Light Waves | 光波 - aleveler.com

📚 Light Waves | 光波

Light waves are a form of electromagnetic radiation that can be detected by the human eye. They are transverse waves with extremely high frequencies and short wavelengths, and they travel at a speed of 3 × 10⁸ m/s in a vacuum. In this revision guide, we will cover the key concepts of reflection, refraction, total internal reflection, lenses, dispersion, and colour, all essential for your IGCSE Edexcel Physics examination.

光波是一种能被人类眼睛感知的电磁辐射。光波是横波，频率极高、波长极短，在真空中的传播速度为 3 × 10⁸ m/s。在本复习指南中，我们将系统梳理反射、折射、全内反射、透镜、色散与颜色等核心概念，这些都是 IGCSE Edexcel 物理考试的重点内容。

1. Nature of Light Waves | 光的本质

Light is part of the electromagnetic spectrum, with visible wavelengths ranging approximately from 400 nm (violet) to 700 nm (red). Unlike sound waves, light waves do not require a medium to travel; they can propagate through a vacuum. Light travels in straight lines in a uniform medium, which is why we describe it using rays.

光属于电磁波谱的一部分，可见光波长范围约为 400 nm（紫光）至 700 nm（红光）。与声波不同，光波不需要介质即可传播，它们可以在真空中行进。光在均匀介质中沿直线传播，因此我们常用光线来描述光的行为。

For IGCSE, you should know that light is a transverse wave, meaning the oscillations are perpendicular to the direction of energy transfer. The wave equation linking speed, frequency, and wavelength is:

在 IGCSE 中，你需要知道光是一种横波，即振动方向与能量传播方向垂直。联系光速、频率和波长的波动方程为：

v = f × λ

where v is the wave speed in metres per second (m/s), f is the frequency in hertz (Hz), and λ (lambda) is the wavelength in metres (m).

其中 v 是波速，单位为米每秒（m/s）；f 是频率，单位为赫兹（Hz）；λ（希腊字母 lambda）是波长，单位为米（m）。

2. Reflection | 反射

Reflection occurs when light bounces off a surface. The law of reflection states that the angle of incidence is equal to the angle of reflection, and that the incident ray, the reflected ray, and the normal all lie in the same plane. The normal is an imaginary line perpendicular to the surface at the point of incidence.

反射是指光从表面弹回的现象。反射定律表明：入射角等于反射角，且入射光线、反射光线和法线在同一平面内。法线是在入射点处垂直于表面的假想线。

There are two types of reflection you need to distinguish:

你需要区分两种类型的反射：

Specular reflection – occurs on a smooth surface, such as a mirror; parallel rays reflect as parallel rays, producing a clear image.
镜面反射 – 发生在光滑表面，如镜子；平行光线反射后仍保持平行，形成清晰图像。
Diffuse reflection – occurs on a rough surface, such as paper; parallel rays are scattered in many directions, so no clear image is formed.
漫反射 – 发生在粗糙表面，如纸张；平行光线向各个方向散射，因此无法形成清晰图像。

For a plane mirror, the image is virtual, upright, laterally inverted, and the same size as the object. The image distance is equal to the object distance.

对于平面镜，所成的像是虚像、正立、左右颠倒，且与物体大小相同。像距等于物距。

3. Refraction | 折射

Refraction is the bending of light when it passes from one transparent medium into another. This bending occurs because light changes speed as it moves between media. If light travels from a less dense to a denser medium (for example, from air to glass), it slows down and bends towards the normal. If it travels from a denser to a less dense medium (glass to air), it speeds up and bends away from the normal.

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。这种偏折是因为光在不同介质中传播速度不同。如果光从密度较小的介质进入密度较大的介质（例如从空气进入玻璃），速度减慢并向法线方向偏折；如果从密度较大的介质进入密度较小的介质（例如从玻璃进入空气），速度加快并远离法线方向偏折。

An important observation is that refraction does not change the frequency of light, but the wavelength and speed do change. The ray direction is reversible: if you reverse the path of a refracted ray, it retraces its original path.

一个重要观察事实是：折射不会改变光的频率，但波长和速度会改变。光线传播具有可逆性：如果令折射光线反向传播，它会沿原路径返回。

Here is a simple example: swimmer looking up from underwater sees objects shifted from their true position because light bends at the water-air boundary. This is why a straight stick placed in water appears broken at the surface.

