📚 Electromagnetic Radiation: Waves, Photons and the Spectrum | 电磁辐射：波、光子与波谱
s carry energy through space, from the radio waves used in communication to the gamma rays emitted by radioactive nuclei. A secure understanding of the electromagnetic spectrum, the wave equation c = fλ and the photon model E = hf is essential for multiple-choice questions, structured questions and practical applications alike.
电磁辐射是 CIE A-Level 物理中最基础的主题之一。它描述振荡的电场和磁场如何在空间中携带能量，从通信所用的无线电波到放射性原子核发射的伽马射线。理解电磁波谱、波动方程 c = fλ 以及光子模型 E = hf，对选择题、结构化题目以及实际应用都至关重要。
1. The Nature of Electromagnetic Waves | 电磁波的本质
Electromagnetic waves are produced by accelerating charges. When a charged particle accelerates, it creates a changing electric field, and that changing electric field generates a changing magnetic field; the two fields sustain each other and propagate outward as a wave. A stationary charge produces only a static field, and a charge moving at constant velocity produces a steady field pattern, so acceleration is the key requirement.
电磁波由加速电荷产生。当带电粒子加速时，它产生变化的电场，变化的电场又产生变化的磁场；这些场相互维持并以波的形式向外传播。静止电荷只产生静态场，匀速运动的电荷产生稳定的场分布，因此"加速"是产生电磁波的关键条件。
The electric field and the magnetic field oscillate at right angles to each other and at right angles to the direction of energy transfer. This mutually perpendicular arrangement is what makes every electromagnetic wave a transverse wave.
电场和磁场彼此垂直振荡，并且都与能量传递方向垂直。这种相互垂直的构型使所有电磁波都成为横波。
lower, and the ratio of the speed in vacuum to the speed in the medium defines the refractive index: n = c ÷ v.
由于不需要介质，电磁波可以在真空中以约 3.00 × 10⁸ m s⁻¹ 的速度传播。在介质中速度会降低，真空中速度与介质中速度之比定义为折射率：n = c ÷ v。
c = 3.00 × 10⁸ m s⁻¹ (vacuum); v = c ÷ n (medium)
2. The Electromagnetic Spectrum | 电磁波谱
The electromagnetic spectrum is the continuous family of all electromagnetic waves, ordered by frequency or wavelength. In order of increasing frequency (and therefore decreasing wavelength) the regions are: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. The boundaries between neighbouring regions overlap, so the classification is based on how the radiation is produced and detected rather than on a sharp physical cut-off.
电磁波谱是按频率或波长排列的全部电磁波构成的连续族。按频率递增（波长递减）的顺序，各区域依次为：无线电波、微波、红外线、可见光、紫外线、X 射线和伽马射线。相邻区域的分界是重叠的，因此这种划分依据的是辐射的产生与探测方式，而不是某个明确的物理分界点。
mma photon carries far more energy than a low-frequency radio photon, even though both travel at the same speed.
在真空中，各区域的传播速度都是 c。不同的是频率与波长，它们由 c = fλ 联系。这正是高频伽马光子比低频无线电光子携带多得多的能量的原因，尽管两者的传播速度相同。
| Region | 区域 | Typical wavelength | 典型波长 | Source / use | 来源与用途 |
| Radio 无线电波 | 10 m – 10 km | Oscillating circuits; broadcasting 振荡电路；广播 |
| Microwave 微波 | 1 mm – 30 cm | Klystron / magnetron; satellites, phones 速调管；卫星与手机 |
| Infrared 红外线 | 700 nm – 1 mm | Molecular vibration; heating, remotes 分子振动；加热与遥控 |
| Visible 可见光 | 400 – 700 nm | Electron transitions in atoms; vision 原子中电子跃迁；视觉 |
| Ultraviolet 紫外线 | 10 – 400 nm | Hot surfaces, discharge lamps; sterilising 高温表面；杀菌 |
| X-ray X 射线 | 0.01 – 10 nm | Rapid deceleration of electrons; imaging 电子急速减速；成像 |
| Gamma 伽马射线 | less than 0.01 nm | Nuclear decay; cancer therapy 核衰变；癌症治疗 |
3. The Wave Equation c = fλ | 波动方程 c = fλ
in hertz (Hz); wavelength λ is the distance between two successive points in phase, measured in metres; the period T = 1 ÷ f is the time for one complete oscillation.
