📚 IB & CIE Science: Light – Key Concepts | IB & CIE 科学：光 考点精讲
Light is a fundamental topic in both IB and CIE science curricula, bridging geometrical optics and wave behaviour. Understanding the dual nature of light, its interactions with matter, and the mathematical models that describe interference and diffraction is essential for success in examinations. This revision guide breaks down the key concepts, formulas, and practical applications that you need to master.
光是 IB 与 CIE 科学课程中的核心主题，连接了几何光学与波动行为。理解光的波粒二象性、光与物质的相互作用以及描述干涉和衍射的数学模型对考试成功至关重要。本考点精讲将逐一梳理你必须掌握的核心概念、公式和实际应用。
1. Nature of Light | 光的本质
Light is a transverse electromagnetic wave with a speed of approximately 3.00 × 10⁸ m s⁻¹ in a vacuum. It exhibits wave–particle duality: it travels as a wave but can interact with matter as discrete packets of energy called photons.
光是一种横电磁波，在真空中传播速度约为 3.00 × 10⁸ m s⁻¹。它表现出波粒二象性：以波的形式传播，但以分立的能量包——光子——与物质相互作用。
The energy of a photon is given by E = h f, where h is Planck’s constant (6.63 × 10⁻³⁴ J s) and f is the frequency. Since c = f λ, we can also write E = h c / λ.
光子的能量由 E = h f 给出，其中 h 是普朗克常数 (6.63 × 10⁻³⁴ J s)，f 是频率。由于 c = f λ，我们也可以写成 E = h c / λ。
E = h f or E = h c / λ
Higher frequency (shorter wavelength) light carries more energy per photon. This explains why ultraviolet radiation can cause more chemical damage than visible light.
频率越高（波长越短）的光，每个光子携带的能量越多。这解释了为何紫外辐射比可见光能造成更大的化学损伤。
2. Reflection of Light | 光的反射
The law of reflection states that the angle of incidence (θᵢ) equals the angle of reflection (θᵣ), and both rays lie in the same plane as the normal. A smooth surface produces specular reflection, while a rough surface causes diffuse scattering.
反射定律指出入射角 (θᵢ) 等于反射角 (θᵣ)，且入射光线、反射光线和法线在同一平面内。光滑表面产生镜面反射，粗糙表面则造成漫反射。
In plane mirrors, the image is virtual, upright, laterally inverted, and the same size as the object. The image distance behind the mirror equals the object distance in front of it.
在平面镜中，像为虚像、正立、左右颠倒且与物等大。像在镜后的距离等于物体在镜前的距离。
Reflection is used in periscopes, corner reflectors, and optical instruments. The law applies to all types of waves, including sound and water waves.
反射原理被用于潜望镜、角反射器和光学仪器中。此定律适用于所有类型的波，包括声波和水波。
3. Refraction of Light | 光的折射
Refraction occurs when light passes from one transparent medium to another, changing speed and direction. The relationship is described by Snell’s law: n₁ sin θ₁ = n₂ sin θ₂, where n is the refractive index and θ is the angle with respect to the normal.
当光从一种透明介质进入另一种时发生折射，其速度和方向均发生变化。这一关系由斯涅尔定律描述：n₁ sin θ₁ = n₂ sin θ₂，其中 n 为折射率，θ 为与法线的夹角。
The refractive index n of a medium is defined as n = c / v, where c is the speed of light in a vacuum and v is its speed in the medium. A medium with a larger n is optically denser; light bends toward the normal when entering a denser medium.
介质的折射率 n 定义为 n = c / v，c 为真空中光速，v 为介质中光速。n 较大的介质光密性更高；光进入光密介质时向法线偏折。
When light travels from a denser to a rarer medium, it bends away from the normal. At a certain angle, the refracted ray grazes the boundary, leading to total internal reflection.
当光从光密射向光疏介质时，会远离法线偏折。在某一角度，折射光线恰好掠过界面，从而引发全反射。
4. Total Internal Reflection | 全反射
Total internal reflection (TIR) occurs when light travels from a denser medium to a rarer medium and the angle of incidence exceeds the critical angle θc. The critical angle is given by sin θc = n₂ / n₁, with n₁ > n₂. For a boundary with air (n₂ ≈ 1), sin θc = 1 / n.
当光从光密介质射向光疏介质且入射角大于临界角 θc 时，发生全反射。临界角满足 sin θc = n₂ / n₁，其中 n₁ > n₂。对于与空气（n₂ ≈ 1）的界面，有 sin θc = 1 / n。
sin θc = 1 / n (to air)
TIR is the principle behind optical fibres, where light signals are transmitted with minimal loss. In endoscopes, bundles of fibres carry images from inside the body. It also explains the brilliance of diamonds and mirages.
全反射是光纤工作的原理，光信号以极低损耗传输。在内窥镜中，光纤束将体内图像传出。它也解释了钻石的闪耀和海市蜃楼现象。
For TIR to occur, two conditions must be met: light must move from a denser to a rarer medium, and the angle of incidence must be greater than the critical angle.
