The Law of Refraction and Its Applications | 光的折射定律与应用

📚 The Law of Refraction and Its Applications | 光的折射定律与应用

Refraction is the bending of light as it passes from one transparent medium into another. This fundamental behaviour of light underpins countless optical devices, from spectacles to submarine periscopes, and is a core topic in physics examinations.

折射是光从一种透明介质进入另一种透明介质时发生的偏折现象。这一光的基本行为支撑着从眼镜到潜艇潜望镜等无数光学器件，也是物理考试中的核心考点。

1. The Law of Refraction | 折射定律

When a ray of light crosses the boundary between two transparent media, its speed changes, causing the ray to change direction. The relationship between the angles of incidence and refraction was discovered experimentally by Willebrord Snell and is known as Snell’s law.

当一束光穿过两种透明介质的边界时，其速度发生变化，导致光线方向改变。入射角与折射角之间的关系由威理博·斯涅耳通过实验发现，称为斯涅耳定律。

n₁ sin θ₁ = n₂ sin θ₂

Here, n₁ and n₂ are the refractive indices of the two media, θ₁ is the angle of incidence, and θ₂ is the angle of refraction. All angles are measured from the normal, an imaginary line perpendicular to the boundary at the point of incidence.

其中，n₁ 和 n₂ 分别为两种介质的折射率，θ₁ 为入射角，θ₂ 为折射角。所有角度均以法线为基准测量，法线是过入射点且垂直于界面的假想直线。

2. Refractive Index | 折射率

The absolute refractive index of a medium is defined as the ratio of the speed of light in vacuum to the speed of light in that medium:

介质的绝对折射率定义为光在真空中的速度与光在该介质中的速度之比：

n = c / v

Since c is always greater than v in any material medium, the refractive index is always greater than 1 for real media. For example, n ≈ 1.0003 for air, n ≈ 1.33 for water, and n ≈ 1.50 for glass.

由于在任何实物介质中 c 始终大于 v，因此真实介质的折射率总是大于 1。例如，空气的折射率约为 1.0003，水约为 1.33，玻璃约为 1.50。

The refractive index also depends on the wavelength of light, which leads to dispersion — the separation of white light into its constituent colours when passing through a prism.

折射率还取决于光的波长，这导致色散现象——白光通过棱镜时被分解为其组成颜色。

3. Relative Refractive Index | 相对折射率

When light travels from medium 1 into medium 2, the relative refractive index of medium 2 with respect to medium 1 is given by:

当光从介质 1 进入介质 2 时，介质 2 相对介质 1 的相对折射率为：

n₂₁ = n₂ / n₁ = v₁ / v₂

If n₂ > n₁, light bends toward the normal; if n₂ < n₁, light bends away from the normal. This direction rule is essential for predicting the path of a refracted ray.

如果 n₂ > n₁，光线向法线偏折；如果 n₂ < n₁，光线远离法线偏折。这一方向规则对于预测折射光线的路径至关重要。

4. Optical Density vs Mass Density | 光密介质与质量密度

Optical density is not the same as mass density. A medium with a higher refractive index is said to be optically denser, even if its mass density is lower. For example, oil has a lower mass density than water but a higher optical density.

光密程度与质量密度不同。折射率较高的介质称为光密介质，即使其质量密度较低。例如，油的质量密度低于水，但其光密程度高于水。

When light enters an optically denser medium, its speed decreases and it bends toward the normal. Conversely, when light enters an optically rarer medium, its speed increases and it bends away from the normal.

当光进入光密介质时，速度减小并向法线偏折；反之，当光进入光疏介质时，速度增大并远离法线偏折。

5. Total Internal Reflection | 全反射

When light travels from an optically denser to a rarer medium, the angle of refraction is larger than the angle of incidence. As the angle of incidence increases, the angle of refraction approaches 90°.

当光从光密介质射向光疏介质时，折射角大于入射角。随着入射角增大，折射角趋近 90°。

The critical angle C is the angle of incidence for which the angle of refraction is exactly 90°. It satisfies:

临界角 C 是折射角恰好为 90° 时的入射角，满足：

sin C = n₂ / n₁ (for n₁ > n₂)

If the angle of incidence exceeds the critical angle, no refracted ray exists. Instead, all the light is reflected back into the denser medium. This phenomenon is called total internal reflection.

如果入射角超过临界角，则不再存在折射光线，所有光被反射回光密介质中。这种现象称为全反射。

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

Two conditions must be satisfied for total internal reflection to occur:

发生全反射必须满足两个条件：

Light must travel from an optically denser medium to an optically rarer medium.
光必须从光密介质射向光疏介质。
The angle of incidence must be greater than the critical angle for the pair of media.
入射角必须大于该两种介质的临界角。

Total internal reflection is widely used in optical fibres, prisms in binoculars, and reflecting road studs.