波动方程把波速与频率、波长联系起来。频率 f 是每秒完整振荡的次数，单位为赫兹（Hz）；波长 λ 是相邻两个同相点之间的距离，单位为米；周期 T = 1 ÷ f 是一次完整振荡所需的时间。
c = fλ f = 1 ÷ T v = fλ (in a medium)
When radiation passes from one medium into another, the frequency is set by the source and does not change, so it is the wavelength and the speed that alter. A common examination trap is to assume that frequency changes on refraction; it does not.
当辐射从一种介质进入另一种介质时，频率由波源决定且保持不变，因此改变的是波长和速度。一个常见的考试陷阱是误以为折射时频率会改变；实际上不会。
um of refractive index 1.5, the speed becomes 2.00 × 10⁸ m s⁻¹ and the wavelength shortens to 2.0 m, while the frequency stays at 100 MHz.
示例：某电台以 100 MHz 广播，空气中的波长为 λ = c ÷ f = (3.00 × 10⁸) ÷ (100 × 10⁶) = 3.0 m。若同一信号进入折射率为 1.5 的介质，速度变为 2.00 × 10⁸ m s⁻¹，波长缩短为 2.0 m，而频率仍为 100 MHz。
4. The Photon Model E = hf | 光子模型 E = hf
tons. The energy of a single photon is directly proportional to its frequency, and the constant of proportionality is the Planck constant h = 6.63 × 10⁻³⁴ J s.
尽管电磁辐射在传播中表现为波，但它与物质相互作用时表现为一束称为光子的离散能量包。单个光子的能量与其频率成正比，比例常数为普朗克常数 h = 6.63 × 10⁻³⁴ J s。
E = hf = hc ÷ λ p = E ÷ c = h ÷ λ
in the photoelectric effect, in Compton scattering and in calculations of radiation pressure.
由于光子没有静止质量，其动量完全由能量携带：p = E ÷ c。这一结果在光电效应、康普顿散射以及辐射压的计算中都很重要。
V. The photoelectric equation KEmax = hf − Φ then shows whether such a photon can release an electron from a given metal, where Φ is the work function.
示例：绿光光子波长 λ = 500 nm，其能量为 E = hc ÷ λ = (6.63 × 10⁻³⁴ × 3.00 × 10⁸) ÷ (500 × 10⁻⁹) = 3.98 × 10⁻¹⁹ J，约合 2.49 eV。光电效应方程 KEmax = hf − Φ 则说明这样的光子能否从某种金属中打出电子，其中 Φ 为逸出功。
5. Transverse Waves and Polarisation | 横波与偏振
All electromagnetic waves are transverse. This means the oscillations of the electric and magnetic fields are perpendicular to the direction of energy transfer, not along it. A longitudinal wave such as sound cannot be polarised, so the existence of polarisation is direct experimental evidence that electromagnetic radiation is transverse.
所有电磁波都是横波。这意味着电场和磁场的振荡方向与能量传递方向垂直，而不是沿着它。像声波这样的纵波无法被偏振，因此偏振现象的存在是电磁辐射为横波的直接实验证据。
pendicular to the direction of travel. When it passes through a polarising filter, only the component parallel to the transmission axis is transmitted, and the intensity of the transmitted beam falls to about half of the original because the randomly oriented oscillations have an average component of cos²θ = ½.
偏振是指把振荡限制在单一平面内。非偏振光包含在垂直于传播方向的所有平面内的电场振荡。当它通过偏振片时，只有平行于透振方向的分量被透过，透射光强降至原来的一半左右，因为随机取向振动的平均分量为 cos²θ = ½。
For a second filter placed after the first, the transmitted intensity follows Malus law, where θ is the angle between the two transmission axes. Setting the axes at 90° blocks the beam completely, which is exactly how sunglasses and LCD screens control glare.