发生全反射必须满足两个条件：光必须从光密介质射向光疏介质，且入射角必须大于临界角。
5. Lenses and Image Formation | 透镜与成像
Converging (convex) lenses bring parallel rays to a real focus, while diverging (concave) lenses spread rays so they appear to come from a virtual focus. Ray diagrams help locate images by tracing principal rays: one parallel to the axis refracted through the focal point, one through the optical centre undeviated, and one through the focal point emerging parallel.
会聚（凸）透镜将平行光线会聚于实焦点，发散（凹）透镜则使平行光线发散，其延长线交于虚焦点。光线图通过追踪主要光线来定位像：平行于主轴的光线经折射后过焦点，过光心的光线不偏折，过焦点的光线折射后平行于主轴。
The thin lens equation relates object distance u, image distance v, and focal length f: 1/f = 1/u + 1/v. Sign conventions are crucial: for a convex lens, f is positive; for a concave lens, f is negative. Real images have positive v, virtual images have negative v.
薄透镜公式联系物距 u、像距 v 和焦距 f：1/f = 1/u + 1/v。符号规则至关重要：凸透镜 f 取正，凹透镜 f 取负；实像 v 正，虚像 v 负。
1/f = 1/u + 1/v
Magnification m is given by m = image height / object height = –v / u. The negative sign indicates an inverted image for real images.
放大率 m 定义为 m = 像高 / 物高 = –v / u。负号表示实像倒立。
6. Dispersion and Colour | 色散与颜色
White light is a mixture of colours, each with a different wavelength. When white light passes through a prism, refraction separates it into a continuous spectrum. This happens because the refractive index of glass varies with wavelength; shorter wavelengths (violet) bend more than longer ones (red).
白光是由不同波长的色光混合而成。当白光通过棱镜时，折射将其分解为连续光谱。这是因为玻璃的折射率随波长变化；短波长的紫光比长波长的红光偏折更大。
Rainbows are formed by dispersion, internal reflection, and refraction in water droplets. The sequence of colours is red, orange, yellow, green, blue, indigo, violet (ROYGBIV).
彩虹由水滴中的色散、内反射和折射形成。颜色顺序为红、橙、黄、绿、蓝、靛、紫。
Dispersion must be corrected in lenses to prevent chromatic aberration. Achromatic doublets combine lenses made from different glasses to bring two colours to the same focus.
透镜中必须校正色散以防止色差。消色差双合透镜将不同玻璃制成的透镜组合，使两种颜色的像重合在同一个焦点。
7. Wave Nature of Light | 光的波动性
As a wave, light has wavelength λ, frequency f, and speed c, related by c = f λ. Its transverse nature is demonstrated by polarisation. A light wave consists of oscillating electric and magnetic fields perpendicular to the direction of propagation.
作为一种波，光有波长 λ、频率 f 和速度 c，遵循 c = f λ。偏振现象证明了光的横波特性。光波由垂直于传播方向振动的电场和磁场组成。
Huygens’ principle states that every point on a wavefront acts as a source of secondary spherical wavelets. The new wavefront is the envelope of these wavelets. This principle explains reflection, refraction, and diffraction.
惠更斯原理指出，波前上的每一点都可视为子波的波源，发出球面次波。新的波前是这些次波的包络面。此原理解释了反射、折射和衍射现象。
The concept of coherence is vital for interference: two sources must be coherent, meaning they emit waves with a constant phase difference and the same frequency. Lasers are excellent coherent sources.
相干性概念对干涉至关重要：两个波源必须相干，即发出的波具有恒定的相位差和相同的频率。激光是极好的相干光源。
8. Interference and Young’s Double Slit | 干涉与杨氏双缝
Young’s double-slit experiment provided the first strong evidence for the wave nature of light. Monochromatic light illuminates two narrow, closely spaced slits, acting as coherent sources. An interference pattern of bright and dark fringes appears on a screen.
杨氏双缝实验为光的波动性提供了首个有力证据。单色光照射两个狭小且紧密相邻的缝，它们作为相干光源。屏幕上出现明暗相间的干涉条纹。
The fringe spacing Δx (distance between adjacent bright fringes) depends on wavelength λ, slit separation d, and distance D from the slits to the screen: Δx = λ D / d.
条纹间距 Δx（相邻亮条纹中心的距离）取决于波长 λ、缝间距 d 以及缝到屏幕的距离 D：Δx = λ D / d。
Δx = λ D / d or λ = d Δx / D
Bright fringes occur where the path difference is a whole number of wavelengths (constructive interference), while dark fringes occur where the path difference is a half-integer number of wavelengths (destructive interference). Increasing the slit separation decreases fringe spacing.
当光程差为波长的整数倍时形成亮纹（相长干涉），光程差为半波长的奇数倍时形成暗纹（相消干涉）。增大双缝间距会减小条纹间距。
9. Diffraction of Light | 光的衍射
Diffraction is the spreading of waves as they pass through an aperture or around an obstacle. The effect is most noticeable when the aperture size is comparable to the wavelength.
