📚 Other types of interference | 其他类型的干涉
Interference is a fundamental wave phenomenon that occurs when two or more coherent waves superpose. While Young's double-slit experiment is the classic demonstration of interference by division of wavefront, there exists a rich variety of interference setups that rely on division of amplitude or involve multiple slits. These other types of interference not only deepen our understanding of wave optics but also lead to practical applications in measurement, spectroscopy, and optical coatings. In this article, we explore thin film interference, Newton's rings, multiple-slit diffraction gratings, and the Michelson interferometer, all of which are key topics in IB Physics.
干涉是当两个或多个相干波叠加时发生的一种基本波动现象。虽然杨氏双缝实验是通过波前分割进行干涉的经典演示，但还存在多种依赖于振幅分割或多缝的干涉装置。这些其他类型的干涉不仅加深了我们对波动光学的理解，还在测量、光谱学和光学涂层等领域有实际应用。本文我们将探讨薄膜干涉、牛顿环、多缝衍射光栅和迈克尔逊干涉仪，这些均为IB物理的核心内容。
1. Division of amplitude versus division of wavefront | 振幅分割与波前分割
Interference devices can be classified by how they produce the two or more coherent sources. In division of wavefront, as in Young's experiment, different portions of the same primary wavefront are selected by slits to act as sources. In division of amplitude, the incident wave is partially reflected and partially transmitted at a surface, and the two resulting beams travel different paths before recombining. Thin films, Newton's rings, and the Michelson interferometer all use amplitude division, which often allows for larger path differences and versatile interferometry.
干涉装置可以根据它们如何产生两个或更多相干光源进行分类。在波前分割中，例如杨氏实验，通过狭缝选择同一初级波前的不同部分作为光源。在振幅分割中，入射波在表面被部分反射和部分透射，产生的两束光沿不同路径传播后重新合并。薄膜干涉、牛顿环和迈克尔逊干涉仪都采用振幅分割，这通常允许更大的光程差和更灵活的干涉测量。
2. Thin film interference: basic principle | 薄膜干涉：基本原理
When light reflects off the top and bottom surfaces of a thin transparent film, the two reflected waves can interfere. The optical path difference between them depends on the film thickness t, its refractive index n, and the angle of refraction θ inside the film. In near-normal incidence, the extra distance travelled by the wave reflected from the bottom surface is approximately 2nt. An additional phase change of π (equivalent to a half‑wavelength shift) occurs if reflection takes place at a boundary from a medium of lower to higher refractive index.
当光线在透明薄膜的上表面和下表面反射时，两束反射光可以发生干涉。它们之间的光程差取决于膜厚 t、膜的折射率 n 以及膜内的折射角 θ。在接近正入射的情况下，从下表面反射的光多走的路程约为 2nt。如果反射发生在从低折射率介质到高折射率介质的界面时，还会产生 π 的相位突变（相当于半个波长的位移）。
3. Phase changes and conditions for constructive interference | 相位变化与相长干涉条件
Because of possible half‑wave losses at interfaces, the net effective path difference must account for any phase reversals. For a film in air (nfilm > 1), the top reflection from air to film undergoes a π phase change, while the bottom reflection from film to air has no phase change. This introduces an extra optical path difference of λ/2. Thus, for normal incidence, constructive interference in reflected light occurs when
由于界面处可能发生半波损失，净有效光程差必须计入任何相位反转。对于空气−薄膜−空气的情况（n_膜 > 1），从空气到膜的上表面反射产生 π 相变，而从膜到空气的下表面反射则无相位突变。这会引入额外的 λ/2 光程差。因此，正入射时，反射光相长干涉的条件为
2 n t = (m + ½) λ, m = 0, 1, 2, …
而反射光相消干涉的条件为
2 n t = m λ, m = 0, 1, 2, …
If the film is on a substrate with an even higher refractive index, the phase conditions may be reversed.
如果薄膜位于折射率更高的基底上，相位条件可能会反转。
4. Soap bubbles and oil slicks | 肥皂泡与油膜
A soap film in air appears coloured because the thickness varies, and each thickness reinforces a different wavelength under white‑light illumination. Where the film is extremely thin (t << λ), the path difference is dominated by the half‑wave loss, leading to destructive interference in reflection – the film looks black. An oil slick on water shows similar colour variations because the oil layer acts as a thin film with varying thickness, producing colourful interference fringes.
空气中的肥皂泡呈现彩色，是因为膜厚度变化，在白光照射下，每种厚度增强不同波长。当薄膜极薄（t << λ）时，光程差主要由半波损失决定，反射光发生相消干涉——薄膜看起来是黑的。水上的油膜也展现出类似的色彩变化，这是由于油层充当了厚度变化的薄膜，产生了彩色的干涉条纹。
5. Newton's rings: a special case of thin film interference | 牛顿环：薄膜干涉的特例
Newton's rings are formed when a plano‑convex lens of large radius of curvature is placed on a flat glass plate. The air film between the lens and the plate has a variable thickness that increases with radial distance from the centre. In reflected monochromatic light, a pattern of concentric bright and dark rings is observed. For an air film, the conditions are reversed relative to a free‑standing film because the bottom reflection (glass to air) involves a phase change. The radius of the m‑th dark ring in reflection is given by
牛顿环是大曲率半径的平凸透镜放在平面玻璃板上时形成的。透镜与平板之间的空气膜厚度随离中心的径向距离增加而变化。在单色反射光中观察到同心明暗环。对于空气膜，干涉条件相对于自由薄膜发生反转，因为底部反射（玻璃到空气）涉及相位突变。反射光中第 m 级暗环的半径由下式给出
rm² = m λ R, m = 0, 1, 2, …
其中 R 是透镜的曲率半径。中央为暗斑，证实了半波损失的相位反转。牛顿环可用于测量波长或检测非常小的厚度变化。
6. Multiple-slit interference: the diffraction grating | 多缝干涉：衍射光栅
When a large number of equally spaced slits are illuminated coherently, the interference pattern becomes much sharper than that from a double slit. Each slit acts as a secondary source, and the superposition of many waves results in principal maxima at angles satisfying the grating equation
当大量等间距的狭缝被相干光照射时，干涉图样比双缝的锐利得多。每条狭缝作为次级光源，大量波的叠加在主极大方向满足光栅方程
d sin θ = n λ, n = 0, ±1, ±2, …
where d is the slit separation (grating spacing) and n is the order number. Between these sharply defined maxima, very weak secondary maxima exist, but they become negligible as the number of slits increases.
