📚 AS Physics: Refraction of Light – Key Points | 光的折射考点精讲
Refraction is a fundamental wave phenomenon observed when light passes from one transparent medium to another, causing a change in speed and direction. In AS Physics, understanding refraction is essential for explaining lenses, optical fibres, and natural phenomena such as rainbows. This article will consolidate key concepts, laws, calculations, and experimental skills required for your examination.
折射是光从一种透明介质进入另一种介质时速度改变并发生方向偏折的基本波动现象。在AS物理中，掌握折射原理对于解释透镜、光纤以及彩虹等自然现象至关重要。本文将系统梳理考试中涉及的核心理念、定律、计算和实验技能。
1. Introduction to Refraction | 折射现象简介
Refraction occurs when light travels across the boundary between two media of different optical densities. The change in speed causes the light ray to bend, unless it strikes the boundary along the normal. The amount of bending depends on the refractive indices of the two media and the angle of incidence.
当光穿过两种不同光密度的介质界面时会发生折射。速度的变化导致光线偏折，除非光线沿法线入射。偏折程度取决于两种介质的折射率以及入射角。
2. Snell’s Law of Refraction | 斯涅尔折射定律
Snell’s law quantifies the relationship between the angles of incidence and refraction. For a ray passing from medium 1 to medium 2, the law states that the product of the refractive index and the sine of the angle to the normal is constant across the boundary:
n₁ sin θ₁ = n₂ sin θ₂
where θ₁ is the angle in medium 1, θ₂ is the angle in medium 2, and n₁, n₂ are the absolute refractive indices of the media. If the ray enters from air (n ≈ 1), the formula simplifies to sin i / sin r = n.
斯涅尔定律量化了入射角与折射角的关系。对于从介质1进入介质2的光线，该定律表明折射率与对应法线夹角正弦的乘积在界面两侧保持不变：n₁ sin θ₁ = n₂ sin θ₂，其中θ₁为介质1中的角度，θ₂为介质2中的角度，n₁和n₂为介质的绝对折射率。若光线从空气（n≈1）射入，则简化为 sin i / sin r = n。
3. Refractive Index (n) | 折射率 (n)
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 the medium (v):
n = c / v
Since v is always less than c, n is always greater than 1 for any material medium. The refractive index also determines how much the light bends; a higher n means a greater change in direction for a given angle of incidence.
介质的绝对折射率 n 定义为真空光速 (c) 与介质中光速 (v) 之比：n = c / v。由于 v 总小于 c，任何材料介质的 n 均大于 1。折射率也决定了光的偏折程度；对于给定的入射角，n 越大，方向变化越大。
4. Absolute and Relative Refractive Index | 绝对折射率与相对折射率
When light passes from medium 1 to medium 2, we can use the relative refractive index, often written as ₁n₂, which equals n₂ / n₁. Snell’s law can be expressed in terms of relative index:
₁n₂ = n₂ / n₁ = sin θ₁ / sin θ₂
For air-to-glass (n ≈ 1.5), the relative index from air to glass is approximately 1.5. This concept simplifies calculations when one medium is vacuum or air.
当光从介质1进入介质2时，我们可以使用相对折射率，常写作 ₁n₂，等于 n₂ / n₁。斯涅尔定律可用相对折射率表示为：₁n₂ = n₂ / n₁ = sin θ₁ / sin θ₂。对于从空气到玻璃（n ≈ 1.5），相对折射率约为 1.5。当其中一个介质为真空或空气时，这一概念可简化计算。
5. Optically Denser and Rarer Media | 光密介质与光疏介质
A medium with a higher refractive index is said to be optically denser. Light travels slower in an optically denser medium. When light enters a denser medium from a rarer one, it bends towards the normal (θ₂ < θ₁). Conversely, when moving from denser to rarer, it bends away from the normal. This concept is crucial for understanding total internal reflection.
折射率较高的介质被称为光密介质。光在光密介质中传播速度较慢。当光从光疏介质进入光密介质时，光线向法线偏折 (θ₂ < θ₁)。相反，从光密到光疏时，光线远离法线。这一概念对于理解全内反射至关重要。
| Medium | Refractive Index n |
|---|---|
| Vacuum | 1 (exact) |
| Air | ≈1.0003 |
| Water | ≈1.33 |
| Crown glass | ≈1.52 |
| Diamond | ≈2.42 |
6. Experimental Determination of Refractive Index | 折射率的实验测定
A standard AS experiment uses a rectangular glass block or a semicircular slab. By directing a ray of monochromatic light at the block and marking the incident and refracted rays, you can measure the angle of incidence i and angle of refraction r. For a rectangular block, the emergent ray is parallel to the incident ray. Using Snell’s law for the entry face (from air to glass):
n = sin i / sin r
A graph of sin i against sin r yields a straight line through the origin, and the gradient gives the refractive index n. Repeating for different angles and using a large number of values reduces the random error.