衍射是波通过狭缝或绕过障碍物时发生的扩展现象。当狭缝尺寸与波长相近时，衍射效应最为显著。
For a single slit of width a, destructive interference produces minima at angles satisfying a sin θ = n λ, where n = ±1, ±2, … The central maximum is twice as wide as the other maxima.
对于缝宽为 a 的单缝，相消干涉产生的暗纹满足 a sin θ = n λ，其中 n = ±1, ±2, … 中央亮纹的宽度是其他亮纹的两倍。
a sin θ = n λ (n = 1, 2, 3, …)
A diffraction grating consists of many equally spaced slits. Constructive interference gives sharp bright fringes when d sin θ = n λ, where d is the slit separation (grating spacing). Gratings are used in spectrometers to analyse light spectra.
衍射光栅由许多等间距的狭缝组成。当 d sin θ = n λ 时发生相长干涉，产生锐利的亮纹，其中 d 为缝间距（光栅常数）。光栅用于光谱仪中分析光谱。
d sin θ = n λ (n = 0, 1, 2, …)
10. Polarization of Light | 光的偏振
Polarization confirms that light is a transverse wave. Unpolarized light vibrates in all directions perpendicular to the direction of travel. A polarizing filter transmits only the component of the electric field along its transmission axis, producing plane-polarized light.
偏振证实了光是一种横波。非偏振光的振动方向在垂直于传播方向的各个方向上均有分布。偏振片只允许沿其透振轴方向的电场分量通过，从而产生平面偏振光。
Malus’s law states that when completely plane-polarized light of intensity I₀ passes through a second polarizer (analyser) whose axis makes an angle θ with the transmission axis of the first, the transmitted intensity is I = I₀ cos² θ.
马吕斯定律指出，强度为 I₀ 的完全平面偏振光通过第二个偏振器（检偏器）时，如果两透振轴夹角为 θ，则透射光强为 I = I₀ cos² θ。
I = I₀ cos² θ
Polarization by reflection occurs at a special angle known as Brewster’s angle, where reflected light is completely polarized parallel to the surface. Brewster’s angle θB satisfies tan θB = n, where n is the refractive index of the reflecting medium.
反射偏振发生在布儒斯特角这一特殊角度，此时反射光完全偏振，偏振方向平行于表面。布儒斯特角 θB 满足 tan θB = n，n 为反射介质的折射率。
tan θB = n
11. Electromagnetic Spectrum | 电磁波谱
Light is only a small part of the electromagnetic (EM) spectrum. The spectrum, in order of increasing frequency (decreasing wavelength), includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. All EM waves travel at speed c in a vacuum.
光只是电磁波谱的一小部分。按频率递增（波长递减）的顺序，电磁波谱包括无线电波、微波、红外线、可见光、紫外线、X 射线和伽马射线。所有电磁波在真空中均以光速 c 传播。
Visible light ranges from approximately 400 nm (violet) to 700 nm (red). Higher-frequency ultraviolet is responsible for fluorescence and skin damage, while X-rays penetrate soft tissue but are absorbed by bones.
可见光的波长范围约从 400 nm（紫光）到 700 nm（红光）。频率更高的紫外线可引起荧光并损伤皮肤，而 X 射线能穿透软组织但被骨骼吸收。
The relationship c = f λ applies to all regions. Different wavelengths interact with matter in distinct ways, leading to diverse applications such as communication, thermal imaging, and medical diagnostics.
关系式 c = f λ 适用于所有波段。不同波长与物质的相互作用方式各不相同，由此产生了通信、热成像和医学诊断等多种应用。
12. Exam Tips and Common Pitfalls | 考试提示与常见误区
In both IB and CIE papers, you must be able to draw and label ray diagrams accurately for lenses and mirrors, using a ruler. Always mark the normal and show angles correctly. For wave phenomena, remember to state which formula applies and define all symbols.
在 IB 和 CIE 考卷中，你必须能用尺规准确绘制并标注透镜和镜子的光线图。务必画出法线并正确标示角度。对于波动现象，记得写出适用的公式并定义所有符号。
A common mistake is confusing the conditions for maxima in a double-slit and a diffraction grating. Double slits give evenly spaced fringes; a grating produces much sharper, brighter maxima. Also, note that single-slit diffraction makes the pattern envelope visible in a double-slit setup.
一个常见错误是混淆双缝和光栅的亮纹条件。双缝产生均匀间隔的条纹；光栅产生的亮纹则更尖锐、更明亮。此外，注意在双缝装置中，单缝衍射会造成条纹包络。
When solving numerical problems, check units: convert all lengths to metres and use consistent SI units. For lens calculations, apply the correct sign convention throughout. And always consider whether approximations (such as small-angle approximations) are valid in the context.
在解答计算题时，检查单位：将所有长度换算为米并使用一致的 SI 单位。透镜计算中要始终贯彻正确的符号法则。还要随时考虑近似条件（如小角度近似）在情境中是否成立。
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