中，务必将两个条件都写出来：从光密到光疏，以及 i > θ_c。
Units: Refractive index has no units. Speeds should be in m s⁻¹, wavelengths in nm or m.
单位：折射率无单位。速度用 m s⁻¹，波长用 nm 或 m。

Practise ray diagrams and always label the normal, angles, and media. A neat, annotated sketch can earn several marks even if the written explanation is a bit rough.

多练习光路图，并始终标出法线、角度和介质。一幅整洁的带标注的示意图，即使在文字解释有些粗糙的情况下，也常常能为你拿下好几分。

Published by TutorHao | Physics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）

A2 Physics: Refraction of Light – Key Exam Points | A2 物理：光的折射 考点精讲