📚 Wave Phenomena: Diffraction, Refraction and Polarization | 波现象：衍射、折射与偏振
Waves transfer energy and information without transporting matter. Understanding how waves behave when they encounter obstacles, boundaries, and filters is essential for mastering IB Physics.
波传递能量和信息，但并不传输物质。理解波在遇到障碍物、边界和过滤器时如何表现，是掌握IB物理的关键。
1. Nature of Waves | 波的本质
Waves can be classified as mechanical or electromagnetic, and as transverse or longitudinal. In a transverse wave, oscillations are perpendicular to the direction of energy transfer; in a longitudinal wave, they are parallel.
波可分为机械波和电磁波，也可分为横波和纵波。在横波中，振动方向垂直于能量传递方向；在纵波中，振动方向与能量传递方向平行。
All waves exhibit reflection, refraction, diffraction, and interference. Polarization, however, is a property unique to transverse waves.
所有波都会表现出反射、折射、衍射和干涉。然而，偏振是横波独有的性质。
2. Huygens’ Principle | 惠更斯原理
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 after a given time.
惠更斯原理指出：波前上的每一点都可以看作一个新的子波源，发出球面次波。经过一段时间后，这些子波的包络面就是新的波前。
This principle explains why waves spread into the geometric shadow region when passing through a slit or around an obstacle, which is the basis of diffraction.
这一原理解释了为什么波通过狭缝或绕过障碍物时会扩散到几何阴影区，这就是衍射的基础。
3. Diffraction | 衍射
Diffraction is the bending of waves around obstacles or through apertures. The amount of spreading depends on the ratio of the wavelength λ to the size of the obstacle or slit a.
衍射是波绕过障碍物或通过孔隙时发生的弯曲现象。扩散程度取决于波长λ与障碍物或狭缝尺寸a的比值。
When a is much larger than λ, diffraction is negligible. When a is comparable to λ, significant spreading occurs. When a is smaller than λ, the wave spreads almost spherically.
当a远大于λ时，衍射可忽略不计；当a与λ相近时，会发生明显的扩散；当a小于λ时，波几乎以球面波的方式向外扩散。
4. Single-Slit Diffraction | 单缝衍射
For a single slit of width a, the first minimum in the diffraction pattern occurs at an angle θ satisfying:
对于宽度为a的单缝，衍射图样中第一级暗纹出现在满足下式的角度θ处：
a sin θ = mλ (m = 1, 2, 3, …)
The central maximum is twice as wide as the secondary maxima, and its intensity is much greater. The intensity decreases rapidly for higher-order fringes.
中央亮纹的宽度是次级亮纹的两倍，且强度远大于次级亮纹。更高阶条纹的强度会迅速减弱。
In IB Physics, you should remember that the central maximum becomes wider and less bright as the slit width decreases.
在IB物理中，你应当记住：随着缝宽减小，中央亮纹会变得更宽、更暗。
5. Interference and Diffraction Combined | 干涉与衍射的结合
In a double-slit experiment, the interference pattern is modulated by the single-slit diffraction envelope. The overall intensity is the product of the diffraction factor and the interference factor.
在双缝实验中，干涉图样会受到单缝衍射包络的调制。总强度是衍射因子与干涉因子的乘积。
The condition for bright fringes from double-slit interference is d sin θ = nλ, where d is the slit separation. However, if a minimum of the diffraction envelope coincides with a bright interference fringe, that fringe disappears.
双缝干涉明纹的条件是d sin θ = nλ，其中d是双缝间距。然而，如果衍射包络的暗纹与某个干涉明纹重合，该明纹就会消失。
6. Refraction and Snell’s Law | 折射与斯涅耳定律
Refraction is the change in direction of a wave as it passes from one medium to another due to a change in speed. The frequency remains constant, while wavelength and speed change.
折射是波因速度改变而在进入另一种介质时方向发生变化的现象。波的频率保持不变，而波长和速度会发生改变。
Snell’s law relates the angles of incidence and refraction to the refractive indices of the media:
斯涅耳定律将入射角、折射角与介质的折射率联系起来：
n₁ sin θ₁ = n₂ sin θ₂
Here n = c / v, where c is the speed of light in vacuum and v is the speed in the medium. A larger refractive index means a smaller wave speed.
