Refraction of Light | 光的折射

📚 Refraction of Light | 光的折射

Refraction is the bending of light as it passes from one transparent medium to another of different optical density. This phenomenon is fundamental to GCSE WJEC Physics and explains everything from the apparent depth of a swimming pool to the working of optical fibres. In this article, we will break down the key concepts, equations, experiments, and exam tips you need to master refraction.

折射是光从一种透明介质进入另一种光密度不同的介质时发生的弯折现象。这一现象是GCSE WJEC物理的基础内容，能够解释从游泳池视深到光纤工作原理的诸多日常现象。本文将分解关键概念、公式、实验和考试技巧，助你掌握折射考点。

1. What Is Refraction? | 什么是折射？

Refraction occurs because light travels at different speeds in different materials. When a light ray enters a new medium at an angle other than 90 degrees to the surface, one side of the wavefront changes speed before the other, causing the ray to change direction. If light enters a denser medium, it slows down and bends towards the normal. If it enters a less dense medium, it speeds up and bends away from the normal.

折射的发生是因为光在不同材料中的传播速度不同。当光线以非90度的角度进入新介质时，波前的一侧比另一侧先改变速度，导致光线改变方向。如果光进入光密介质，速度减慢并向法线偏折；如果进入光疏介质，速度增大并偏离法线。

The normal is an imaginary line perpendicular to the boundary at the point of incidence. All angles in refraction are measured from the normal, not the surface. This is a critical detail for both understanding and drawing ray diagrams accurately.

法线是一条在入射点处垂直于界面的虚拟直线。折射中的所有角度都是从法线开始测量的，而不是从界面。这是理解和准确绘制光线图的关键细节。

2. The Speed of Light in Different Media | 光在不同介质中的速度

In a vacuum, light travels at approximately 3.00 × 10⁸ m/s. In air, the speed is only slightly less and often taken to be the same for GCSE calculations. However, in water or glass, the speed is significantly reduced. It is this change in speed that causes refraction.

真空中光速约为3.00 × 10⁸ m/s。空气中的光速仅略低，在GCSE计算中通常视为相同。但在水或玻璃中，光速显著降低。正是这种速度变化导致了折射。

The optical density of a material determines how much the speed of light is reduced. The greater the optical density, the more light slows down. For example, in glass (approx. 2.0 × 10⁸ m/s), light travels about 1.5 times slower than in a vacuum.

材料的光密度决定了光速降低的程度。光密度越大，光减速越多。例如，光在玻璃中（约2.0 × 10⁸ m/s）的传播速度大约是真空中的1.5分之1。

3. Refractive Index | 折射率

The refractive index (n) of a material is a measure of how much light slows down in that material. It is defined as the ratio of the speed of light in a vacuum (c) to the speed of light in the medium (v):

折射率（n）是衡量光在材料中减速程度的量。它被定义为真空中光速（c）与介质中光速（v）之比：

n = c / v

Since c is always greater than or equal to v, the refractive index of any material is always greater than or equal to 1. Air has a refractive index of approximately 1.0003, so it is often taken as 1. Water has n ≈ 1.33, and crown glass has n ≈ 1.5.

由于c始终大于或等于v，任何材料的折射率总是大于或等于1。空气的折射率大约为1.0003，因此常取为1。水的n≈1.33，冕牌玻璃的n≈1.5。

The refractive index of a material can also be determined using Snell’s law, which is a very common exam calculation.

材料的折射率也可以通过斯涅尔定律来确定，这是非常常见的考试计算。

4. Snell’s Law | 斯涅尔定律

Snell’s law relates the angles of incidence and refraction to the refractive indices of the two media. It states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media:

斯涅尔定律将入射角和折射角与两种介质的折射率联系起来。它表明，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：

n₁ sin θ₁ = n₂ sin θ₂

Here, n₁ is the refractive index of the first medium, θ₁ is the angle of incidence, n₂ is the refractive index of the second medium, and θ₂ is the angle of refraction. If one medium is air (n=1), the formula simplifies to sin i / sin r = n, where i is the angle in air and r is the angle in the material.

这里，n₁是第一介质的折射率，θ₁是入射角，n₂是第二介质的折射率，θ₂是折射角。如果一种介质是空气（n=1），公式简化为sin i / sin r = n，其中i是空气中的角度，r是材料中的角度。

You must be able to both use this formula to calculate unknowns and explain how to verify Snell’s law experimentally by plotting sin i against sin r.

