wave_motion

# wave_motion - Electromagnetic Waves and Optics(overview...

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Wave motion Electromagnetic Waves and Optics 2 Electromagnetic Waves and Optics (overview) • Wave motion (partly review) • Electromagnetism and electromagnetic waves (partly review) • Scattering, reflection, refraction • Optical imaging • Electromagnetic radiation • Superposition • Interference • Diffraction • Polarization • Fourier transforms in optics (as time permits) Wave motion Electromagnetic Waves and Optics 3 What are waves? two answers: mathematical: – waves are solutions to the wave equation: ψ = wave function c = phase velocity (or “celerity”) physical: – waves transport energy (and momentum) without transporting matter 2 2 2 2 2 1 t c x = ψ Where does wave equation come from? What do solutions look like? How much energy do they carry? Look at examples: waves on stretched string ocean waves sound waves electromagnetic waves (light) •… .

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Wave motion Electromagnetic Waves and Optics 4 Physics of waves on string each small piece of string obeys Newton’s Laws: small displacement, so net force is proportional to curvature: Τ Σ F x m x x x y T F y + ) ( 2 x x y T F y ) ( 1 x x y T x x y x x x y T F y + 2 2 ) ( ) ( F 1 F 2 a m F r r = Σ θ x y = θ tan sin Wave motion Electromagnetic Waves and Optics 5 Physics of waves on string Newton’s 2nd Law. .. » (mass density μ= m / x ) ...leads to the wave equation with – wave function = transverse displacement – phase velocity 2 2 2 2 2 2 2 2 t y T x y t y m x x y T ma F y y = = = Σ µ 2 2 2 2 2 1 t c x = ψ () y t x = , T c = Å restoring force Å inertia
Wave motion Electromagnetic Waves and Optics 6 Solutions of wave equation travelling waves: – harmonic travelling waves: linear combinations of travelling waves – e.g., standing waves, beats, interference,… – Fourier theorem: any function as weighted sum of sinusoids ) ( ) ( ct x f ct x f + = = ψ [ ] ) ( cos ct x k A = () ( ) L + + + = ct x bg ct x af Wave motion Electromagnetic Waves and Optics 8 Solutions of wave equation

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wave_motion - Electromagnetic Waves and Optics(overview...

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