Refraction of Light | 光的折射

📚 Refraction of Light | 光的折射

Refraction is a fundamental wave phenomenon where light changes direction as it passes from one transparent medium to another. This bending occurs because the speed of light is different in different materials. In the GCSE AQA Physics course, you need to understand the laws of refraction, how to calculate refractive index, the conditions for total internal reflection, and practical applications such as optical fibres. This article breaks down every key concept with clear explanations, followed by equivalent Chinese translations, to help you master the topic.

折射是一种基本的波动现象：当光从一种透明介质进入另一种透明介质时，传播方向会发生改变。这种偏折是由于光在不同介质中的速度不同而引起的。在GCSE AQA物理课程中，你需要理解折射定律、如何计算折射率、全内反射的条件以及光纤等实际应用。本文拆解每一个关键概念，并以清晰的中英对照讲解，助你彻底掌握该主题。

1. What Is Refraction? | 什么是折射？

Refraction is the change in direction of a wave when it travels from one medium to another, caused by a change in its speed. For light, this is most clearly seen when a ray enters glass or water from air. If the light hits the boundary at an angle, it bends. If it hits along the normal (perpendicular to the surface), it will not change direction but its speed and wavelength will still alter.

折射是指波从一种介质传播到另一种介质时，由于速度改变而导致的方向变化。对于光来说，当光线从空气进入玻璃或水时，这种现象最为明显。如果光以一定角度射向界面，就会发生偏折。如果光沿法线（垂直于界面）入射，则方向不变，但速度和波长仍会改变。

The reason refraction happens is that one side of the wavefront slows down before the other, causing the whole ray to pivot. In terms of the ray model, we say the light ray bends towards the normal when it slows down, and away from the normal when it speeds up.

折射发生的原因是波阵面的一侧先于另一侧减速，导致整个光线发生旋转。用光线模型描述就是：当光减速时，光线偏向法线；当光加速时，光线偏离法线。

2. Key Terms: Incident Ray, Refracted Ray and the Normal | 关键术语：入射光线、折射光线与法线

When drawing refraction diagrams, you must label the incident ray, the refracted ray, and the normal. The normal is an imaginary line drawn at right angles to the boundary at the point where the ray hits. All angles are measured from the normal, not from the surface.

在画折射图时，必须标出入射光线、折射光线和法线。法线是一条在入射点处垂直于界面的假想线。所有角度都是从法线开始测量，而不是从界面测量。

The angle of incidence (i) is the angle between the incident ray and the normal. The angle of refraction (r) is the angle between the refracted ray and the normal. In the AQA exam, you may be asked to measure these angles using a protractor on a printed ray diagram.

入射角（i）是入射光线与法线之间的夹角。折射角（r）是折射光线与法线之间的夹角。在AQA考试中，你可能需要在给定的光线图上用量角器测量这些角度。

3. The Laws of Refraction | 折射定律

There are two key laws that describe how light behaves during refraction. First, the incident ray, the refracted ray and the normal all lie in the same plane. Second, for two given media, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant. This is known as Snell’s law.

描述光在折射时的行为有两条关键定律。第一，入射光线、折射光线和法线都在同一平面内。第二，对于给定的两种介质，入射角的正弦与折射角的正弦之比是一个常数。这就是斯涅尔定律。

n = sin i / sin r

Here, n is the refractive index of the second medium with respect to the first. In GCSE AQA Physics, we almost always consider light entering a material from air. The refractive index of air is taken as approximately 1. So this formula gives the absolute refractive index of the material.

这里，n 是第二种介质相对于第一种介质的折射率。在GCSE AQA物理中，我们几乎总是考虑光从空气进入某种材料。空气的折射率近似取为1。因此该公式给出了该材料的绝对折射率。

4. Refractive Index and the Speed of Light | 折射率与光速

The refractive index (n) of a material tells us how much the speed of light reduces inside it. It is defined by the equation:

折射率（n）表示光在该材料中的速度减慢了多少。其定义式为：

n = c / v

Where c is the speed of light in a vacuum (3.0 × 10⁸ m/s) and v is the speed of light in the material. Because light travels at its maximum speed in a vacuum, v is always less than c, so n is always greater than 1 for any material (except air, where n ≈ 1). Glass typically has a refractive index around 1.5, meaning light travels 1.5 times slower in glass than in a vacuum.

其中 c 为真空中的光速（3.0 × 10⁸ m/s），v 为光在该材料中的速度。因为光在真空中速度最快，所以 v 总是小于 c，因此任何材料的 n 总是大于1（空气除外，n ≈ 1）。玻璃的折射率通常在1.5左右，意味着光在玻璃中的速度是真空中速度的1/1.5。

This relationship also explains why light bends. The side of the beam that enters the denser medium first slows down, causing the whole light ray to swing towards the normal.

