题型概述：波动与光学长题Question types: waves and optics long questions
Section 2 用一道长题串联推导、作图、计算和解释。本页选取 2021、2020、2019 年三题，覆盖驻波、几何光学和干涉；前两题按 25 分，2019 题按所给源文件小问分值合计 27 分。常见失分点是漏掉边界条件、混淆两类角度、忽略反射相位，以及把发射时差当作传播时差。Section 2 combines derivation, sketches, calculation and explanation in a long question. These 2021, 2020 and 2019 examples cover standing waves, geometrical optics and interference. The first two carry 25 marks; the supplied 2019 part allocations total 27. Frequent errors involve boundaries, angle conventions, reflection phases and confusing emission delays with travel delays.
1边界条件决定模态Boundaries determine modes
先判断两端是波节还是波腹，再决定能容纳多少个半波长或四分之一波长。轻触弦增加波节约束。Identify nodes and antinodes before counting half or quarter wavelengths. A light touch adds a node constraint.
fₙ = nv/(2ℓ); fclosed = (2m−1)v/[4(ℓ+ε)]波速决定传播快慢，边界条件决定允许频率。Wave speed controls propagation; boundaries select frequencies.
2路程差与相位差Path difference and phase
晶体、海面和油膜的共同问题是两条路径的相位差。先求光程差，再加入反射引入的半周期相位变化。Crystals, the sea and oil films all compare two phases. Calculate optical path difference, then include reflection phase reversals.
Δφ = 2πΔopt/λ + Δφreflection; I ∝ cos²(Δφ/2)等振幅两波的归一化强度；相位差 180° 时相消。Normalized intensity for equal amplitudes; 180° gives cancellation.
3折射、色散与小角近似Refraction, dispersion and small angles
斯涅尔定律的角从法线量；布拉格角却从晶面量。小角近似中的角必须用弧度。Snell angles are measured from the normal, whereas Bragg angles use the plane. Small-angle formulas require radians.
n₁sinθ₁ = n₂sinθ₂; δthin ≈ A(n−1); s ≈ fΔθ频率跨界面保持不变，速度与波长改变。Frequency stays fixed at an interface; speed and wavelength change.
| 子题型Sub-type | 识别特征Recognize | 核心步骤Core step | 真题Question |
|---|---|---|---|
| 驻波与传播Standing waves | fixed / closed / pulsefixed / closed / pulse | 定波节、写波速、积分时间Set nodes, speed, integrate time | 2021 Q2 |
| 棱镜与折射Prisms and refraction | deviation / refractive indexdeviation / refractive index | 法线角、斯涅尔、小角近似Normal angles, Snell, small angles | 2020 Q4 |
| 多路径干涉Multipath interference | phase / reflected / filmphase / reflected / film | 路程差加反射相位Path difference plus reflection phase | 2019 Q6 |