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PH 103

PH 103. Dr. Cecilia Vogel Lecture 11. Review. diffraction resolution. Outline. Interference Coherence double-slit diffraction grating Spectral analysis Cool stuff. Interference. If two hoses spray water at a wall, twice as much water. 1+1=2 If two waves strike a wall,

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PH 103

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  1. PH 103 Dr. Cecilia Vogel Lecture 11

  2. Review diffraction resolution Outline • Interference • Coherence • double-slit • diffraction grating • Spectral analysis • Cool stuff

  3. Interference • If two hoses spray water at a wall, twice as much water. 1+1=2 • If two waves strike a wall, add wave functions. 1+1=… anywhere from 0 thru 4!!

  4. Constructive Interference • Occurs when crest meets crest and trough meets trough: • waves are in phase • Overall intensity (brightness) is four times as bright as a single wave

  5. Destructive Interference • Occurs when crest meets trough: • waves are ½-cycle (180o) out of phase • Overall intensity (brightness) is 0!

  6. Interference Generally • Also, can have anything between fully constructive and fully destructive. • Waves might be out of phase, but not 180o out of phase. • For two beams of equal amplitude, • you can have brightness that is anything from 0 to 4 times as bright as one beam.

  7. Incoherence Do you see interference between two light bulbs? • No! • Light from bulb is produced by many atoms • each atom doing its own thing. • So phase changes randomly and rapidly. • Waves go in and out of phase -- bright to dark -- faster than we can observe kinda Bright Bright Dark Bright See average of brightness (0 thru 4) = 2 times as bright

  8. Coherence How do you get two waves that are coherent? Take one source, split it, bring it back together Then when one wave changes randomly, the other does the same thing! They stay in phase or out of phase or whatever.

  9. Coherence How do you get two waves that are coherent? Take one source, split it, bring it back together Examples: light passing through two (or more) slits light passing around opposite sides of obstacle light reflecting from top and bottom surface of thin film light passing through and reflecting from a partially-silvered mirror

  10. Two-slit interference AKA Young’s experiment Two waves start out in phase, but one travels farther one wave gets behind (analogy: cars) Geometry: slits Observation screen 

  11. Two-slit interference Geometry: d=distance btwn slit centers if slits d and l << L difference in distance traveled ≈ dsinq or dy/L

  12. Two-slit interference Constructive interference if difference in distance traveled = integer # of wavelengths – BACK IN PHASE dsinq= ml or dy/L = ml Destructive interference if difference in distance traveled = (integer-1/2) wavelengths – ½-CYCLE OUT OF PHASE dsinq= (m-1/2)l or dy/L = (m-1/2)l

  13. Two-slit interference • Bright fringes: y = mlL/d m= integer =“order” 1st fringe from center is 1st order, etc • Distance between fringes: Dy = lL/d • How does interference pattern depend on • slit separation? • Larger d, smaller y & Dy -- fringes closer • Wavelength? • Longer l, larger y & Dy -- fringes farther • longer wavelengths diffract more

  14. Many-slits = diffraction grating Each pair of slits behaves like double-slit Constructive interference if dsinq= ml or dy/L = ml Destructive interference if dsinq= (m-1/2)l or dy/L = (m-1/2)l Fringes are in same place as for double-slit, but sharper

  15. Many-slits = diffraction grating How far apart are the slits? Suppose the are 10 lines/cm, then there is one line every 1/10 cm = 0.1 cm the lines are 0.1 cm apart generally d = 1/(number of lines per unit length)

  16. Diffraction Spectrum Because the position of the bright fringes depends on wavelength, shorter wavelengths at smaller angles, different colors show bright at different positions, thus spreading light into its spectrum of wavelengths

  17. Spectral Analysis Diffraction grating’s spectrum can be used to analyze the source of the light Is the spectrum a single wavelength? probably a laser Is the spectrum made up of bands of color? could be fluorescence Is the spectrum continuous? probably created by a hot solid or liquid or plasma

  18. Spectral Analysis Diffraction grating’s spectrum can be used to analyze the source of the light Is the spectrum continuous? probably created by a hot solid or liquid or plasma Is the spectrum continuous, but with some lines missing? probably created by a hot object as above but there is a cool gas* between you and the source & that gas absorbs some wavelengths Is the spectrum made up of individual lines of color? probably made by a glowing gas* *The wavelengths of the lines identifies the gas

  19. Beyond slits If pattern of openings is bunch of slits light is spread perpendicular to slit axis If pattern of openings is more interesting light is spread into a more interesting pattern! exs: Laser pointer patterns Holograms Computer generated holograms

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