📚 IB Physics: Diffraction of Light Key Points | IB 物理：光的衍射考点精讲
Diffraction is a fundamental wave phenomenon that occurs when a wave encounters an obstacle or a slit. It explains how light can bend around corners and spread out after passing through narrow openings. In IB Physics, understanding diffraction is crucial for explaining interference patterns, the behaviour of gratings, and the resolution limits of optical instruments.
衍射是一种基本的波动现象，发生在波遇到障碍物或狭缝时。它解释了光如何绕弯传播，并在通过窄缝后扩散开来。在IB物理中，理解衍射对于解释干涉图样、光栅行为以及光学仪器的分辨率极限至关重要。
1. What is Diffraction? | 什么是衍射？
Diffraction refers to the spreading of waves as they pass through an aperture or around an obstacle. The amount of diffraction depends on the ratio of the wavelength λ to the size of the opening or obstacle. Significant diffraction occurs when the aperture size is comparable to the wavelength.
衍射是指波通过孔径或绕过障碍物时发生的扩散现象。衍射的程度取决于波长λ与孔径或障碍物尺寸之比。当孔径大小与波长相近时，会发生明显的衍射。
2. Huygens' Principle | 惠更斯原理
Diffraction can be explained using Huygens' Principle: Every point on a wavefront acts as a source of secondary spherical wavelets. The envelope of these wavelets forms the new wavefront. When a wavefront passes through a slit, only a portion contributes, causing the wave to spread into the geometric shadow.
衍射可以用惠更斯原理解释：波前上的每一点都可以看作子波波源，发出球面次级波。这些子波的包络面形成新的波前。当波前通过狭缝时，只有一部分子波起作用，导致波扩散到几何阴影区。
3. Single-Slit Diffraction | 单缝衍射
sisting of a broad central maximum flanked by alternating dark and bright fringes of decreasing intensity. The first minimum occurs at an angle θ given by a sinθ = λ.
当单色光通过宽度为a的窄缝时，在远处的屏幕上会形成典型的衍射图样，由宽大的中央明纹和两侧交替出现的暗纹和次级明纹组成，强度递减。第一级暗纹对应的角度θ满足 a sinθ = λ。
4. Intensity Distribution for Single-Slit | 单缝衍射的强度分布
The intensity I of the single-slit diffraction pattern as a function of the phase difference β is given by the square of a sinc function. The central maximum is twice as wide as the secondary maxima, and most of the light energy is concentrated in the central bright fringe.
单缝衍射图样的强度I随相位差β变化，由sinc函数的平方给出。中央明纹的宽度是次级明纹的两倍，大部分光能量集中在中央亮纹。
I = I₀ (sinβ/β)², β = (πa sinθ)/λ
5. Single-Slit Dark Fringe Positions | 单缝暗纹位置
the central maximum. The angular width of the central maximum can be approximated by 2λ/a.
单缝衍射暗纹（极小）的条件是 a sinθ = mλ，其中 m = ±1, ±2, ±3, ... 且 m ≠ 0。注意，m = 0 对应于中央明纹。中央明纹的角宽度近似为 2λ/a。
a sinθ = mλ (m = ±1, ±2, ±3, ...)
6. Diffraction Grating | 衍射光栅
A diffraction grating consists of a large number of equally spaced parallel slits. When light passes through or reflects from a grating, the constructive interference from multiple slits produces sharp, bright principal maxima at specific angles. The grating equation relates these angles to the wavelength.
衍射光栅由大量等距平行狭缝组成。当光通过或从光栅反射时，来自多个狭缝的相长干涉在特定角度产生尖锐明亮的主极大。光栅方程将这些角度与波长联系起来。
7. The Grating Equation | 光栅方程
rder number. The zeroth order (n=0) is always at θ=0. The angular positions of bright fringes can be determined if λ and d are known.
对于缝间距为d（光栅常数）的透射光栅，主极大条件为 d sinθ = nλ，其中 n = 0, ±1, ±2, ... 为级数。零级（n=0）始终位于 θ=0。已知λ和d，可以确定亮纹的角位置。
d sinθ = nλ (n = 0, ±1, ±2, ...)
8. Resolving Power of a Grating | 光栅的分辨本领
Nn, where N is the total number of illuminated slits and n is the order. A higher number of slits and higher order increase the resolution.
衍射光栅分离两个相近波长的能力由其分辨本领 R = λ/Δλ = Nn 给出，其中 N 为被照明的狭缝总数，n 为级数。狭缝数越多、级数越高，分辨率越高。
R = λ/Δλ = Nn
9. Diffraction vs. Interference | 衍射与干涉的区别
Diffraction and interference both arise from superposition of waves. Diffraction refers to the bending of waves around obstacles and the resulting pattern from a single aperture. Interference refers to the superposition of waves from two or more separate coherent sources. In a grating, multiple-slit interference is combined with a single-slit diffraction envelope.
衍射和干涉都源于波的叠加。衍射指的是波绕过障碍物的弯曲以及由单个孔径产生的图样。干涉指的是来自两个或多个独立相干源的波叠加。在光栅中，多缝干涉与单缝衍射包络相结合。
10. Circular Aperture Diffraction and Rayleigh Criterion | 圆孔衍射与瑞利判据
When light passes through a circular aperture (like a lens or pupil), it produces a diffraction pattern with a central bright spot (Airy disk) surrounded by rings. The angular resolution of an optical instrument is limited by diffraction. According to the Rayleigh criterion, two point sources are just resolvable when the central maximum of one coincides with the first minimum of the other.
当光通过圆孔（如透镜或瞳孔）时，会产生衍射图样，中心是亮斑（艾里斑），周围是环。光学仪器的角分辨率受衍射限制。根据瑞利判据，当一点源的中央极大与另一点源的第一极小重合时，两点源刚好能被分辨。
θ = 1.22 λ/D (small angle, in radians)
For a circular aperture of diameter D, the minimum resolvable angle θ (in radians) is given by the formula above. This principle applies to telescopes, microscopes, and the human eye.
对于直径为D的圆孔，最小可分辨角θ（弧度）由上述公式给出。这一原理适用于望远镜、显微镜和人眼。
11. Applications of Diffraction | 衍射的应用
Diffraction phenomena are used in many areas: X-ray crystallography uses diffraction to determine crystal structures; the diffraction limit sets the maximum resolution of microscopes and telescopes; diffraction gratings are core components in spectrometers for analysing light spectra; holography relies on diffraction to reconstruct wavefronts.
衍射现象应用于许多领域：X射线晶体学利用衍射确定晶体结构；衍射极限决定了显微镜和望远镜的最大分辨率；衍射光栅是光谱仪中分析光谱的核心部件；全息摄影依赖衍射再现波前。
12. Typical IB Exam Questions and Tips | IB典型考题与技巧
umber of lines per mm, and applying the Rayleigh criterion to calculate the maximum resolvable distance or aperture size. Always convert units and use small-angle approximations (sinθ ≈ tanθ ≈ θ in radians) where appropriate. Be careful to distinguish between a (slit width) and d (grating spacing).
常见的IB考题包括根据单缝图样计算缝宽、利用光栅测定波长、求每毫米刻线数、以及应用瑞利判据计算最大可分辨距离或孔径大小。记得转换单位，并在合适处使用小角度近似（sinθ ≈ tanθ ≈ θ弧度）。务必分清 a（单缝宽度）和 d（光栅间距）。
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