一个简单例子：游泳者从水下向上看时，会看到物体偏离真实位置，因为光在水-空气界面发生偏折。这也是为什么插入水中的直棒在水面处看起来像是折断了一样。

4. Refractive Index and Snell’s Law | 折射率与斯涅尔定律

The refractive index (n) of a medium is a measure of how much light slows down in that medium compared to its speed in a vacuum. It is defined by:

折射率（n）是衡量光在该介质中相对于真空中的速度减慢程度的物理量。其定义为：

n = c / v

where c is the speed of light in a vacuum (approximately 3 × 10⁸ m/s) and v is the speed of light in the medium. Because light always slows down in a medium, n is always greater than 1 for real media.

其中 c 是真空中的光速（约 3 × 10⁸ m/s），v 是光在该介质中的速度。由于光在介质中总是减速，所以实际介质的折射率总是大于 1。

Snell’s law relates the angle of incidence (i) and the angle of refraction (r) when light passes between two media:

斯涅尔定律将光通过两种介质时的入射角（i）和折射角（r）联系起来：

n₁ sin i = n₂ sin r

If light passes from air (n ≈ 1) into a material of refractive index n, this simplifies to n = sin i / sin r. For example, if light enters glass at an angle of incidence of 45° and refracts at 28°, then:

如果光从空气（n ≈ 1）进入折射率为 n 的材料，上式简化为 n = sin i / sin r。例如，光以 45° 入射角进入玻璃，折射角为 28°，则：

n = sin 45° / sin 28° ≈ 0.707 / 0.469 ≈ 1.51

This value is typical for flint glass. In the IGCSE exam, you may be asked to determine the refractive index using this formula, so make sure your calculator is in degree mode.

这个数值是燧石玻璃的典型值。在 IGCSE 考试中，可能会要求你用此公式计算折射率，因此务必确保计算器处于度数模式。

5. Total Internal Reflection | 全内反射

When light travels from a denser medium into a less dense medium, it bends away from the normal. As the angle of incidence increases, the angle of refraction also increases until it reaches 90°. The angle of incidence that produces a refracted angle of 90° is called the critical angle (c).

当光从光密介质射向光疏介质时，折射光线远离法线偏折。随着入射角增大，折射角也随之增大，直到折射角达到 90°。使折射角等于 90° 时的入射角称为临界角（c）。

If the angle of incidence is greater than the critical angle, the light does not emerge at all. Instead, it is completely reflected back into the denser medium. This is called total internal reflection.

如果入射角大于临界角，光完全不会射出，而是全部被反射回光密介质内部，这种现象称为全内反射。

The critical angle is calculated using the formula:

临界角由以下公式计算：

sin c = 1 / n

where n is the refractive index of the denser medium (assuming the less dense medium is air with n ≈ 1). For glass with n = 1.5, the critical angle is approximately 41.8°.

其中 n 是光密介质的折射率（假设光疏介质为空气，n ≈ 1）。对于折射率为 1.5 的玻璃，临界角约为 41.8°。

The conditions for total internal reflection are:

发生全内反射的条件是：

Light must travel from a denser medium to a less dense 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.
入射角必须大于临界角。

Total internal reflection is used in optical fibres, which are thin glass strands that transmit light over long distances with very little energy loss. The light repeatedly undergoes total internal reflection against the walls of the fibre, allowing signals to travel through curved paths.

全内反射广泛应用于光纤中。光纤是一种极细的玻璃丝，能够以极小的能量损失远距离传输光。光在光纤内壁上反复发生全内反射，从而可以沿弯曲路径传输信号。

6. Lenses | 透镜

A lens is a transparent piece of material, usually glass or plastic, that refracts light to form an image. There are two main types:

透镜是由透明材料（通常是玻璃或塑料）制成的光学元件，通过折射光线来成像。主要有两种类型：

Converging (convex) lens – thicker in the middle than at the edges; brings parallel rays to a focal point.
凸透镜（会聚透镜） – 中间厚、边缘薄；使平行光线会聚于焦点。
Diverging (concave) lens – thinner in the middle than at the edges; spreads parallel rays outward as if they came from a virtual focal point.
凹透镜（发散透镜） – 中间薄、边缘厚；使平行光线发散，看起来像是从虚焦点发出的。

Key terms you must know:

你必须掌握以下关键术语：

Principal axis – the imaginary line passing through the centre of the lens.
主光轴 – 通过透镜中心的假想直线。
Principal focus (F) – the point on the principal axis where parallel rays converge (or appear to diverge from) after passing through the lens.
焦点（F） – 平行光线通过透镜后会聚（或反向延长线会聚）在主光轴上的点。
Focal length (f) – the distance between the centre of the lens and the principal focus.
焦距（f） – 透镜中心到焦点之间的距离。

A real image is formed when light rays actually meet; it can be projected on a screen. A virtual image is formed where rays only appear to meet; it cannot be projected. Real images are usually inverted, while virtual images are usually upright.

