https://teddyrookbook.com/physics/waves-optics-modern-physics/Recent content in Waves, Optics and Modern Physics on Teddy Rook Bookhttps://teddyrookbook.com/img/share.jpghttps://teddyrookbook.com/img/share.jpgHugoenhttps://teddyrookbook.com/physics/waves-optics-modern-physics/wave-function/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/wave-function/A sinusoidal wave is y = A sin(kx − ωt), with k = 2π/λ, ω = 2πf and speed v = ω/k. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/wave-equation/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/wave-equation/Any shape moving at speed v satisfies ∂²y/∂x² = (1/v²)·∂²y/∂t². Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/wave-power/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/wave-power/A wave on a string carries power P = ½μω²A²v, so doubling the amplitude carries four times the power. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/phase-interference/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/phase-interference/Two equal waves with phase difference φ add to amplitude 2A cos(φ/2), and a path difference Δr gives φ = 2πΔr/λ. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/standing-wave-math/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/standing-wave-math/Two opposite traveling waves add to y = 2A sin kx cos ωt, with nodes that never move. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/sound-waves/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/sound-waves/Sound is a pressure wave moving at v = √(B/ρ); pressure nodes sit where the displacement swings most. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/beats/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/beats/Two tones of nearly equal frequency throb at the beat frequency |f₁ − f₂|. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/shock-waves/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/shock-waves/A source faster than sound drags a cone of wavefronts with sin θ = v_sound/v_source. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/huygens-principle/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/huygens-principle/Every point on a wavefront acts as a source of wavelets, which explains refraction and diffraction. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/brewster-angle/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/brewster-angle/Light reflected at Brewster's angle, tan θ_B = n₂/n₁, is completely polarized. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/two-slit-intensity/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/two-slit-intensity/Two slits give I = I₀cos²(πd sin θ/λ), and more slits make sharper bright lines. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/diffraction-envelope/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/diffraction-envelope/A single slit's pattern sets the envelope of a double-slit pattern, and some bright orders vanish. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/resolution/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/resolution/Two points can just be told apart when their angular separation is θ = 1.22λ/D. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/michelson-interferometer/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/michelson-interferometer/Moving one mirror a distance λ/2 shifts the pattern by one whole fringe. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/thin-film-design/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/thin-film-design/A quarter-wave coating cancels a reflection, and counting fringes in an air wedge measures tiny thicknesses. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/bragg-diffraction/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/bragg-diffraction/Crystal planes a distance d apart reflect X-rays strongly when 2d sin θ = mλ. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/lensmaker/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/lensmaker/A lens's focal length comes from its shape and material: 1/f = (n − 1)(1/R₁ − 1/R₂). Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/two-lens-systems/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/two-lens-systems/The image made by the first lens is the object for the second, and the magnifications multiply. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/eye-and-glasses/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/eye-and-glasses/A lens's power is P = 1/f in diopters; nearsighted eyes need diverging lenses and farsighted eyes converging ones. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/microscopes/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/microscopes/A magnifier gives M = 25 cm/f, and a microscope multiplies the objective's magnification by the eyepiece's. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/telescope-optics/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/telescope-optics/A refracting telescope magnifies by M = −f_objective/f_eyepiece, and its aperture sets how faint and how fine it can see. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/relativity-postulates/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/relativity-postulates/The laws of physics and the speed of light are the same in every inertial frame. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/simultaneity/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/simultaneity/Two events at the same time in one frame can happen at different times in another. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/time-dilation/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/time-dilation/A moving clock runs slow: Δt = γΔτ, with γ = 1/√(1 − v²/c²). Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/length-contraction/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/length-contraction/A moving object is shorter along its motion: L = L₀/γ. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/lorentz-transformation/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/lorentz-transformation/x′ = γ(x − vt) and t′ = γ(t − vx/c²) convert events between frames. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/spacetime-interval/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/spacetime-interval/The interval s² = (cΔt)² − Δx² is the same for every observer. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/velocity-addition/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/velocity-addition/Velocities combine as u′ = (u − v)/(1 − uv/c²), so no speed passes c. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/relativistic-doppler/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/relativistic-doppler/Light from an approaching source arrives at f = f₀√((1 + β)/(1 − β)), with β = v/c. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/relativistic-energy/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/relativistic-energy/p = γmu and E = γmc², linked by E² = (pc)² + (mc²)². Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/planck-blackbody/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/planck-blackbody/Planck's quantized energies explain the blackbody spectrum, and Wien's and Stefan's laws follow from it. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/compton-formula/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/compton-formula/Conserving energy and momentum gives Δλ = (h/mc)(1 − cos θ). Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/bohr-hydrogen/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/bohr-hydrogen/Quantized angular momentum gives E_n = −13.6 eV/n² and r_n = n²a₀. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/hydrogen-series/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/hydrogen-series/Lyman, Balmer and Paschen lines follow 1/λ = R(1/n_f² − 1/n_i²). Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/uncertainty-principle/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/uncertainty-principle/Δx·Δp ≥ ħ/2: the more sharply a position is fixed, the more spread its momentum must have. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/wavefunction-probability/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/wavefunction-probability/|ψ|² is a probability density, normalized so the total probability is 1. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/schrodinger-equation/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/schrodinger-equation/−(ħ²/2m)ψ″ + Uψ = Eψ: check whether a function solves it and read off its energy. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/particle-in-box/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/particle-in-box/Confining a particle to a length L allows only E_n = n²h²/(8mL²). Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/tunneling/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/tunneling/Wave functions leak into barriers, so a particle can tunnel through one with probability about e^(−2κL). Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/quantum-oscillator/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/quantum-oscillator/The energies are evenly spaced, E_n = (n + ½)ħω, starting from a nonzero zero-point energy. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/quantum-numbers/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/quantum-numbers/The labels n, l, m_l and m_s name each state, and shell n holds 2n² states. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/exclusion-principle/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/exclusion-principle/No two electrons in an atom share all four quantum numbers, which builds the periodic table. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/band-theory/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/band-theory/Energy bands and the gaps between them decide how a solid conducts, and doping and LEDs follow from them. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/nuclear-binding/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/nuclear-binding/Nuclei have radius R = r₀A^(1/3), and the binding energy per nucleon peaks near iron. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/decay-law/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/decay-law/N = N₀e^(−λt), the activity is A = λN, and the half-life is ln 2/λ. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/q-values/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/q-values/Q = (mass before − mass after)c², at 931.5 MeV for each atomic mass unit. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/radioactive-dating/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/radioactive-dating/The fraction of a parent isotope left gives an age: t = (T½/ln 2)·ln(N₀/N). Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/particle-families/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/particle-families/Leptons are fundamental, baryons hold three quarks and mesons a quark and an antiquark. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/antimatter/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/antimatter/Making an electron–positron pair takes at least 2mc², and annihilation turns the pair back into gamma rays. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/conservation-laws-particles/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/conservation-laws-particles/Charge, baryon number and lepton number decide which reactions can happen. Waves, Optics and Modern Physics · Physics Ladderhttps://teddyrookbook.com/physics/waves-optics-modern-physics/fundamental-forces/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/physics/waves-optics-modern-physics/fundamental-forces/Gravity, electromagnetism and the weak and strong forces; the last three are carried by photons, W and Z bosons and gluons. Waves, Optics and Modern Physics · Physics Ladder