其中 d 为狭缝间距（光栅常数），n 为级次。在这些锐利的主极大之间，存在非常弱的次极大，但随着狭缝数增多可以忽略不计。
7. Spectral dispersion and resolving power | 光谱色散与分辨本领
ng power R = λ/Δλ = nN, where N is the total number of illuminated slits, quantifies the ability to separate two close wavelengths. This makes gratings essential in spectrometers for analysing atomic spectra.
衍射光栅将白光分解为组成波长，因为每种颜色在稍微不同的角度满足光栅方程。角色散 dθ/dλ = n/(d cos θ) 表明较高级次和较小的光栅常数会使光谱更展宽。分辨本领 R = λ/Δλ = nN，其中 N 是总照明狭缝数，量化了分离两个相近波长的能力。这使得光栅在光谱仪中用于原子光谱分析时不可或缺。
8. Intensity distribution and missing orders | 强度分布与缺级
tensity for N slits is modulated by both the interference of multiple slits and the single‑ eously satisfies a sin θ = pλ (p ≠ 0), that particular order is missing because the single‑ ay between interference and diffraction is crucial for understanding real grating spectra.
多缝的强度同时受到多缝干涉和单缝衍射包络的调制。主极大的角位置仍由 d sin θ = nλ 给出，但振幅受到宽度为 a 的单缝衍射图样的限制。如果 d sin θ = nλ 同时满足 a sin θ = pλ (p ≠ 0)，该特定级次就会缺级，因为单缝包络在该处为零。干涉与衍射的这种相互作用对于理解实际光栅光谱至关重要。
9. The Michelson interferometer: division of amplitude in action | 迈克尔逊干涉仪：振幅分割的实际应用
h difference changes by 2Δx. Shifting the mirror by λ/2 causes one fringe shift. Counting ΔN fringes passing a reference point allows measurement of the mirror displacement using Δx = ΔN · λ/2.
迈克尔逊干涉仪利用分束器将一束光分成两路相互垂直的光，经反射镜反射后重新合并。补偿板确保两臂中的玻璃光程相同。当可动镜平移距离 Δx 时，光程差改变 2Δx。移动镜移动 λ/2 产生一个条纹移动。数出经过参考点的条纹数目 ΔN，即可利用 Δx = ΔN · λ/2 测量镜的位移。
10. White light fringes and precise measurements | 白光条纹与精密测量
With a monochromatic source, the circular fringes are equally sharp for large path differences, but with white light, fringes are only visible when the two arms have nearly equal optical paths. The zero‑order fringe is unique and appears as a central dark or bright fringe, allowing the identification of zero path difference. This feature is used to calibrate the interferometer and to measure thin film thicknesses or small refractive index changes by comparing the shift of white‑light fringes.
使用单色光源时，对于较大的光程差，圆条纹同样清晰；但使用白光时，仅当两臂光程几乎相等时条纹才可见。零级条纹是独特的，表现为中央暗或亮的条纹，可用来识别零光程差。这一特性用于校准干涉仪，以及通过比较白光条纹的移动来测量薄膜厚度或微小的折射率变化。
11. Coherence requirements in amplitude‑division interferometers | 振幅分割干涉仪中的相干性要求
All interference phenomena rely on coherence – ngth (e.g. a laser). White light has a very short coherence length (≈ 1 μm), so fringes occur only near zero path difference. Understanding these constraints is essential when designing or interpreting interferometric experiments described in the IB Physics syllabus.
所有干涉现象都依赖于相干性——时间相干性和空间相干性。在薄膜干涉中，为了看到可见条纹，膜厚必须小于光的相干长度。在迈克尔逊干涉仪中，两束光必须保持稳定的相位关系；较大的光程差要求光源具有较长的相干长度（如激光）。白光的相干长度非常短（约 1 μm），因此条纹只在零光程差附近出现。在设计或解释IB物理大纲所描述的干涉实验时，理解这些限制至关重要。
12. Summary: unifying the types of interference | 总结：干涉类型的统一
Whether by division of wavefront or division of amplitude, interference produces predictable intensity variations that reveal wave properties of light. Thin films demonstrate colour‑selective reinforcement and destructive interference. Newton's rings provide a geometric method of mapping film thickness. Diffraction gratings create highly directional maxima that resolve spectral lines with outstanding precision. The Michelson interferometer turns fringe counting into a precise tool for length and refractive index metrology. Mastery of these other types of interference equips IB Physics students with a versatile problem‑solving toolkit for both examinations and practical optics.
无论是通过波前分割还是振幅分割，干涉都会产生可预测的强度变化，揭示了光的波动性。薄膜展示了颜色选择性增强和相消干涉；牛顿环提供了一种以几何方式描绘膜厚的方法；衍射光栅产生高度方向性的极大，能以出色的精度解析光谱线；迈克尔逊干涉仪将条纹计数变为长度和折射率计量学的精密工具。掌握这些其他类型的干涉，为IB物理学生提供了应对考试和实际光学的多用途问题解决工具箱。
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