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Light & Optics

Light & Optics. Wave Optics Updated 2010Apr13 Dr. Bill Pezzaglia. 2. Outline. Wavespeed Theoretical Calculation of Wavespeed of Light Dispersion Doppler Effect Reflection Total Reflection Partial Reflection Reflectivity and Impedance Diffraction Interference of Sound

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Light & Optics

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  1. Light & Optics Wave Optics Updated 2010Apr13 Dr. Bill Pezzaglia

  2. 2 Outline • Wavespeed • Theoretical Calculation of Wavespeed of Light • Dispersion • Doppler Effect • Reflection • Total Reflection • Partial Reflection • Reflectivity and Impedance • Diffraction • Interference of Sound • Huygen’s Principle of wave propagation • Diffraction through a slit (e.g. sound through a doorway) • Refraction • Fermat’s problem: the path of “least time” • Snell’s Law for angle of refraction • Critical Angles • References

  3. 3 A. Wavespeed • Theory Calculation of Speed • Dispersion • Doppler Effect

  4. 4 1. Theory of Speed of Light • Speed of light depends upon the properties of the medium through which it travels: • “” electric permittivity • “” magnetic permeability • “v” speed in meters/second • “c” is speed of light in vacuum • “n” is the “index of refraction”

  5. 5 2. Dispersion • Gassendi: demonstrated speed of sound is independent of pitch by comparing measurements from cannon and rifle (no “dispersion”) • Speed of light (in vacuum) does not depend on wavelength or frequency • Speed of light (in vacuum) does not depend upon amplitude (brightness) Pierre Gassendi(1592-1655)

  6. 6 2b. Dispersion of Light • In media however, the speed of light depends upon wavelength (color) • Sellmeier Equation (1871) shows index of refraction decreases for bigger wavelength, approaching n0 • Index of refraction goes to infinity at “color” 0 of media (e.g. green for emerald)

  7. 7 3. Doppler Effect 1842 Christian Doppler shows “detected” frequency fd of sound depends upon: • fs frequency of source • vs velocity of source (towards detector) • vd velocity of detector (towards source) • c velocity of sound in medium 1848 Fizeau detects effect in light, however the formula is different, due to the constraints of relativity. • v is the relative velocity between source and detector (towards each other)

  8. 8 B. Reflection • Total Reflection • Impedance & Partial Reflection • Absorption & Skin Depth

  9. 9 1. Total Reflection • Wave hitting a perfect “mirror” (perfect conductor) will be reflected • Reflected wave is inverted (electric field is inverted, magnetic field is not).

  10. 10 2. Partial Reflection • Wave passing from one medium to another will be partially reflected. • Some of the wave is “transmitted” through

  11. 11 2b. Impedance & Reflection • The amount of reflected energy: • The amount of transmitted energy: • “Z” is the “impedance” of the medium (resistance to vibration) units “ohms” • For non-magnetic media, formulacan be expressed in terms of theindex of refraction:

  12. 12 3. Absorption & Reflection • Light striking a resistive conductor will partially penetrate to “skin depth” and be partially absorbed. • The skin depth depends upon resistivity  and frequency f. • The remainder of the wave will be reflected.

  13. 13 3b The Skin Effect • At higher frequencies the skin depth is very small, and so electricity will travel only on the outside of a conductor (hence increasing its resistance). • At 60 cycles the skin dept is 8.5 mm for copper, so making a bigger diameter wire is a waste of metal. • Instead, use Litz wire, made of many small wires.

  14. 14 C. Diffraction • Huygen’s Principle • Interference • Young slit diffraction

  15. 15 1. Huygen’s Principle (1678)

  16. 16 2. Interference Two waves added together can cancel each other out if “out of phase” with each other. CombinedWave Wave 1 Wave 2 Coherent waves (in phase) add together to make bigger wave Waves 180° out of phase will cancel each other!

  17. 17 3. Diffraction Patterns • Two wave sources close together (such as two speakers) will create “diffraction patterns”. At certain angles the waves cancel!

  18. 18 D. Refraction • Fermat’s Principle of Least Time • Snell’s Law (1621) • Total Reflection (Snell’s Window)

  19. 19 1. Fermat’s Principle Lifeguard Dilemma: What is the fastest path to drowning man? Note you can run twice as fast as you can swim. • Run straight to river, then swim • Run further to shore adjacent swimmer then swim • Optimal path obeys Snell’s Law This is the path light (sound, any wave) will take! Lifeguard Tower

  20. 20 2. Snell’s Law (1621) Path of wave is bent toward normal when enters media with lower wavespeed (i.e. higher index of refraction)

  21. 21 3. Total Reflection (Snell’s Window) • At the “critical angle” the refracted beam is at 90, so it can’t get out. • Greater than the critical angle there is 100% reflection • Snell’s Window: fromunderwater a fish sees theentire area above surface ina cone. Outside the conelight is totally reflected

  22. 22 References • Wave Animations: http://www.sciencejoywagon.com/physicszone/09waves/ • Huygen’s Animation: http://www.sciencejoywagon.com/physicszone/otherpub/wfendt/huygens.htm • Hugens & Diffraction http://www.launc.tased.edu.au/online/sciences/Physics/diffrac.html • More animations http://www.launc.tased.edu.au/online/sciences/Physics/tutes1.htmlh • http://id.mind.net/~zona/mstm/physics/waves/propagation/huygens1.html • http://www.springerlink.com/content/q70853654x88pv47/

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