实像是实际光线会聚形成的，可以在光屏上呈现；虚像是光线的反向延长线会聚形成的，无法在光屏上呈现。实像通常是倒立的，虚像通常是正立的。

7. Converging Lens Ray Diagrams | 凸透镜光路图

To draw ray diagrams for a converging lens, you must use three principal rays from a point on the object:

绘制凸透镜光路图时，需要利用从物体某一点发出的三条特殊光线：

A ray parallel to the principal axis refracts through the principal focus on the other side.
平行于主光轴的光线，经透镜折射后通过另一侧的焦点。
A ray passing through the centre of the lens travels in a straight line.
通过透镜中心的光线沿直线传播，不发生偏折。
A ray passing through the principal focus (on the same side) emerges parallel to the principal axis.
通过（物体一侧）焦点的光线，经透镜折射后平行于主光轴射出。

The point where the refracted rays meet (or appear to meet) is the image point. The nature of the image depends on the object’s position relative to the focal point:

折射光线会聚（或其反向延长线会聚）的点就是像点。像的性质取决于物体相对焦点的位置：

Object position	物体位置	Image characteristics	像的特征
Beyond 2F	大于二倍焦距	Real, inverted, diminished, between F and 2F	实像、倒立、缩小，位于 F 与 2F 之间
At 2F	等于二倍焦距	Real, inverted, same size, at 2F	实像、倒立、等大，位于 2F 处
Between F and 2F	焦点与二倍焦距之间	Real, inverted, magnified, beyond 2F	实像、倒立、放大，位于 2F 之外
At F	在焦点上	No image is formed (rays emerge parallel)	不成像（折射光线平行射出）
Inside F	在焦点以内	Virtual, upright, magnified	虚像、正立、放大

The last case is exactly how a magnifying glass works: you place the object closer than the focal length, and you see a magnified upright virtual image on the same side of the lens as the object.

最后一种情况正是放大镜的工作原理：将物体放在焦距以内，你会在透镜同侧看到一个放大的正立虚像。

8. Diverging Lens | 凹透镜

For a diverging (concave) lens, parallel rays spread out after passing through the lens. The extensions of these rays appear to come from a virtual focus on the same side as the incident light. The ray diagram is drawn using three rules:

对于凹透镜（发散透镜），平行光线经过透镜后向外发散。这些光线的反向延长线似乎从入射光同侧的虚焦点发出。绘制光路图时使用三条规则：

A ray parallel to the principal axis diverges as if it came from the virtual focus on the same side.
平行于主光轴的光线，经透镜折射后发散，反向延长线通过同侧虚焦点。
A ray passing through the centre of the lens continues in a straight line.
通过透镜中心的光线沿直线传播。
A ray directed towards the virtual focus on the other side emerges parallel to the principal axis.
指向另一侧虚焦点的光线，经透镜折射后平行于主光轴射出。

Regardless of the object position, a diverging lens always produces a virtual, upright, and diminished image on the same side as the object. This makes diverging lenses useful for correcting short-sightedness (myopia), as they diverge light before it enters the eye.

无论物体位于何处，凹透镜总是在物体同侧形成虚像、正立、缩小的像。因此凹透镜可用于矫正近视眼（myopia），它使进入眼睛之前的光线发散。

9. Lens Power | 透镜焦度

The power of a lens is a measure of how strongly it converges or diverges light. It is defined as the reciprocal of the focal length:

透镜的焦度是衡量透镜会聚或发散光线强弱的物理量，定义为焦距的倒数：

P = 1 / f

where P is the power in dioptres (D) and f is the focal length in metres (m). A converging lens has positive power, while a diverging lens has negative power.

其中 P 是焦度，单位是屈光度（D）；f 是焦距，单位是米（m）。凸透镜的焦度为正值，凹透镜的焦度为负值。

For example, a converging lens with a focal length of 25 cm (0.25 m) has a power of:

例如，焦距为 25 cm（0.25 m）的凸透镜的焦度为：

P = 1 / 0.25 = +4.0 D

A diverging lens with a focal length of −40 cm (−0.40 m) has a power of:

焦距为 −40 cm（−0.40 m）的凹透镜的焦度为：

P = 1 / (−0.40) = −2.5 D

These values are often used in optometry to describe spectacle lenses. Always remember to convert centimetres to metres before substituting into the formula.

这些数值常用于验光配镜中。请务必先将厘米换算成米，再代入公式计算。

10. Dispersion and Colour | 色散与颜色

White light is a mixture of all visible colours. When it passes through a glass prism, it is split into a spectrum of colours: red, orange, yellow, green, blue, and violet. This phenomenon is called dispersion.

