📚 Mastering Light: IB & AQA Physics Revision | 光：IB AQA 物理考点精讲
Light is a cornerstone of both IB and AQA physics, bridging classical optics with modern quantum ideas. Mastering its behaviour – from reflection and interference to the photoelectric effect – is essential for top marks. This revision guide distils every key concept into clear, exam-focused explanations, supported by essential equations and real-world applications.
光是 IB 与 AQA 物理的共同核心，架起了经典光学与现代量子观念的桥梁。掌握从反射、干涉到光电效应的各种行为，是获取高分的关键。这份复习指南将每一个重要概念浓缩为清晰、紧扣考点的讲解，并配以必备方程和实际应用。
1. The Nature of Light: Waves and Photons | 光的本质：波动与光子
Light exhibits a dual nature: it behaves as a transverse electromagnetic wave and also as a stream of particles called photons. The wave model explains interference and diffraction, while the photon model accounts for the photoelectric effect. The electromagnetic spectrum ranges from radio waves to gamma rays, with visible light occupying wavelengths roughly between 400 nm and 700 nm.
光具有二象性：它既表现为横电磁波，也可视为一束称为光子的粒子流。波动模型能解释干涉和衍射，而光子模型则能说明光电效应。电磁波谱覆盖从无线电波到伽马射线的范围，可见光的波长大致位于 400 纳米到 700 纳米之间。
In a vacuum, all electromagnetic waves travel at the speed of light c = 3.00 × 10⁸ m s⁻¹. The wave speed, frequency and wavelength are related by c = fλ. For a photon, the energy is E = hf, where h is the Planck constant (6.63 × 10⁻³⁴ J s). This energy is directly proportional to frequency and inversely proportional to wavelength.
在真空中，所有电磁波均以光速 c = 3.00 × 10⁸ m s⁻¹ 传播。波速、频率和波长满足关系 c = fλ。对光子而言，能量 E = hf，其中 h 为普朗克常量 (6.63 × 10⁻³⁴ J s)。该能量与频率成正比，与波长成反比。
c = fλ E = hf
2. Reflection and Refraction | 反射与折射
When light strikes a smooth boundary between two media, part of it is reflected and part is transmitted with a change in direction – refraction. The law of reflection states that the angle of incidence equals the angle of reflection (θᵢ = θᵣ), measured from the normal.
当光照射到两种介质的光滑界面时，一部分发生反射，另一部分则透射并改变方向——即折射。反射定律指出，入射角等于反射角 (θᵢ = θᵣ)，均从法线量起。
Refraction is governed by Snell’s law: n₁ sinθ₁ = n₂ sinθ₂, where n is the refractive index. The index of a medium indicates how much the speed of light is reduced: n = c/v. A higher refractive index means light travels more slowly and bends towards the normal when entering from a less dense medium.
折射由斯涅尔定律支配：n₁ sinθ₁ = n₂ sinθ₂，其中 n 为折射率。介质的折射率表示光速减慢的程度：n = c/v。折射率越高，光传播越慢，当光从光疏介质进入光密介质时会向法线偏折。
n₁ sinθ₁ = n₂ sinθ₂
3. Total Internal Reflection | 全内反射
When light travels from a medium with a higher refractive index to one with a lower index (e.g. from water to air), the refracted ray bends away from the normal. At a certain critical angle θc, the angle of refraction reaches 90°. For any angle of incidence greater than θc, all light is reflected internally – this is total internal reflection (TIR).
当光从折射率较高的介质射向折射率较低的介质（例如从水到空气），折射光线会偏离法线。在某一临界角 θc 处，折射角达到 90°。当入射角大于 θc 时，所有光都被内表面反射——这就是全内反射 (TIR)。
The critical angle is derived from Snell’s law with sinθ₂ = 1: sinθc = n₂ / n₁ (where n₁ > n₂). TIR is the working principle behind optical fibres, which guide light along transparent cores with minimal loss, used in telecommunications and endoscopy.
临界角由斯涅尔定律令 sinθ₂ = 1 导出：sinθc = n₂ / n₁ (其中 n₁ > n₂)。TIR 是光纤工作的原理，光纤使光沿透明纤芯以极低损耗传输，广泛应用于通信和内窥镜。
sinθc = n₂ / n₁ (for n₁ > n₂)
4. Interference: Young’s Double-Slit Experiment | 干涉：杨氏双缝实验
Thomas Young’s classic experiment demonstrates the wave nature of light through interference. Coherent light passing through two narrow slits produces an interference pattern of bright and dark fringes on a screen. Constructive interference occurs when the path difference is an integer multiple of the wavelength, Δ = nλ, while destructive interference occurs when Δ = (n + ½)λ.
