Refraction of Light: A-Level Key Concepts | 光的折射：A-Level 考点精讲

📚 Refraction of Light: A-Level Key Concepts | 光的折射：A-Level 考点精讲

Refraction is a fundamental wave phenomenon that frequently appears in A-Level Physics examinations. Understanding how light bends when entering a different medium, applying Snell’s Law, and analysing total internal reflection are essential skills. This article consolidates the key concepts, derivations, and common pitfalls to help you master the topic.

折射是A-Level物理考试中常见的基本波动现象。理解光进入不同介质时如何偏折、应用斯涅尔定律以及分析全内反射是必备技能。本文汇总了核心概念、推导过程和常见误区，助你掌握这一主题。

1. Introduction to Refraction | 折射的基本原理

When a ray of light travels from one transparent medium to another, its direction changes at the boundary unless it strikes perpendicularly. This bending is called refraction and arises from the change in the speed of light between media.

当一束光从一种透明介质进入另一种时，除非垂直入射，否则其传播方向会在界面处发生改变。这种偏折称为折射，是由光在不同介质中速度的差异引起的。

In a vacuum, light travels at c = 3.00 × 10⁸ m s⁻¹. In any material medium, the speed v is slower. The refractive index n quantifies this slowdown. The frequency of the wave remains constant, so the wavelength changes upon entering a new medium.

真空中光速为 c = 3.00 × 10⁸ m s⁻¹。在任何材料介质中，速度 v 较慢。折射率 n 量化了这一减速。波的频率保持不变，因此进入新介质后波长会发生变化。

The ratio of speeds also determines the relative bending. The continuity of wavefronts at the boundary forces the ray to tilt unless it is normal to the surface.

速度之比也决定了相对偏折程度。界面处波前的连续性迫使光线倾斜，除非光线垂直于表面。

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2. Snell’s Law and Refractive Index | 斯涅尔定律与折射率

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

角度与折射率之间的精确关系由斯涅尔定律给出。对于绝对折射率分别为 n₁ 和 n₂ 的两种介质，定律为：

n₁ sin θ₁ = n₂ sin θ₂

where θ₁ is the angle of incidence in medium 1 and θ₂ is the angle of refraction in medium 2. Angles are always measured from the normal to the boundary.

其中 θ₁ 是介质1中的入射角，θ₂ 是介质2中的折射角。角度始终从界面法线量起。

The absolute refractive index of a medium is defined as the ratio of the speed of light in vacuum to the speed in the medium: n = c/v. Since v ≤ c, we have n ≥ 1. For air, n ≈ 1.00.

介质的绝对折射率定义为真空中光速与该介质中光速之比：n = c/v。由于 v ≤ c，因此 n ≥ 1。空气的折射率近似为1.00。

When light enters an optically denser medium (higher n), it bends towards the normal (θ₂ < θ₁). Conversely, when moving into an optically rarer medium, it bends away from the normal.

当光进入光密介质（n较大）时，会向法线偏折（θ₂ < θ₁）。反之，进入光疏介质时，会偏离法线。

The relative refractive index from medium 1 to medium 2 can be written as n₂₁ = n₂/n₁ = v₁/v₂ = sin θ₁/sin θ₂. This is often useful when both media are not vacuum.

从介质1到介质2的相对折射率可写为 n₂₁ = n₂/n₁ = v₁/v₂ = sin θ₁/sin θ₂。当两种介质均非真空时，这往往很有用。

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3. Refractive Index and Wave Speed | 折射率与波速

Because frequency f is invariant across boundaries, the wave relationship v = fλ means that a reduction in speed v leads to a proportional reduction in wavelength λ. Therefore, λ in a medium is given by λ = λ₀/n, where λ₀ is the wavelength in vacuum.

由于频率 f 在界面两侧保持不变，波速关系 v = fλ 意味着速度 v 减小会导致波长 λ 成正比减小。因此，介质中的波长可由 λ = λ₀/n 求得，其中 λ₀ 为真空中的波长。

This explains why a light ray changes direction: the change in speed and wavelength alters the wavefront orientation. Huygens’ principle provides a geometric construction in which each point on a wavefront acts as a source of secondary wavelets; the new wavefront is their envelope. The asymmetry in speed across the boundary causes the envelope to tilt.

这解释了为什么光线会改变方向：速度和波长的变化改变了波前取向。惠更斯原理提供了一个几何构建：波前上的每一点可视为次波源，新波前是这些次波的包络。界面两侧速度的不对称导致包络发生倾斜。

When light passes from a rarer to a denser medium, the wavelength shortens and the ray bends towards the normal. The inverse occurs when light moves into a faster medium.