这一关系也解释了光为什么会偏折。光束中先进入光密介质的一侧先减速，从而导致整条光线摆向法线。

5. Light Entering a Denser Medium (Air to Glass) | 光进入光密介质（从空气到玻璃）

When light travels from air into a denser medium such as glass or water, it slows down and bends towards the normal. The angle of refraction (r) is smaller than the angle of incidence (i). For a ray striking the boundary at 0° (along the normal), it enters without bending, but still slows down.

当光从空气进入玻璃或水等光密介质时，速度减慢，光线偏向法线。折射角（r）小于入射角（i）。若光线以0°（沿法线）射向界面，则进入时不偏折，但速度仍然减慢。

You can use the refractive index equation to predict the path. If a light ray in air hits a glass block with n = 1.5 at an incident angle of 30°, the angle of refraction is given by sin r = sin 30° / 1.5 = 0.5 / 1.5 ≈ 0.333, so r ≈ 19.5°.

你可以用折射率公式来预测路径。如果空气中一条光线以30°入射角射向折射率为1.5的玻璃块，则折射角满足 sin r = sin 30° / 1.5 = 0.5 / 1.5 ≈ 0.333，因此 r ≈ 19.5°。

6. Light Leaving a Denser Medium (Glass to Air) | 光离开光密介质（从玻璃到空气）

When light travels from a denser medium to a less dense medium, such as from glass to air, it speeds up and bends away from the normal. The angle of refraction is larger than the angle of incidence. If the ray strikes the boundary along the normal, it leaves without changing direction but its speed increases.

当光从光密介质进入光疏介质，例如从玻璃到空气时，速度加快，光线偏离法线。折射角大于入射角。如果光线沿法线射向界面，则离开时方向不变，但速度加快。

Using the same refractive index, if a ray inside glass (n = 1.5) hits the boundary with air at an angle of 20°, you must rearrange Snell’s law. The incident medium is glass, so n₁ = 1.5, n₂ = 1.0. sin r = (n₁/n₂) × sin i = 1.5 × sin 20° ≈ 1.5 × 0.342 = 0.513, so r ≈ 30.9°, which is larger than i.

利用同样的折射率，如果玻璃（n=1.5）内的一条光线以20°角射向空气界面，则需要重新排列斯涅尔定律。入射介质是玻璃，因此 n₁ = 1.5，n₂ = 1.0。sin r = (n₁/n₂) × sin i = 1.5 × sin 20° ≈ 0.513，得出 r ≈ 30.9°，大于入射角。

7. Optical Density and Wave Properties | 光密度与波的特性

Optical density is not the same as physical density, although often a physically dense material is also optically dense. A medium with a higher refractive index is said to be optically denser. When light enters an optically denser medium, its wavelength decreases, but its frequency remains constant. This is because the colour of light does not change during refraction. The relationship is v = fλ, so if v decreases and f is constant, λ must decrease.

光密度不同于物理密度，尽管物理上致密的材料通常也具有较高的光密度。折射率较高的介质称为光密介质。当光进入光密介质时，波长变短，但频率保持不变。这是因为光的颜色在折射过程中不会改变。关系式为 v = fλ，如果 v 减小而 f 恒定，则 λ 必定减小。

Property	When entering optically denser medium
Speed	Decreases
Wavelength	Decreases
Frequency	Stays the same
Direction (unless i=0°)	Bends towards normal

属性（进入光密介质时）: 速度 – 减小；波长 – 减小；频率 – 不变；方向（除非 i=0°）- 偏向法线。

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

Total internal reflection (TIR) is a special case that occurs when light travels from a denser medium to a less dense medium and the angle of incidence is greater than a certain threshold called the critical angle (c). At the critical angle, the refracted ray emerges along the boundary (r = 90°). At larger angles, all light is reflected back into the denser medium.

全内反射（TIR）是一种特殊情况，发生在光从光密介质进入光疏介质，且入射角大于某一特定阈值——临界角（c）时。当入射角等于临界角时，折射光线沿界面射出（r = 90°）。当入射角更大时，所有光线全部反射回光密介质。

The critical angle is related to the refractive index by:

临界角与折射率的关系为：

sin c = 1 / n

Where n is the refractive index of the denser medium (taking the less dense medium as air, n = 1). For glass with n = 1.5, sin c = 1/1.5 ≈ 0.667, so c ≈ 41.8°. For water (n ≈ 1.33), c ≈ 48.8°.

其中 n 是光密介质的折射率（光疏介质为空气，n=1）。对于 n=1.5 的玻璃，sin c = 1/1.5 ≈ 0.667，因此 c ≈ 41.8°。对于水（n≈1.33），c ≈ 48.8°。

Two conditions must be met for TIR: the light must be travelling from a higher refractive index material to a lower one, and the angle of incidence must exceed the critical angle.

发生全内反射必须满足两个条件：光必须从折射率较高的材料射向折射率较低的材料，且入射角必须大于临界角。

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

Optical fibres are thin strands of glass or plastic that carry light signals over long distances. They rely on total internal reflection. The core of the fibre has a high refractive index, while the outer cladding has a lower refractive index. Light enters the core at one end and strikes the core-cladding boundary at an angle greater than the critical angle, so it undergoes repeated TIR and travels along the fibre with very little loss.