全反射广泛应用于光纤、双筒望远镜中的棱镜以及道路反光道钉。

7. Refraction by a Parallel-Sided Block | 平行玻璃砖的折射

When a ray passes through a rectangular glass block, it undergoes refraction at the first surface and again at the second surface. The emergent ray is parallel to the incident ray but laterally displaced.

当光线穿过矩形玻璃砖时，在第一个表面和第二个表面分别发生折射。出射光线与入射光线平行，但发生侧向位移。

The lateral displacement d depends on the thickness of the block, the angle of incidence, and the refractive index. For small angles, a thin block produces a barely noticeable shift; a thick block produces a larger shift.

侧向位移 d 取决于玻璃砖的厚度、入射角和折射率。对于小角度入射，薄玻璃砖产生的位移几乎不可察觉，厚玻璃砖则产生较大位移。

8. Refraction through a Prism | 棱镜的折射

A triangular prism deviates a ray of light because refraction occurs at two non-parallel surfaces. The angle of deviation D depends on the prism angle A, the refractive index, and the angle of incidence.

三棱镜使光线发生偏折，因为光在两个不平行的表面上发生折射。偏向角 D 取决于棱镜顶角 A、折射率以及入射角。

For a given prism, the angle of deviation passes through a minimum value Dₘ, called the minimum deviation. At minimum deviation, the ray passes symmetrically through the prism, and the refractive index can be calculated using:

对于给定棱镜，偏向角存在最小值 Dₘ，称为最小偏向角。在最小偏向角时，光线对称地穿过棱镜，折射率可用下式计算：

n = sin[(A + Dₘ)/2] / sin(A/2)

This formula is a standard result in exam questions involving prism refraction.

该公式是考试中涉及棱镜折射时的标准结论。

9. Applications: Lenses and Vision | 应用：透镜与视觉

Lenses use refraction to form images. A convex lens converges parallel rays to a focal point, while a concave lens diverges them. The power of a lens is given by P = 1/f, measured in dioptres (D) when f is in metres.

透镜利用折射成像。凸透镜使平行光线会聚于焦点，凹透镜则使其发散。透镜的焦度为 P = 1/f，当 f 以米为单位时，焦度单位为屈光度（D）。

The human eye relies on refraction by the cornea and the crystalline lens to focus light onto the retina. Defects such as myopia and hyperopia are corrected by concave and convex lenses respectively.

人眼依靠角膜和晶状体的折射将光线聚焦在视网膜上。近视和远视等缺陷分别用凹透镜和凸透镜矫正。

10. Applications: Optical Fibres | 应用：光纤

Optical fibres consist of a transparent core surrounded by a cladding of lower refractive index. Light entering the fibre at an angle greater than the critical angle undergoes repeated total internal reflection, allowing the signal to travel long distances with little loss.

光纤由透明纤芯和折射率较低的包层组成。以大于临界角的角度进入光纤的光发生反复全反射，从而使信号在低损耗下长距离传输。

Optical fibres are used in telecommunications, medical endoscopes, and high-speed internet connections. Their advantages include high bandwidth, immunity to electromagnetic interference, and low signal attenuation.

光纤用于电信、医用内窥镜和高速互联网连接。其优点包括高带宽、抗电磁干扰和低信号衰减。

11. Applications: Mirage and Atmospheric Refraction | 应用：海市蜃楼与大气折射

A mirage is an optical illusion caused by atmospheric refraction. On a hot road, air near the surface is hotter and less dense, so its refractive index is lower. Light from the sky bends gradually upward, creating the appearance of a pool of water.

海市蜃楼是由大气折射引起的光学幻象。在炎热的路面上，靠近地面的空气温度更高、密度更低，因此其折射率较低。来自天空的光逐渐向上弯曲，形成水洼的假象。

Similarly, the sun appears to be above the horizon when it is actually below it, at sunrise and sunset. This happens because the atmosphere refracts sunlight around the curvature of the Earth.

类似地，在日出和日落时，太阳实际上位于地平线以下，但看起来却在地平线之上。这是因为大气使阳光绕地球曲率发生折射。

12. Problem-Solving Strategy | 解题策略

When solving refraction problems, follow these steps:

在解答折射问题时，请遵循以下步骤：

Draw a clear ray diagram and label the normal at each boundary.
画出清晰的光路图，并在每个界面标出法线。
Identify the media and assign refractive indices or speeds.
确定介质并标出折射率或光速。
Apply Snell’s law: n₁ sin θ₁ = n₂ sin θ₂.
应用斯涅耳定律：n₁ sin θ₁ = n₂ sin θ₂。
Check whether the ray bends toward or away from the normal.
检查光线是向法线偏折还是远离法线偏折。
For total internal reflection, compare the angle of incidence with the critical angle.
对于全反射，将入射角与临界角进行比较。
Use angle geometry (triangles, parallel lines) to find unknown angles.
利用角度几何关系（三角形、平行线）求出未知角度。

Careful attention to angle definitions and units will help you avoid common pitfalls.

认真关注角度定义和单位，能帮助你避免常见错误。

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The Law of Refraction and Its Applications | 光的折射定律与应用