你必须既能使用该公式计算未知数，又能解释如何通过绘制sin i与sin r的图来实验验证斯涅尔定律。

5. Refraction at Boundaries | 边界处的折射

When light passes from a less dense to a more dense medium, the ray bends towards the normal, and the angle of refraction is smaller than the angle of incidence. When it passes from a denser to a less dense medium, it bends away from the normal, and the angle of refraction is larger.

当光从光疏介质进入光密介质时，光线向法线偏折，折射角小于入射角。当光从光密介质进入光疏介质时，光线偏离法线，折射角大于入射角。

If the light hits the boundary along the normal (incident angle = 0°), it does not bend but continues straight. Its speed and wavelength change, but the frequency remains constant. The direction does not change.

如果光沿法线方向入射（入射角=0°），则不会弯折，而是继续直线传播。其速度和波长改变，但频率保持不变。方向不变。

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

When light travels from a denser medium to a less dense medium (e.g., from glass to air), as the angle of incidence increases, the angle of refraction also increases. At a certain incident angle, the refracted ray emerges exactly along the boundary, with a refraction angle of 90°. This incident angle is called the critical angle (c).

当光从光密介质进入光疏介质（例如从玻璃到空气）时，随着入射角的增大，折射角也增大。在某一个人射角下，折射光线恰好沿界面射出，折射角为90°。这个入射角称为临界角（c）。

If the angle of incidence exceeds the critical angle, the light is no longer refracted but completely reflected back into the denser medium. This is total internal reflection (TIR). TIR only occurs when light moves from a denser to a less dense medium, and the angle of incidence is greater than the critical angle.

如果入射角大于临界角，光不再折射，而是完全反射回光密介质中。这就是全内反射。全内反射仅当光从光密介质射向光疏介质，且入射角大于临界角时发生。

The critical angle is related to refractive index by the formula:

临界角与折射率的关系公式为：

sin c = 1 / n

where 1 is the refractive index of air and n is the refractive index of the denser medium. For glass (n=1.5), the critical angle is about 42°.

其中1是空气的折射率，n是光密介质的折射率。对于玻璃（n=1.5），临界角约为42°。

7. Total Internal Reflection in Optical Fibres | 光纤中的全内反射

Optical fibres are thin, flexible strands of glass or plastic that use total internal reflection to transmit light signals over long distances. The core of the fibre has a higher refractive index than the cladding. Light entering at one end strikes the core-cladding boundary at an angle greater than the critical angle and undergoes repeated TIR, bouncing along the fibre with very little loss.

光纤是一种细而柔韧的玻璃或塑料丝，利用全内反射长距离传输光信号。光纤的纤芯折射率高于包层。从一端进入的光线以大于临界角的角度射到纤芯与包层的界面，发生多次全内反射，在光纤内几乎无损耗地反射前进。

This principle is used in telecommunications to send data as pulses of light, and in medical endoscopes to view inside the body. Optical fibres are preferred because they allow high-speed transmission, are lightweight, and are immune to electromagnetic interference.

这一原理应用于电信领域，以光脉冲形式发送数据；也用于医用内窥镜，以便观察体内。光纤因其高速传输、轻质和抗电磁干扰等优势而备受青睐。

8. Dispersion of White Light | 白光色散

Dispersion occurs when white light passes through a prism and splits into its constituent colours (the spectrum). This happens because the refractive index of glass is slightly different for each wavelength (colour) of light. Violet light slows down more and bends the most, while red light is bent the least.

色散发生在白光通过棱镜时，分解为组成它的各种颜色（光谱）。发生色散是因为玻璃对不同波长（颜色）的光的折射率略有不同。紫光减速更多，偏折最大，而红光偏折最小。

The order of colours in a spectrum is: red, orange, yellow, green, blue, indigo, violet (ROYGBIV). Each colour runs into the next, forming a continuous band. Dispersion demonstrates that white light is a mixture of many different colours, each with a unique wavelength.

光谱中的颜色顺序为：红、橙、黄、绿、蓝、靛、紫。每个颜色与相邻颜色融合，形成连续色带。色散证明了白光是由许多不同波长、不同颜色的光混合而成的。

There is no complete GCSE WJEC experiment required solely on dispersion, but you should be able to describe it and recognise that a rainbow is a natural example of dispersion by water droplets.

