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32. Interference & Diffraction

32. Interference & Diffraction. Topics. Interference & Coherence Destructive & Constructive Interference Two-Slit Interference Interference in Thin Films Diffraction. Interference and Coherence. Waves can interfere: that is, combine together to form complex wave patterns

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32. Interference & Diffraction

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  1. 32. Interference & Diffraction

  2. Topics • Interference & Coherence • Destructive & Constructive Interference • Two-Slit Interference • Interference in Thin Films • Diffraction

  3. Interference and Coherence Waves can interfere: thatis, combine togetherto form complexwave patterns But interference is bestdemonstrated usingcoherent waves

  4. Interference and Coherence Coherence means thatwaves have a phaserelationship that ismaintained for manycycles Laser light is coherent

  5. Destructive and Constructive Interference Destructive interferenceoccurs when two interfering waves are completely out of phase. Constructive interferenceoccurs when two interfering waves are in phase. http://phet.colorado.edu/simulations/sims.php?sim=Wave_Interference

  6. Two-Slit Interference Consider to two coherent waves emitted from slits A and B. Constructive interference will occur if the path difference Dr = rB – rA= ml

  7. Two-Slit Interference Destructive interference will occur if Dr = (m + ½)l

  8. Two-Slit Interference How does the path difference depend on the angle q ? Note that r = (rB + rA)/2 when d << r q

  9. Two-Slit Interference From 2r = rB + rA and Dr = rB – rA we obtain q which leads to Dr = d sin q

  10. MasteringPhysics Problem: Double Slit with Reflections • Wave reflection off a balloon • Find maximum wavelength that will interfere destructively • 2. Find maximumwavelength thatwill interfereconstructively Note: reflections from a medium of lower to a higher index cause a 1/2-wavelength shift

  11. Two-Slit Interference: Intensity To find the average wave intensity S = EB/m0 = E2/cm0 at P, we need to add the electric fields of the two waves at that point and average the intensity over one cycle: E = EA + EB =Epsinwt + Epsin(wt + f)

  12. Two-Slit Interference: Intensity By definition, the phase is f = 2p (Dr / l), so

  13. Interference in Thin Films

  14. Interference in Thin Films Examples of thin film interference http://www.microscopy-uk.org.uk

  15. Interference in Thin Films 1 2 Consider a thin film in air. There are reflections at surfaces A and B with a ½ wavelength shift at A, but none at B. If l is the wavelength in air then lf = l/ n in the film A d thin film B The path difference between waves 1 and 2 is 2d for normal incidence

  16. Interference in Thin Films 1 2 For constructive interference at surface A, we need (m + ½)lf = 2d (m + ½)l/n = 2d That is, we get constructive interference for incident wavelengths l = 2nd/(m + ½) A d thin film B

  17. Interference in Thin Films 1 2 For destructive interference at surface A, we need mlf = 2d ml/n = 2d That is, we get destructive interference for incident wavelengths l = 2nd / m A d thin film B Of course, if there were no additional phase shifts, the formulas would be reversed

  18. Diffraction

  19. Diffraction Grating A device with multiple slits is called a diffraction grating The greater the number of slits the brighter and narrower the maxima The greater the number of slits the greater the contrast between the maxima and regions between them

  20. Diffraction Gratings and Spectroscopy A grating is used to separate light according to wavelength. The resolution of a grating is its ability to distinguish nearby wavelengths m order of fringe N number of slits A grating spectrometer

  21. Diffraction Diffraction is the bending of waves around boundaries Huygens’ Principle A wave behaves as if each point on its wave-front is a source of spherical wavelets

  22. Single-Slit Diffraction Rays 1 and 3 differ in path length by ½ a sinq. So, if this equals ½ l there will be destructive interference In general, the condition for destructive interference is a sinq = m l

  23. Diffraction Patterns Sharp edge Cross hairs

  24. The Diffraction Limit Two objects become indistinguishable when their central diffraction maxima overlap.

  25. Applications: Storage Media CDs use infrared lasers DVDs red lasers Blu-ray violet lasers

  26. Summary • Interference • Caused by stable phase differences between waves • Diffraction • Caused by the tendency of waves to bend around edges. • Limits the size of resolvable objects

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