托马斯·杨的经典实验通过干涉展示了光的波动性。相干光通过两道狭缝后在屏幕上产生明暗相间的干涉条纹。当光程差为波长的整数倍时发生相长干涉，Δ = nλ；当光程差为半波长的奇数倍时发生相消干涉，Δ = (n + ½)λ。
The fringe spacing (Δy) between adjacent bright fringes is given by Δy = λD / d, where λ is the wavelength, D is the distance from slits to screen, and d is the slit separation. This formula is valid for small angles and allows precise determination of wavelength.
相邻亮纹的间距 Δy 由公式 Δy = λD / d 给出，其中 λ 为波长，D 为双缝到屏幕的距离，d 为双缝间距。该公式在小角度下成立，可用于精确测定波长。
Δy = λD / d
5. Diffraction Gratings | 衍射光栅
A diffraction grating consists of many equally spaced slits, producing sharper and brighter interference maxima compared to a double slit. The condition for principal maxima is d sinθ = nλ, where d is the grating spacing (the reciprocal of the number of lines per metre), n is the order number (n = 0, 1, 2, …), and θ is the angle of diffraction.
衍射光栅由大量等间距狭缝组成，能产生比双缝更锐利、更明亮的干涉极大。主极大的条件是 d sinθ = nλ，其中 d 为光栅常数（每米刻线数的倒数），n 为级次 (n = 0, 1, 2, …)，θ 为衍射角。
Gratings are routinely used in spectrometers to analyse light from sources. The maximum number of observable orders is limited by sinθ ≤ 1, giving nₘₐₓ ≤ d / λ. The greater the number of slits, the narrower the maxima, improving the instrument’s resolving power.
光栅常用于光谱仪中分析光源。可观测的最大级次受 sinθ ≤ 1 限制，即 nₘₐₓ ≤ d / λ。狭缝数目越多，极大越窄，仪器分辨率越高。
d sinθ = nλ
6. Single-Slit Diffraction | 单缝衍射
When light passes through a single narrow slit of width a, it spreads out and produces a central bright fringe flanked by progressively weaker secondary maxima. The first minimum on either side of the central maximum occurs at an angle θ satisfying a sinθ = λ. For subsequent minima, a sinθ = nλ, where n = 1, 2, 3, … (excluding n = 0).
当光通过宽度为 a 的单缝时，会发生扩散并在屏幕形成中央亮纹和两侧逐渐减弱的次级极大。中央极大两侧的第一暗纹满足条件 a sinθ = λ。更高阶暗纹的条件为 a sinθ = nλ，其中 n = 1, 2, 3, …（不含 0）。
The angular width of the central maximum is 2λ/a radians, indicating that diffraction effects become more pronounced as the slit width approaches the wavelength. This spreading limits the ability to form sharp images and introduces the concept of resolution.
中央极大的角宽度为 2λ/a 弧度，表明当狭缝宽度接近波长时衍射效应更加显著。这种扩散限制了形成清晰图像的能力，并引入了分辨率的概念。
a sinθ = nλ (minima, n = 1, 2, 3, …)
7. Thin-Film Interference | 薄膜干涉
A thin film, such as a soap bubble or an oil slick on water, displays colourful patterns due to interference between light reflected from the top surface and light reflected from the bottom surface. The effective path difference depends on film thickness, refractive index, and any phase changes upon reflection.
薄膜（例如肥皂泡或水面油膜）因上表面与下表面反射光之间的干涉而呈现彩色图样。有效光程差取决于膜厚、折射率以及反射时可能发生的相位变化。
When light reflects off a medium of higher refractive index, it undergoes a phase change of π (equivalent to a half-wavelength shift). For normal incidence, constructive interference for reflected light occurs when 2nt = (m + ½)λ (with phase reversal on one reflection), while destructive interference occurs when 2nt = mλ. Here t is the film thickness and n is the refractive index of the film.
光从折射率较高的介质反射时发生 π 相位突变（相当于半波长位移）。垂直入射时，若一次反射有相位反转，反射光相长干涉的条件为 2nt = (m + ½)λ，相消干涉的条件为 2nt = mλ。其中 t 为膜厚，n 为薄膜折射率。
2nt = mλ or 2nt = (m + ½)λ
8. Polarisation | 偏振
Polarisation provides direct evidence that light is a transverse wave. Unpolarised light has electric field oscillations in all directions perpendicular to the direction of propagation. A polarising filter transmits only the component of the electric field parallel to its transmission axis, reducing intensity by 50% for an ideal polariser.
偏振为光是一种横波提供了直接证据。非偏振光的电场在垂直于传播方向的所有方向上振荡。偏振片只允许与其透射轴平行的电场分量通过，理想偏振片会使强度减半。
When a second polariser (analyser) is placed after the first, the transmitted intensity follows Malus’s law: I = I₀ cos²θ, where θ is the angle between the transmission axes. Polarisation by reflection occurs at Brewster’s angle, where the reflected and refracted rays are perpendicular, given by tanθ_B = n₂ / n₁.