标准的AS实验使用矩形玻璃砖或半圆形玻璃砖。将单色光线射向玻璃块并标记入射光线和折射光线，可以测量入射角 i 和折射角 r。对于矩形玻璃块，出射光线与入射光线平行。利用入射面的斯涅尔定律（从空气到玻璃）：n = sin i / sin r。绘制 sin i 对 sin r 的图像是一条过原点的直线，其斜率即为折射率 n。重复测量不同角度并取多组数据可以减少随机误差。
7. Critical Angle and Total Internal Reflection | 临界角与全内反射
When light travels from an optically denser medium to a rarer medium (e.g., glass to air), there exists a critical angle of incidence, c, for which the angle of refraction is 90°. Applying Snell’s law at the boundary:
n₁ sin c = n₂ sin 90°
If the rarer medium is air (n₂ = 1) and the denser medium has index n, this reduces to:
sin c = 1 / n
If the angle of incidence exceeds the critical angle, total internal reflection (TIR) occurs—all light is reflected back into the denser medium, with no refracted ray. TIR only happens when light meets a boundary with a less optically dense medium.
当光从光密介质射向光疏介质（例如玻璃到空气）时，存在一个临界角 c，此时折射角为 90°。在界面应用斯涅尔定律：n₁ sin c = n₂ sin 90°。若光疏介质为空气（n₂=1），光密介质折射率为 n，则简化为 sin c = 1 / n。如果入射角大于临界角，就会发生全内反射（TIR）——所有光线都被反射回光密介质，没有折射光线。TIR 仅在光遇到与光疏介质的界面时发生。
8. Applications of Total Internal Reflection: Optical Fibres | 全内反射的应用：光纤
Optical fibres exploit 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 cladding of lower refractive index. Light entering the core at an angle greater than the critical angle undergoes repeated TIR along the fibre. This principle is used in endoscopes, high-speed internet cables, and decorative lighting. The acceptance angle depends on the refractive indices of core and cladding.
光纤利用全内反射以极低的损耗长距离传输光信号。光纤由高折射率的纤芯和较低折射率的包层组成。以大于临界角的角度进入纤芯的光线会在光纤内反复发生全内反射。该原理被应用于内窥镜、高速互联网电缆和装饰照明。接收角取决于纤芯和包层的折射率。
9. Dispersion of Light by a Prism | 棱镜的色散现象
Dispersion occurs because the refractive index of a material varies slightly with the wavelength (colour) of light; this is called dispersion. In a glass prism, violet light is refracted more than red light because its refractive index is higher for shorter wavelengths. When white light passes through a prism, it splits into a continuous spectrum of colours (red, orange, yellow, green, blue, indigo, violet). This demonstrates that white light is a mixture of wavelengths. The same principle explains rainbows formed by water droplets.
色散的发生是由于材料的折射率随光波长（颜色）略有变化，这称为色散。在玻璃棱镜中，紫光比红光折射更多，因为较短波长对应的折射率更高。当白光通过棱镜时，会分解成连续的光谱（红、橙、黄、绿、蓝、靛、紫）。这表明白光是多种波长的混合。同样的原理可以解释水滴形成的彩虹。
10. Common Misconceptions and Exam Tips | 常见误区和考试技巧
Misconception 1: ‘Refractive index is always the same for a given material.’ Actually, it depends on the wavelength; exam questions often specify ‘monochromatic light’ to avoid dispersion effects. Misconception 2: ‘Total internal reflection can happen when light goes from air to glass.’ This is false; TIR requires light to travel from denser to rarer medium. Exam tip: always draw a clear normal and label angles. When solving Snell’s law problems, ensure you use the correct indices for the correct media. For critical angle problems, remember sin c = 1/n only when the second medium is air/vacuum. Pay attention to significant figures and units, and check if your calculated angles are physically sensible (e.g., sin θ cannot exceed 1).
误区一：“给定材料的折射率总是相同。”其实它依赖于波长；考题通常会指定“单色光”以避免色散效应。误区二：“当光从空气射向玻璃时会发生全内反射。”这是错误的；全内反射要求光从光密介质射向光疏介质。考试技巧：始终画出清晰的法线并标记角度。在解斯涅尔定律问题时，确保对相应介质使用正确的折射率。对于临界角问题，记住 sin c = 1/n 仅在第二介质为空气或真空时成立。注意有效数字和单位，并检查计算出的角度在物理上是否合理（例如 sin θ 不能大于1）。
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