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光学·几何/波动/仪器
12
engines
球面镜成像(凹面镜 / 凸面镜)
Spherical mirrors — concave & convex
1/f=1/do+1/di · m=−di/do · f=R/2 · 实/虚像光路
Ray diagrams from the mirror equation 1/f = 1/dₒ + 1/dᵢ and m = −dᵢ/dₒ
磨镜者公式(薄透镜焦距)
Lensmaker's equation — thin-lens focal length
1/f=(n−1)(1/R1−1/R2) · 曲率+折射率→焦距
How the surface radii and index set the focal length: 1/f = (n−1)(1/R₁ − 1/R₂)
凹透镜成像(发散透镜)
Diverging (concave) lens imaging
凹透镜恒正立缩小虚像 · 三主光线 · f<0
A diverging lens (f<0): always an upright, reduced, virtual image, at any object distance
三棱镜色散
Prism dispersion
δ=θi+θe−A · 最小偏向角 · n(λ)白光分光
Deviation, minimum deviation, and dispersion from index varying with wavelength
单缝夫琅禾费衍射
Single-slit Fraunhofer diffraction
a·sinθ=mλ极小 · 中央加倍 · sinc²强度包络
Minima at a·sinθ = mλ, a central maximum twice as wide, intensity I/I0 = (sin β / β)²
瑞利判据与衍射极限
Rayleigh criterion & the diffraction limit
θ=1.22λ/D衍射极限 · 艾里斑 · 两点可分辨
Airy disk from a circular aperture, θ = 1.22·λ/D, two points just resolved
迈克耳孙干涉仪
Michelson interferometer
双臂程差2Δd · ΔN=2Δd/λ · 测波长/位移
Move one mirror by Δd: the path difference changes by 2Δd and the fringes shift by ΔN = 2Δd/λ
牛顿环
Newton's rings
空气膜干涉 · 暗环r=√(mλR) · r∝√m
Thin-air-gap interference under a plano-convex lens: dark rings r = √(mλR), bright rings r = √((m+½)λR)
法布里-珀罗标准具
Fabry–Pérot etalon
多光束干涉 · FSR=λ²/2nd · 精细度F=π√r/(1−r)
Multi-beam interference between two parallel mirrors: FSR = λ²/(2nd), finesse 𝓕 = π√r/(1−r)
光纤数值孔径(NA)与全反射导光
Optical-fibre numerical aperture (NA) & TIR guiding
NA=√(n_core²−n_clad²) · 接收锥角 · 全反射导光
From core / cladding indices to numerical aperture, acceptance angle and V-number, with the acceptance cone and guided ray
复式显微镜放大率与光路
Compound microscope magnification & ray path
M=(L/fo)(25/fe)=物镜×目镜 · 两透镜光路
Total magnification M = objective × eyepiece = (L / fo) × (25 cm / fe)
开普勒(折射)望远镜角放大率与光路
Refracting (Keplerian) telescope magnification & ray path
开普勒式M=fo/fe · 物镜+目镜 · 筒长≈fo+fe
Angular magnification M = fo / fe; tube length ≈ fo + fe; distant object re-collimated after a real inverted image