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From last time…

From last time…. Waves. Interference. Please pick up pack of color sheets. constructive interference,loud tone. destructive interference quit tone. Interference of 2 speakers. crest trough. A little more detail. Path-length difference  = (Path 2) - (Path 1) = 0.

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From last time…

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  1. From last time… • Waves Interference Please pick up pack of color sheets Phy208 Lecture 2

  2. constructive interference,loud tone destructive interferencequit tone Interference of 2 speakers cresttrough Phy208 Lecture 2

  3. A little more detail Path-length difference  = (Path 2) - (Path 1) = 0 Same distance, same phase Path 1 Path 2 Path 1 Path 2 d Phy208 Lecture 2

  4. Other angles? Path-length difference 0 Interference: Constructive: = Destructive: = Path 1 Path 2   = Extra path length d Phy208 Lecture 2

  5. Question Suppose that the frequency of the sound wave increases by a factor of two. The adjacent maxima are A) Farther apart B) Closer together C) Same D) Need to know speaker spacing Higher frequency, -> shorter wavelength Less path length diff required to make 1 wavelength diff. Phy208 Lecture 2

  6. Question In your room you have two speakers in different corners. At your desk you are exactly 1 meter from each, so that there is no interference. Your roommate moved one of your speakers 0.25 m further away from your desk. At what frequency will you hear destructive interference? • 170 Hz • 340 Hz • 680 Hz • 1000 Hz • 1350 Hz Phy208 Lecture 2

  7. Path 2  Path 1  = Extra path length d Math Analysis Constructive interference:  = 0.347 rad = 19.9˚ Phy208 Lecture 2

  8. with  in radians For small , e.g. Exact value: For small angles… Small angle approximation for constructive interference Approx breaks down for large  Phy208 Lecture 2

  9. Light waves • Light is a wave just like sound. • But can propagate in vacuum • at speed c = 3x108 m/s • Has same wave properties, e.g. • Can also propagate in glass, water, but slower • Speed in medium = v = c/n • n = Index of refraction • Has same superposition / interference properties Phy208 Lecture 2

  10. Interference of light Phy208 Lecture 2

  11. y  L Recording plate Projection on screen • Light wavelength much shorter than sound • Interference fringes much closer together Light beam Foil with two narrow slits Phy208 Lecture 2

  12. Extra path length =  Small-angle approximation  = Extra path length y = position on screen = Phy208 Lecture 2

  13. Bright Fringe separation = Fringe separation & wavelength • For bright fringes: extra path length = m • For dark fringes: extra path length = (m+1/2)  Phy208 Lecture 2

  14. Question A two-slit interference pattern is observed in air (n=1). Then the entire system is immersed in water (n=1.33). The interference fringes are A) 1.33 times closer together B) 1.33 times farther apart C) 2.66 times closer together D) 2.66 times farther apart E) Spacing unchanged Phy208 Lecture 2

  15. Evenly-spaced slits have maxima at same location as two-slits. • Maxima become sharper, more intense • Interference of multiple sources often called diffraction Interference of multiple sources Phy208 Lecture 2

  16. Diffraction gratings • Diffraction grating is pattern of multiple slits. • Very narrow, very closely spaced. • Expect very narrow interference peaks. (15,000 lines/inch)x(1 inch/2.54 cm)x(100 cm/m)=5.9x105/m So a spacing of 1/(5.9x105/m) = 1.7x10-6 m = 1700 nm. 1700 nm Phy208 Lecture 2

  17. Question Suppose white light is shined through a diffraction grating. What would the pattern on the screen look like? A) B) C) D) Phy208 Lecture 2

  18. Diffraction: only one slit, but “wide” • Huygen’s principle: each portion of the slit acts as a source of waves • These sources interfere according to path-length difference. Phy208 Lecture 2

  19. Diffraction minima • Interference-like pattern from a single slit. How wide is wide? Phy208 Lecture 2

  20. General reln: Phase difference • Waves start in phase • Travel different distances (extra path length = ) • No longer in phase when combined (Phase diff ) =/2  =π =  =2π Constructive: =2πm Destuctive: =2π(m+1/2) Phy208 Lecture 2

  21. Thin film interference Black Colors changing with thickness Phy208 Lecture 2

  22. Thin film interference  180˚ (π radians) phase shift • If film is much thinner than wavelength, ~ no phase shift from extra path length • But top reflection has 180˚ phase shift, bottom not • Destructive interference for all wavelengths, film appears black no phase shift air: n=1 n>1 /n t Phy208 Lecture 2

  23. destructive 180˚ phase shiftfrom reflection Thicker parts  • Phase difference comes from • Phase shift from reflection (top) • Phase shift from extra path length • Extra path length for normal incidence = 2t air: n=1 n>1 Extra path length=2t t vac/n air: n=1 Phase difference = Reflection phase shift # wavelengths in extra path length Phy208 Lecture 2

  24. Constructive interference constructive interference destructive interference Phy208 Lecture 2

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