GCSE WJEC没有单独要求色散实验，但你需要能够描述色散，并认识到彩虹是水滴造成的自然色散现象。

9. Practical Applications of Refraction | 折射的实际应用

Lenses in cameras, glasses, and telescopes use refraction to focus light. Convex lenses bring parallel rays together at the focal point.
相机、眼镜和望远镜中的透镜利用折射聚焦光线。凸透镜将平行光线会聚在焦点上。
Mirages on hot roads are caused by refraction of light through layers of hot air of varying density.
炎热路面上的海市蜃楼是由光线穿过不同密度热空气层发生折射而引起的。
Pencil appearing bent in water is a classic observation. The light from the part of the pencil underwater refracts as it travels from water to air, shifting the apparent position.
水中的铅笔看起来弯折是经典现象。从水下铅笔部分发出的光在由水进入空气时发生折射，导致视在位置偏移。
Sparkling of diamonds is due to total internal reflection and a high refractive index (n ≈ 2.42), which creates a small critical angle (about 24.4°), trapping light inside.
钻石的闪光源于全内反射和高折射率（n≈2.42），产生了很小的临界角（约24.4°），将光困在内部多次反射。

10. Experiment: Measuring Refractive Index | 实验：测量折射率

The standard GCSE experiment uses a rectangular glass block, a ray box, and a protractor. A beam of light is directed at one edge of the block at an angle, and the path of the ray is traced on paper. The angle of incidence (i) and angle of refraction (r) are measured for several different incident angles.

标准GCSE实验使用矩形玻璃块、光线盒和量角器。将一束光以一定角度射向玻璃块一边，在纸上描出光线路径。测量多个不同入射角对应的入射角（i）和折射角（r）。

For each pair, calculate sin i and sin r, then plot a graph of sin i (y-axis) against sin r (x-axis). The graph should be a straight line through the origin. The gradient of this line gives the refractive index of the glass: n = sin i / sin r.

对每对角度计算sin i和sin r，然后绘制sin i（y轴）对sin r（x轴）的图。图像应是一条过原点的直线。该直线的斜率即为玻璃的折射率：n = sin i / sin r。

Common sources of error include inaccurate protractor alignment, poor ray tracing, and failure to measure from the normal. Using a sharper, narrower beam and repeating measurements improves accuracy.

常见误差来源包括量角器对位不准、光线描迹不良以及未从法线开始测量角度。使用更细更窄的光束和重复测量可以提高准确度。

11. Common Misconceptions | 常见误解

Myth: Light bends towards the normal when entering a less dense medium. Fact: It bends towards the normal only when entering a denser medium.
误解：光进入光疏介质时向法线偏折。事实：只有进入光密介质时才向法线偏折。
Myth: The ray changes direction because it changes wavelength. Fact: Both speed and wavelength change, but it is the change in speed that causes direction change; frequency remains constant.
误解：光线改变方向是因为波长改变。事实：速度和波长都改变，但方向改变是由速度变化引起的；频率保持不变。
Myth: Total internal reflection can happen when light moves from air to glass. Fact: TIR requires light to be in the denser medium and attempting to escape into a less dense one.
误解：光从空气到玻璃可以发生全内反射。事实：全内反射要求光在光密介质中并试图进入光疏介质。
Myth: The critical angle is the angle of refraction when the incident angle is 90°. Fact: It is the incident angle in the denser medium that gives a refraction angle of 90° in the less dense medium.
误解：临界角是入射角为90°时的折射角。事实：临界角是光密介质中使得光疏介质中折射角为90°的入射角。

12. Exam Tips for WJEC Physics | WJEC物理考试技巧

Always label the normal as a dashed line at 90 degrees to the boundary. Mark and measure angles from the normal, not from the surface.
始终用法线为垂直于界面的虚线进行标注。从法线而非界面标记和测量角度。
For Snell’s law calculations, ensure your calculator is in degree mode, not radians. Show all steps clearly, starting with the formula.
进行斯涅尔定律计算时，确保计算器处于角度模式，而非弧度模式。清晰地展示所有步骤，从公式开始。
When describing TIR, mention three essential conditions: light travels from denser to less dense medium, the angle of incidence is greater than the critical angle, and the boundary is smooth.
描述全内反射时，要提到三个必要条件：光从光密介质传播到光疏介质，入射角大于临界角，界面光滑。
In diagrams, use a ruler and pencil. Refracted rays must be continuous, and the direction of bending must be accurate (towards/away from normal).
在绘图中使用尺子和铅笔。折射光线应连续，且偏折方向准确（向法线/偏离法线）。
For the practical graph of sin i vs sin r, remember the slope equals the refractive index. The line must pass through the origin.
对于sin i对sin r的实验图，记住斜率等于折射率。直线必须通过原点。
Know typical refractive indices: air = 1, water = 1.33, glass = 1.5. Being familiar with these helps you check if your answers are reasonable.
记住典型的折射率：空气=1，水=1.33，玻璃=1.5。熟悉这些值有助于判断你的答案是否合理。

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Refraction of Light | 光的折射