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Light is electromagnetic radiation!

Light is electromagnetic radiation!. = Electric Field = Magnetic Field Assume linear, isotropic, homogeneous media. Maxwell’s Equations. Published by J.C. Maxwell in 1861 in the paper “On Physical Lines of Force”. Unite classical electricity and magnetism.

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Light is electromagnetic radiation!

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  1. Light is electromagnetic radiation! • = Electric Field • = Magnetic Field • Assume linear, isotropic, homogeneous media. PHY 530 -- Lecture 01

  2. Maxwell’s Equations • Published by J.C. Maxwell in 1861 in the paper “On Physical Lines of Force”. • Unite classical electricity and magnetism. • Predict the propagation of electromagnetic energy away from time varying sources (current and charge) in the form of waves. PHY 530 -- Lecture 01

  3. Maxwell’s Equations • Four partial differential equations involving E, B that govern ALL electromagnetic phenomena. • Gauss’s Law (elec, mag) • Faraday’s Law, Ampere’s Law PHY 530 -- Lecture 01

  4. Gauss’s Law (elec) Charge density Electric permittivity constant of medium E dS= q Total charge enclosed dS– outward normal Electric charges give rise to electric fields. PHY 530 -- Lecture 01

  5. Gauss’s Law (mag) B  dS = 0 No Magnetic Monopoles! PHY 530 -- Lecture 01

  6. Faraday’s Law where: = mag. flux A changing B field gives rise to an Efield E field lines close on themselves (form loops) PHY 530 -- Lecture 01

  7. Ampere’s Law Where: Magnetic permeability of medium If Econst in time: Electric current j = current density Electric currents give rise to B fields. PHY 530 -- Lecture 01

  8. What Maxwell’s Equations Imply In the absence of sources, all components of E, B satisfy the same (homogeneous) equation: The properties of an e.m. wave (direction of propagation, velocity of propagation, wavelength, frequency) can be determined by examining the solutions to the wave equation. PHY 530 -- Lecture 01

  9. What does it mean to satisfy the wave equation? Imagine a disturbance traveling along the x coordinate (1-dim case). PHY 530 -- Lecture 01

  10. What does a wave look like mathematically? General expression for waves traveling in +ve, -ve directions: Argument affects the translation of wave shape. is the velocity of propagation. PHY 530 -- Lecture 01

  11. Waves satisfy the wave equation • Try it for f! Use the chain rule, differentiate: • This is the (homogeneous) 1-dim wave equation. PHY 530 -- Lecture 01

  12. E, B satisfy the 3-dim wave equation!! can be and PHY 530 -- Lecture 01

  13. Index of Refraction (1) Okay, Velocity of light in a medium dependent on medium’s electric, magnetic properties. In free space: PHY 530 -- Lecture 01

  14. Index of Refraction (2) For any l.i.h. medium, define index of refraction as: NOTE: dimensionless. PHY 530 -- Lecture 01

  15. Index of Refraction (3) PHY 530 -- Lecture 01

  16. Plane waves Back to the 3-dim wave equation, but assume has constant value on planes: PHY 530 -- Lecture 01

  17. Seek solution to wave eqn Solving PDEs is hard, so assume solution of the form: (so-called “separable” solution…) Now, Becomes: PHY 530 -- Lecture 01

  18. Voilà! Two ordinary differential equations! Note! and PHY 530 -- Lecture 01

  19. We know the solutions to these... where . (Sines and cosines!) PHY 530 -- Lecture 01

  20. How to build a wave Choose w positive, +ve z dir, then have Any linear combination of solutions of this form is also a solution. Start with sines and cosines, make whatever shape like. PHY 530 -- Lecture 01

  21. Let’s get physical Sufficient to study Harmonic wave kz-ωt - phase (radians) ω - angular frequency k – propagation number/vector wavelength frequency PHY 530 -- Lecture 01

  22. 3-D wave equation Solution: Reduces to the 1-D case when PHY 530 -- Lecture 01

  23. Back to Plane Waves Assume we have (plane waves in the z-direction, E0 a constant vector) , Similar equations for B. PHY 530 -- Lecture 01

  24. Electromagnetic Waves are Transverse Differentiate first equation of previous slide, can show then using Maxwell’s equations that: Try it! PHY 530 -- Lecture 01

  25. EM Waves are Transverse (2) This implies: Fields must be perpendicular to the propagation direction! PHY 530 -- Lecture 01

  26. EM Waves are Transverse (3) Also, fields are in phase in the absence of sources and E is perpendicular to B since E k B PHY 530 -- Lecture 01

  27. What light looks like close up Moving charge(s) Electric Field Waves + The Electric and Magnetic components of light are perpendicular (in vacuum). Waves propagate with speed 3x108 m/s. Magnetic Field Waves PHY 530 -- Lecture 01

  28. The Poynting Vector S is parallel to the propagation direction. In free space, S gives us the energy transport of waveform. Energy/time/area I = <|S|>time=1/2(c ε0) E02 - irradiance (time average of the magnitude of the Poynting vector) PHY 530 -- Lecture 01

  29. The Electromagnetic Spectrum PHY 530 -- Lecture 01

  30. The Electromagnetic Spectrum PHY 530 -- Lecture 01

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