对于放在第一片之后的第二片偏振片，透射光强遵循马吕斯定律，其中 θ 是两透振方向之间的夹角。当两透振方向成 90° 时，光束被完全阻挡，这正是太阳镜和液晶显示屏控制眩光的原理。
I = I₀ cos²θ (after a polariser: I = ½ I₀)
Applications worth quoting in structured answers include reducing reflected glare from water and roads, stress analysis in transparent plastics placed between crossed polarisers, and the alignment of radio and television aerials, where the receiving rod must be parallel to the electric field of the incoming wave.
在结构化答题中值得引用的应用包括：减少水面和路面反射的眩光；把透明塑料放在正交偏振片之间进行应力分析；以及无线电和电视天线的取向，其中接收杆必须与来波的电场方向平行。
6. Energy, Intensity and the Inverse Square Law | 能量、强度与平方反比定律
Intensity is defined as the power transmitted per unit area perpendicular to the direction of propagation, measured in W m⁻². For a point source radiating uniformly in all directions, the same power spreads over a sphere of area 4πr², so the intensity falls as the square of the distance from the source.
强度定义为单位时间内垂直通过单位面积的功率，单位为 W m⁻²。对于向各方向均匀辐射的点光源，同样的功率分布在面积为 4πr² 的球面上，因此强度随离源距离的平方衰减。
I = P ÷ (4πr²) I ∝ 1 ÷ r²
Doubling the distance reduces the intensity to one quarter. Note carefully what does not change: the energy of each individual photon, and therefore its frequency and colour, stay the same. Only the number of photons arriving per second per unit area decreases.
距离加倍，强度降为四分之一。要特别注意哪些量不变：每个光子的能量，因而其频率和颜色，都保持不变。减少的只是每秒钟每单位面积到达的光子数目。
Intensity is also proportional to the square of the amplitude of the wave. This is the relationship used when a light source is moved along a ruler and the reading of a light meter or the count rate of a photocell is plotted against 1 ÷ r² to verify the inverse square law experimentally.
强度还与波振幅的平方成正比。这一关系常用于实验：把光源沿直尺移动，绘制光强计读数或光电池计数率对 1 ÷ r² 的图像，以验证平方反比定律。
7. Electromagnetic Radiation in Communication | 电磁辐射在通信中的应用
Different regions of the spectrum are chosen for communication because of how they behave in the atmosphere. Long and medium radio waves diffract strongly around obstacles such as hills and buildings, and can also be reflected by the ionosphere, so they travel beyond the horizon. Short waves are reflected by the ionosphere and are used for long-distance broadcasting, while VHF and UHF waves are largely line of sight and need repeater stations or satellites.
不同波段的电磁波因其在大气中的行为而被选用于通信。长波和中波无线电波能强烈绕过山丘和建筑物等障碍物发生衍射，还能被电离层反射，因此可以传向地平线以外。短波被电离层反射，用于远距离广播；而甚高频和特高频波基本上是视距传播，需要中继站或卫星。
Microwaves pass through the ionosphere and are therefore used for satellite links and mobile telephony. Because they are strongly absorbed by water, they also heat food in microwave ovens by exciting the rotational modes of water molecules.
微波能穿透电离层，因此用于卫星链路和移动电话。由于被水强烈吸收，微波炉通过激发水分子的转动模式来加热食物。
Optical fibres use infrared radiation because glass is most transparent at those wavelengths. Light is trapped by total internal reflection when the core has a higher refractive index than the cladding, provided the angle of incidence at the boundary exceeds the critical angle. Signal degradation comes from absorption, from modal dispersion in multimode fibres and from material dispersion because different wavelengths travel at slightly different speeds. Digital signals are preferred because they can be regenerated without amplifying the accumulated noise.
光纤使用红外线，因为玻璃在这些波长处最透明。当纤芯折射率高于包层，并且入射到边界处的角度大于临界角时，光靠全反射被限制在纤芯中传播。信号衰减来自吸收、多模光纤中的模间色散，以及因不同波长传播速度略有差异而产生的材料色散。数字信号更受青睐，因为它们可以被再生而无需放大累积的噪声。
8. Ionising Radiation and its Interaction with Matter | 电离辐射及其与物质的相互作用
A photon is ionising when its energy is greater than the ionisation energy of the atoms it meets. Ultraviolet photons cause photoelectric emission from some metals and can damage biological molecules, which is why sunscreens and ozone in the stratosphere matter. X-ray and gamma photons are far more energetic and ionise atoms deep inside tissue, which makes them both medically useful and hazardous.