当光从光疏介质进入光密介质时，波长变短，光线向法线偏折。反之，进入更快介质时则相反。

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4. Principle of Reversibility | 光路可逆原理

Light paths are reversible. If a ray undergoes refraction from medium 1 to 2 with angles θ₁ and θ₂, then a ray travelling from medium 2 to 1 along the reverse direction will have an angle of incidence θ₂ and angle of refraction θ₁. This is consistent with Snell’s law since n₁ sin θ₁ = n₂ sin θ₂ implies n₂ sin θ₂ = n₁ sin θ₁.

光路是可逆的。如果一条光线从介质1到介质2发生折射，入射角为 θ₁，折射角为 θ₂，那么从介质2沿相反方向射向介质1的光线，其入射角为 θ₂，折射角为 θ₁。这与斯涅尔定律一致，因为 n₁ sin θ₁ = n₂ sin θ₂ 意味着 n₂ sin θ₂ = n₁ sin θ₁。

This principle is crucial in understanding why, when you look at a fish underwater, the fish sees you at a similarly displaced position. It also simplifies calculations in multi-layered systems, as the product of successive relative refractive indices equals the overall index ratio.

这一原理对于理解以下现象至关重要：当你观看水下的鱼时，鱼也会在类似偏移的位置看到你。它还能简化多层系统中的计算，因为连续相对折射率的乘积等于总折射率之比。

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

When light travels from an optically denser medium to a rarer medium (e.g., from glass to air), the refracted ray bends away from the normal. As the angle of incidence increases, the angle of refraction approaches 90°. The particular incidence angle at which the refracted angle equals 90° is called the critical angle, θc.

当光从光密介质射向光疏介质（例如从玻璃到空气）时，折射光线偏离法线。随着入射角增大，折射角趋近于90°。当折射角恰好为90°时的入射角称为临界角，记作 θc。

For angles of incidence greater than the critical angle, all the light is reflected back into the denser medium; no refraction occurs. This is total internal reflection (TIR).

当入射角大于临界角时，所有光线被反射回光密介质，不发生折射。这就是全内反射（TIR）。

Using Snell’s law with θ₂ = 90°, we obtain:

将 θ₂ = 90° 代入斯涅尔定律，可得：

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

where n₁ > n₂. For a glass (n≈1.5)–air (n=1) interface, sin θc = 1/1.5, giving θc ≈ 41.8°. For water (n≈1.33), θc ≈ 48.8°.

其中 n₁ > n₂。对于玻璃（n≈1.5）与空气（n=1）界面，sin θc = 1/1.5，得 θc ≈ 41.8°。对于水（n≈1.33），θc ≈ 48.8°。

Two conditions must be met for TIR: light must travel from denser to rarer medium, and the incidence angle must exceed the critical angle.

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。

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6. Optical Fibres | 光纤

Optical fibres rely on total internal reflection to transmit light signals over long distances with minimal loss. A fibre consists of a high-refractive-index core surrounded by a lower-index cladding. Light entering within an acceptance cone undergoes repeated TIR at the core–cladding boundary.

光纤利用全内反射以极低损耗长距离传输光信号。光纤由高折射率的芯和外围较低折射率的包层构成。在接收角锥内进入的光线在芯-包层界面上发生多次全内反射。

The cladding serves several purposes: it protects the core from scratches and contamination that would otherwise cause light leakage; it provides a well-defined lower-index boundary to maintain TIR; and it enables a narrower acceptance angle to reduce modal dispersion.

包层有几个作用：保护纤芯免受划伤和污染，否则会导致光泄漏；提供明确的低折射率界面以维持全内反射；并且有助于减小接收角，以降低模式色散。

At the core–cladding interface, total internal reflection occurs if the angle of incidence in the core exceeds the critical angle between core and cladding. The maximum acceptance angle outside the fibre can be related to the refractive indices via numerical aperture.

在芯-包层界面，若芯中的入射角大于芯与包层之间的临界角，则发生全内反射。光纤外部的最大接收角可通过数值孔径与折射率关联起来。

Applications include high-speed internet, endoscopy in medicine, and sensing technologies. Students may be asked to calculate the critical angle for a given fibre or explain why the cladding is essential.

应用包括高速互联网、医用内窥镜和传感技术。学生可能遇到计算给定光纤的临界角或解释包层为何必不可少等问题。

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7. Refraction through a Prism | 棱镜折射

A triangular prism with refractive index n and apex angle A causes light to deviate by an angle D. The relationship involves refraction at two faces. The total deviation D = i₁ + i₂ – A, where i₁ is the angle of incidence at the first face and i₂ is the angle of emergence at the second face.

折射率为 n、顶角为 A 的三棱镜会使光线偏转一个角度 D。这一关系涉及两个面的折射。总偏向角 D = i₁ + i₂ – A，其中 i₁ 是第一面的入射角，i₂ 是第二面的出射角。

At the minimum deviation position Dₘ, the ray passes symmetrically through the prism: i₁ = i₂ and the internal angles at both faces are equal. This gives the useful formula:

在最小偏向角位置 Dₘ 处，光线

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