在第一块偏振片后放置第二块偏振片（检偏器）时，透射光强遵循马吕斯定律：I = I₀ cos²θ，其中 θ 为两透射轴之间的夹角。反射偏振发生在布儒斯特角，此时反射光线与折射光线垂直，满足 tanθ_B = n₂ / n₁。
I = I₀ cos²θ tanθ_B = n₂ / n₁
9. The Photoelectric Effect | 光电效应
The photoelectric effect is the emission of electrons from a metal surface when light of sufficiently high frequency shines on it. Experimental observations – existence of a threshold frequency f₀, instantaneous emission, and independence of maximum kinetic energy from intensity – cannot be explained by the wave model, but are fully accounted for by the photon model.
光电效应是指当频率足够高的光照射金属表面时，电子从表面逸出的现象。实验观测结果——存在截止频率 f₀、瞬时发射、最大动能与光强无关——均无法用波动模型解释，但光子模型能完美说明。
Einstein’s photoelectric equation relates the maximum kinetic energy of emitted electrons to the photon energy and the work function φ of the metal: Eₖ max = hf – φ. The work function is the minimum energy required to remove an electron from the surface. The stopping potential Vₛ is given by eVₛ = hf – φ.
爱因斯坦光电方程将逸出电子的最大动能与光子能量和金属的功函数 φ 联系起来：Eₖ max = hf – φ。功函数是从表面移除一个电子所需的最小能量。截止电压 Vₛ 满足 eVₛ = hf – φ。
Eₖ max = hf – φ eVₛ = hf – φ
10. Wave-Particle Duality and de Broglie Wavelength | 波粒二象性与德布罗意波长
The principle of wave-particle duality asserts that all particles exhibit both wave and particle properties. Light, previously thought of as a wave, shows particle behaviour in the photoelectric effect; electrons, traditionally considered particles, produce diffraction patterns, confirming their wave nature.
波粒二象性原理指出，所有粒子都同时表现出波动性和粒子性。原先被视为波的光，在光电效应中展现出粒子行为；而被传统视为粒子的电子，则能产生衍射图样，证实了其波动性。
De Broglie proposed that any particle with momentum p has an associated wavelength λ = h / p. For an electron accelerated through a potential difference V, the kinetic energy is eV = p²/(2m), giving λ = h / √(2meV). This wavelength predicts the diffraction pattern observed in electron diffraction experiments.
德布罗意提出，任何动量为 p 的粒子都有一个关联波长 λ = h / p。对于被电势差 V 加速的电子，动能 eV = p²/(2m)，可得 λ = h / √(2meV)。这一波长能够预测电子衍射实验中的图样。
λ = h / p λ = h / √(2meV)
11. Resolution and Rayleigh Criterion | 分辨率与瑞利判据
When light passes through a circular aperture, diffraction produces a central bright spot called the Airy disk surrounded by rings. The Rayleigh criterion states that two point sources are just resolvable when the central maximum of one image coincides with the first minimum of the other. The angular separation for just-resolved points is θ = 1.22λ / D, where D is the aperture diameter.
当光通过圆形孔径时，衍射会产生称为艾里斑的中央亮斑及外围光环。瑞利判据指出，当一个像的中央极大与另一个像的第一暗纹重合时，两点光源恰可分辨。恰可分辨的角间距为 θ = 1.22λ / D，其中 D 为孔径直径。
This limit affects the performance of optical instruments such as telescopes and microscopes. Improving resolution can be achieved by using shorter wavelength radiation (e.g. ultraviolet or electron microscopes) or by increasing the lens or mirror aperture.
这一限制影响着望远镜和显微镜等光学仪器的性能。提高分辨率可以通过使用更短波长的辐射（如紫外光或电子显微镜）或增大透镜/反射镜的孔径来实现。
θ ≈ 1.22λ / D
12. Doppler Effect for Light | 光的多普勒效应
The Doppler effect for light describes the change in observed frequency (and wavelength) when a light source moves relative to an observer. For velocities much smaller than c, the fractional shift is Δλ / λ₀ ≈ v / c, where v is the relative radial velocity (positive for recession, negative for approach). A receding source increases wavelength (redshift), while an approaching source decreases wavelength (blueshift).
光的多普勒效应描述了光源与观察者相对运动时观测频率（和波长）的变化。当速度远小于光速时，波长相对偏移量为 Δλ / λ₀ ≈ v / c，其中 v 为相对径向速度（远离为正，靠近为负）。远离的光源波长增加（红移），靠近的光源波长减小（蓝移）。
Astronomers use redshift measurements to determine the recessional velocities of galaxies, providing evidence for the expansion of the universe. In the laboratory, laser Doppler techniques measure tiny frequency shifts to study fluid flow and vibrations.
天文学家利用红移测量来确定星系的退行速度，为宇宙膨胀提供了证据。在实验室中，激光多普勒技术通过测量微小频移来研究流体和振动。
Δλ / λ₀ ≈ v / c
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