光纤是由玻璃或塑料制成的纤细丝束，用于长距离传输光信号。它们依赖全内反射。光纤的纤芯具有高折射率，外包层折射率较低。光从一端射入纤芯，并以大于临界角的角度射向纤芯-包层界面，从而发生多次全内反射，几乎无损地沿光纤传播。

This technology is used in high-speed internet cables (broadband), medical endoscopes to view inside the body, and decorative lighting. AQA questions may ask you to explain why the cladding is necessary: it protects the core, prevents light loss, and improves the fibre’s strength.

该技术用于高速互联网电缆（宽带）、医用内窥镜观察体内以及装饰照明。AQA考试可能会问你为什么需要包层：它可以保护纤芯、防止光泄漏并提高光纤的强度。

10. Dispersion of White Light by a Prism | 棱镜对白光的色散

When a beam of white light passes through a triangular glass prism, it is refracted twice – once when entering and once when leaving – and it splits into the colours of the visible spectrum. This phenomenon is called dispersion. It happens because different colours (wavelengths) of light travel at slightly different speeds in glass, meaning they have slightly different refractive indices. Violet light slows down more than red light, so violet bends more towards the normal, causing the colours to spread out.

当一束白光通过三角形玻璃棱镜时，它会发生两次折射——一次进入，一次离开——并分解成可见光谱的各种颜色。这一现象称为色散。原因是不同颜色（波长）的光在玻璃中的速度略有不同，即它们的折射率稍有差异。紫光比红光减速更多，因此紫光更偏向法线，导致颜色分散开来。

The order of colours from top to bottom (if the prism is base-down) is: red, orange, yellow, green, blue, indigo, violet (ROYGBIV). Red is deviated the least, violet the most. Isaac Newton demonstrated that the colours could be recombined into white light using a second prism, proving that white light is a mixture of colours.

颜色从上至下的顺序（棱镜底边朝下）为：红、橙、黄、绿、蓝、靛、紫（ROYGBIV）。红光偏折最小，紫光偏折最大。艾萨克·牛顿用第二个棱镜将彩色光重新合成白光，证明了白光是多种颜色的混合。

11. Required Practical: Investigating Refraction | 必修实验：探究折射

The AQA GCSE Physics required practical involves shining a ray of light through a transparent block (often a rectangular glass or Perspex block) and tracing the path of the incident and refracted rays. You will be expected to measure the angles of incidence and refraction, record the data in a table, and plot a graph of sin i against sin r to determine the refractive index.

AQA GCSE物理的必修实验要求让一束光线穿过透明块（通常是矩形玻璃或有机玻璃块），描出入射光线和折射光线的路径。你需要测量入射角和折射角，将数据记录在表中，并绘制 sin i 对 sin r 的图像以求折射率。

Key steps: Place the block on a sheet of paper and draw around it. Direct a narrow ray of light from a ray box so it enters at a non-zero angle. Mark the incident ray and the emergent ray with pencil crosses. Remove the block and draw the rays, then draw the normal at the point of incidence. Measure i and r with a protractor. Repeat for a range of i values. Plot sin i (y-axis) vs sin r (x-axis); the gradient of the best-fit straight line equals the refractive index n. Use appropriate safety precautions, such as not looking directly into the ray box lamp.

关键步骤：将玻璃块放在白纸上，描出轮廓。用光线盒发出一束窄光，以非零角度射入。用铅笔叉号标出入射光线和出射光线。移开玻璃块，画出光线，然后在入射点处作法线。用量角器测量 i 和 r。对一系列 i 值重复操作。以 sin i 为 y 轴、sin r 为 x 轴作图；最佳拟合直线的斜率就是折射率 n。采取适当的安全措施，如不要直视光线盒灯泡。

12. Exam Tips and Common Mistakes | 考试技巧与常见错误

Many students lose marks by not drawing normals as dashed lines or forgetting to label angles clearly. Always measure angles from the normal, not from the surface. When a question asks for the critical angle, check you use the correct formula: sin c = 1/n, but only when the second medium is air. If the surrounding medium is not air, you must use sin c = n₂/n₁ where n₁ > n₂.

许多学生因为没有把法线画成虚线，或者没有清晰地标出角度而丢分。一定要从法线而非界面测量角度。当题目要求临界角时，确认使用正确的公式：sin c = 1/n，但仅当第二介质为空气时适用。如果周围介质不是空气，则必须使用 sin c = n₂/n₁，其中 n₁ > n₂。

Another pitfall is confusing the speed and wavelength changes. Remember: frequency never changes during refraction. In total internal reflection questions, ensure you check both conditions, not just one. Finally, in calculations, round your final answer to an appropriate number of significant figures, typically two or three, matching the data given.

另一个易错点是混淆速度和波长的变化。记住：频率在折射中永不改变。在全内反射问题中，确保检查两个条件，而不是只写一个。最后，在计算中，将最终答案四舍五入到合适的有效数字，通常是两到三位，与所给数据匹配。

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Refraction of Light | 光的折射