wk5bh - So far Geometrical Optics Reflection and refraction...

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So far Geometrical Optics – Reflection and refraction from planar and spherical interfaces – Imaging condition in the paraxial approximation – Apertures & stops – Aberrations (violations of the imaging condition due to terms of order higher than paraxial or due to dispersion) Limits of validity of geometrical optics: features of interest are much bigger than the wavelength λ – Problem: point objects/images are smaller than λ !!! – So light focusing at a single point is an artifact of our approximations – To understand light behavior at scales ~ λ we need to take into account the wave nature of light. MIT 2.71/2.710 10/06/04 wk5-b-1
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Step #1 towards wave optics: electro-dynamics Electromagnetic fields (definitions and properties) in vacuo Electromagnetic fields in matter Maxwell’s equations – Integral form – Differential form – Energy flux and the Poynting vector The electromagnetic wave equation MIT 2.71/2.710 10/06/04 wk5-b-2
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Electric and magnetic forces MIT 2.71/2.710 10/06/04 wk5-b-3 + + r d l F r I q F free charges Magnetic force Coulomb force 2 0 4 1 r q q = πε F r I I l π µ 2 d d 0 = F (dielectric) permitivity of free space (magnetic) permeability of free space
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Note the units… 2 0 Distance Charge 1 force Electric = ε 2 0 4 1 r q q = πε F r I I l π µ 2 d d 0 = F 2 0 Time Charge force Magnetic = () Speed Time Distance 2 / 1 0 0 MIT 2.71/2.710 10/06/04 wk5-b-4
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Electric and magnetic fields MIT 2.71/2.710 10/06/04 wk5-b-5 + v F B E electric charge velocity Lorentz force magnetic induction electric field () B v E F × + = q Observation Generation + E static charge: electric field q v + + B electric current (moving charges): magnetic field
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Gauss Law: electric fields E + + E d a d a A V ∫∫ ∫∫∫ = AV V d 1 d 0 ρ ε a E Gauss theorem 0 = E charge density MIT 2.71/2.710 10/06/04 wk5-b-6
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Gauss Law: magnetic fields B A V there are no magnetic charges d a ∫∫ = A 0 d a B “magnetic charge” density 0 = B Gauss theorem MIT 2.71/2.710 10/06/04 wk5-b-7
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Faraday’s Law: electromotive force d l E B ( t ) (in/de)creasing C A ∫∫ = CA t l a B E d d d d Stokes theorem t = × B E MIT 2.71/2.710 10/06/04 wk5-b-8
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Ampere’s Law: magnetic induction d l B C A I MIT 2.71/2.710 10/06/04 wk5-b-9 ∫∫ ∫∫ + = CA A t l a E a J B d d d 0 0 ε µ current d l B capacitor Stokes theorem + = × t E J B 0 0 Maxwell’s extension, Displacement current current density
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Maxwell’s equations (in vacuo) ∫∫ ∫∫∫ = AV V d 1 d 0 ρ ε a E 0 = E Gauss/electric ∫∫ = A 0 d a B 0 = B Gauss/magnetic t = × B E ∫∫ = CA t l a B E d d d d Faraday + = t l a E J B d d 0 0 µ + = × t E J B 0 0 Ampere-Maxwell MIT 2.71/2.710
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This note was uploaded on 04/17/2011 for the course ME 525 taught by Professor Lucth during the Spring '11 term at Purdue University-West Lafayette.

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wk5bh - So far Geometrical Optics Reflection and refraction...

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