当光子能量大于它所遇到原子的电离能时，该光子就是电离辐射。紫外光子能从某些金属中引起光电发射，并可能损伤生物分子，这就是防晒霜和平流层臭氧重要的原因。X 射线和伽马光子能量高得多，能电离组织深处的原子，这使它们既有医学价值又具危害性。
Three interaction mechanisms are examined at A-Level. In photoelectric absorption the photon transfers all its energy to an electron and disappears. In Compton scattering the photon transfers part of its energy and continues with a longer wavelength. In pair production, which requires a photon energy of at least 1.02 MeV, the photon is converted into an electron-positron pair in the field of a nucleus.
A-Level 阶段考查三种相互作用机制。在光电吸收中，光子把全部能量交给电子并消失。在康普顿散射中，光子只转移部分能量，并以更长的波长继续前进。在电子对产生中，光子需要在原子核场中且能量至少为 1.02 MeV，转化为一个电子-正电子对。
The attenuation of a narrow beam follows an exponential law in which μ is the attenuation coefficient of the material and x is its thickness. Lead has a high μ because of its high density and high atomic number, which is why it is used for shielding in hospitals and laboratories.
窄束辐射的衰减遵循指数规律，其中 μ 是材料的衰减系数，x 是其厚度。铅的 μ 很高，因为它密度大、原子序数高，这就是医院和实验室用铅做屏蔽的原因。
I = I₀ e−μx
9. Black-Body Radiation | 黑体辐射
All bodies emit electromagnetic radiation because of their temperature, and a black body is an ideal emitter and absorber that radiates the maximum possible power at every wavelength. The spectrum of a black body is continuous, and as the temperature rises the peak of the curve moves to shorter wavelengths and the total radiated power increases rapidly.
所有物体都因自身温度而发射电磁辐射。黑体是理想发射体和吸收体，在每个波长上都辐射可能的最大功率。黑体的光谱是连续的；温度升高时，曲线峰值向短波方向移动，总辐射功率迅速增大。
λmax T = 2.9 × 10⁻³ m K L = σAT⁴, σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴
temperature T. Both are used to estimate the surface temperatures of stars: the Sun has λmax near 500 nm, giving T = (2.9 × 10⁻³) ÷ (500 × 10⁻⁹) ≈ 5800 K.
维恩位移定律给出峰值波长，斯特藩-玻尔兹曼定律给出表面积为 A、热力学温度为 T 的表面所辐射的总功率。两者都用于估算恒星表面温度：太阳的 λmax 约为 500 nm，因此 T = (2.9 × 10⁻³) ÷ (500 × 10⁻⁹) ≈ 5800 K。
10. Wave-Particle Duality | 波粒二象性
Electromagnetic radiation shows wave behaviour in phenomena such as interference, diffraction and polarisation, and particle behaviour in the photoelectric effect, Compton scattering and the emission of single photons in photon-counting experiments. This dual nature is now accepted as fundamental, and the same duality applies to matter.
电磁辐射在干涉、衍射和偏振等现象中表现出波的行为，在光电效应、康普顿散射以及光子计数实验中单个光子的发射中表现出粒子的行为。这种二象性现已被视为基本性质，同样的二象性也适用于物质。
ron of mass m accelerated through a potential difference V, the wavelength becomes λ = h ÷ √2meV ¹⁰ m, comparable to atomic spacing, which is why electron diffraction from graphite is used as the classic experimental evidence.
德布罗意提出，任何动量为 p 的粒子都对应一个波长 λ = h ÷ p。对于经电势差 V 加速、质量为 m 的电子，波长可写为 λ = h ÷ √2meV。当 V = 100 V 时约为 1.2 × 10⁻¹⁰ m，与原子的间距相当，这就是用石墨对电子衍射作为经典实验证据的原因。
λ = h ÷ p = h ÷ (mv)
11. Practical Skills and Exam Technique | 实验技能与考试技巧
= 1.60 × 10⁻¹⁹ J, so photon energies calculated in joules can be converted to electronvolts by dividing by 1.60 × 10⁻¹⁹.