白光是由所有可见颜色混合而成的。当白光通过玻璃棱镜时，会被分解成一系列颜色：红、橙、黄、绿、蓝、紫。这种现象称为色散。

Dispersion occurs because different colours (wavelengths) of light travel at slightly different speeds in glass. Violet light slows down the most and is refracted the most, while red light slows down the least and is refracted the least. Thus, violet appears at one end of the spectrum and red at the other, with the order always fixed.

色散的原因是不同颜色（波长）的光在玻璃中的传播速度略有不同。紫光减速最多，偏折程度也最大；红光减速最少，偏折程度也最小。因此，紫光位于光谱的一端，红光位于另一端，颜色顺序固定不变。

Colour filters work by absorbing certain wavelengths and transmitting only selected colours. For example, a red filter transmits only red light and absorbs most other colours. In the IGCSE syllabus, you should know the three primary colours of light: red, green, and blue. When mixed, they produce secondary colours:

滤色器通过吸收某些波长的光、只透过特定颜色的光来实现。例如，红色滤光片只透过红光，吸收其他大部分颜色。在 IGCSE 大纲中，你需要知道光的三原色：红、绿、蓝。它们混合后产生二次色：

Red + Green = Yellow
红 + 绿 = 黄
Red + Blue = Magenta
红 + 蓝 = 品红
Green + Blue = Cyan
绿 + 蓝 = 青
Red + Green + Blue = White
红 + 绿 + 蓝 = 白光

An object appears a certain colour because it reflects that colour and absorbs the others. For example, a green leaf absorbs most colours and reflects green light.

物体呈现某种颜色，是因为它反射该颜色并吸收其他颜色。例如，绿叶吸收大部分色光，只反射绿光。

11. Applications of Light Waves | 光波的应用

Optical fibres are a major application of total internal reflection. They are used in telecommunications, internet cable networks, endoscopy, and decorative lighting. Because light travels through the fibre with little loss, signals can be transmitted over long distances.

光纤是全内反射的重要应用。光纤用于电信、互联网光缆、内窥镜和装饰照明。由于光在光纤中传播损失极小，信号可以远距离传输。

Lenses have countless applications: cameras use converging lenses to focus light onto a film or sensor; magnifying glasses enlarge small objects; telescopes use large lenses to observe distant stars; and eyeglasses correct vision defects.

透镜的应用数不胜数：照相机使用凸透镜将光会聚到底片或传感器上；放大镜放大小物体；望远镜使用大透镜观察遥远的恒星；眼镜矫正视力缺陷。

Reflection is used in periscopes and mirrors. In a simple periscope, two mirrors arranged at 45° to the light ray allow you to see over walls. Reflectors on bicycles use a special arrangement of small prisms that reflect light back toward its source, making them highly visible at night.

反射应用于潜望镜和镜子中。在简单潜望镜中，两面与光线成 45° 角的镜子使你可以看到墙后的物体。自行车上的反射器利用特殊排列的小棱镜将光反射回光源方向，使其在夜间非常显眼。

12. Summary | 总结

Here is a quick revision checklist for light waves:

以下是光波的快速复习清单：

Light is a transverse electromagnetic wave that travels at 3 × 10⁸ m/s in a vacuum.
光是横波，是一种电磁波，在真空中的传播速度为 3 × 10⁸ m/s。
Law of reflection: angle of incidence equals angle of reflection.
反射定律：入射角等于反射角。
Refraction occurs because light changes speed when moving between media; n = c / v and n₁ sin i = n₂ sin r.
折射是因为光在介质间传播速度改变；n = c / v 和 n₁ sin i = n₂ sin r。
Total internal reflection requires a denser-to-less-dense direction and an incidence angle greater than the critical angle; sin c = 1 / n.
全内反射要求光从光密介质射向光疏介质且入射角大于临界角；sin c = 1 / n。
Converging lenses form real or virtual images depending on object position; diverging lenses always form virtual, upright, diminished images.
凸透镜根据物体位置成实像或虚像；凹透镜总是成虚像、正立、缩小的像。
Lens power P = 1 / f, measured in dioptres; convex positive, concave negative.
透镜焦度 P = 1 / f，单位是屈光度；凸透镜为正，凹透镜为负。
White light disperses into a spectrum because different wavelengths refract differently.
白光发生色散是因为不同波长的光折射程度不同。

Make sure you can draw ray diagrams for both converging and diverging lenses, and that you can explain real-life applications. Practising past paper questions with ray diagrams will greatly improve your confidence for the exam.

请确保你能正确绘制凸透镜和凹透镜的光路图，并能解释它们在现实生活中的应用。通过练习包含光路图的历年真题，你的考试信心将大大增强。

Published by TutorHao | Physics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）

Light Waves | 光波