其中n = c / v，c是真空中的光速，v是介质中的光速。折射率越大，波速越小。
7. Total Internal Reflection | 全内反射
When light travels from a denser medium to a rarer medium, the refracted ray bends away from the normal. If the angle of incidence exceeds the critical angle, no refraction occurs — all light is reflected internally.
当光从光密介质射向光疏介质时，折射光线会偏离法线。如果入射角超过临界角，则不再发生折射——所有光都在介质内部被反射。
The critical angle θc is given by:
临界角θc由下式给出：
sin θc = n₂ / n₁ (n₁ > n₂)
This principle is used in optical fibres, where light is trapped inside a core by repeated total internal reflections.
这一原理应用于光纤中，光通过反复的全内反射被限制在纤芯内部传播。
8. Dispersion | 色散
Dispersion occurs when the refractive index of a medium depends on the frequency of the wave. As a result, different colours of white light are refracted by different amounts.
当介质的折射率取决于波的频率时，就会发生色散。因此，白光中的不同颜色会被折射到不同程度。
In a glass prism, violet light is deviated more than red light because violet has a higher frequency and therefore a larger refractive index in glass.
在三棱镜中，紫光比红光偏折得更多，因为紫光频率更高，在玻璃中的折射率也更大。
9. Polarization | 偏振
Polarization is the restriction of oscillations of a transverse wave to one plane. Longitudinal waves cannot be polarized because their oscillations are along the direction of propagation.
偏振是将横波的振动限制在单一平面内的现象。纵波不能发生偏振，因为其振动方向与传播方向相同。
An unpolarized wave has oscillations in all directions perpendicular to propagation. A polarizer transmits only the component of the wave oscillating parallel to its transmission axis.
非偏振波的振动方向在垂直于传播方向的平面内各方向都有。偏振片只允许振动方向与其透振方向平行的分量通过。
10. Malus’s Law | 马吕斯定律
When linearly polarized light passes through a second polarizer (analyzer) at an angle θ to the first polarizer, the transmitted intensity is given by Malus’s law:
当线偏振光通过第二个偏振片（检偏器）时，若其透振方向与第一个偏振片成θ角，透射强度由马吕斯定律给出：
I = I₀ cos²θ
When θ = 90°, I = 0 and the light is completely blocked. When θ = 0°, I = I₀ and all light passes.
当θ = 90°时，I = 0，光被完全阻挡；当θ = 0°时，I = I₀，光全部通过。
11. Brewster’s Angle | 布儒斯特角
When light reflects off a surface, the reflected light is partially or fully polarized. At Brewster’s angle θB, the reflected and refracted rays are perpendicular to each other, and the reflected light is completely polarized.
当光在表面反射时，反射光会部分或完全偏振。在布儒斯特角θB处，反射光线与折射光线互相垂直，反射光为完全偏振光。
Brewster’s law is expressed as:
布儒斯特定律表示为：
tan θB = n₂ / n₁
This principle explains why glare from water or roads is polarized horizontally, which is why polarized sunglasses often block horizontal light.
这一原理解释了为什么水面或路面产生的眩光是水平偏振的，因此偏光太阳镜通常阻挡水平方向的光。
12. Applications and Exam Tips | 应用与考试提示
Diffraction gratings are used in spectrometers to measure wavelengths precisely. Optical fibres rely on total internal reflection. Polarization is used in 3D cinema, LCD screens, and stress analysis in materials.
衍射光栅用于光谱仪中精确测量波长；光纤依赖全内反射；偏振应用于3D电影、液晶屏幕和材料应力分析。
In exams, always identify whether a wave is transverse or longitudinal, and remember that only transverse waves exhibit polarization. For diffraction, state the condition a ≈ λ or a < λ for noticeable spreading.
在考试中，务必判断波是横波还是纵波，并记住只有横波才能发生偏振。对于衍射，要说明明显的扩展需要满足a ≈ λ或a < λ的条件。
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