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Agenda

Agenda. Review from last class The Lorentz model beyond one electron Refractive index for many atoms Break-out discussion: measuring n What is the wavelength? Refractive index in gases: the Cauchy formula Light scattering. M.E.: pp. 27-39. M.E.: pp. 40-44. M.E.: pp. 49-54.

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Agenda

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  1. Agenda • Review from last class • The Lorentz model beyond one electron • Refractive index for many atoms • Break-out discussion: measuring n • What is the wavelength? • Refractive index in gases: the Cauchy formula • Light scattering M.E.: pp. 27-39 M.E.: pp. 40-44 M.E.: pp. 49-54 Aside: Pick up your PS1 at the end of class. (Median: 77%) MIDTERM: 26 October 2004 7PM-8:30PM Location: Stirling412A and 412B Final Exam: PRELIMINARY schedule – December 13, 2004 7PM Laser Optics – Phys460

  2. + 1. Review: the Lorentz model H.A. Lorentz (Nobel prize 1902) polarizability refractive index Laser Optics – Phys460

  3. Recall: Group velocity= 1. Review: n dispersion curve n Example: resonance at 300THz and Notice: 1) 2) n purely imaginary in shaded region Frequency (THz) Laser Optics – Phys460

  4. 2. Refractive index beyond one electron • Consider atom has Z electrons, each with its own resonance: • Consider many different species of atoms in sample “one electron” “Z electrons” Sum over different species Species “a” has Za electrons Laser Optics – Phys460

  5. 2. Refractive index, cont. Example: resonance at 300THz and Example: resonances at 295THz 300 THz and 305ThZ and n Frequency (THz) Laser Optics – Phys460

  6. 2. Refractive index measurement A sample that appears to be a tiny glass shred was found at a crime science. You need to identify the glass type by measuring its index of refraction. How do you do it? Break out! Laser Optics – Phys460

  7. 2. One method: Abbe refractometer light source Abbe refractometer: 1893 Abbe refractometer: 2004 Laser Optics – Phys460

  8. 2. Another method of measuring n camera Light source heater Laser Optics – Phys460

  9. In the Lorentz model, what frequency does P oscillate at? 3.  in the Lorentz model • We find  from the index of refraction: • Other notation: Back to only one electron/atom Electric susceptibility And index of refraction: Laser Optics – Phys460

  10. Laser Optics – Phys460

  11. 4. n in gasses: the Cauchy formula Rewrite n in terms of vacuum wavelength: A.L. Cauchy (1830) for N atoms with Z electrons each is the vacuum wavelength Usually measure n>1, therefore > i If >> i : For n close to 1: Laser Optics – Phys460

  12. 5. Light scattering But clouds are white? • Why is the sky blue? …and sunsets red? Laser Optics – Phys460

  13. 5. Light scattering, cont. Our model: ? p For one dipole Size< Higher frequency means more scattered energy! Laser Optics – Phys460

  14. 5. Light scattering, cont: Subtle but very important point Coherent sum! • To calculate P, we added all p together • For scattering, we added all the POWER terms together (not electric fields) • Much “scattering” must be considered using a coherent sum: • characteristic length scale is longer than wavelength. • Electric field from dipoles add in phase. Recall from slide 2: Incoherent sum! Laser Optics – Phys460

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