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Agenda

Agenda. Monday Diffraction – Problems How small? How many? Tuesday Diffraction – Laboratory, Quiz on Interference Wed Review Fri Bonus Quiz. Basic Diffraction Formula. D x = m l (constructive) D x = (m+1/2) l (constructive) m integer Open question What is D x?. Multiple Slits.

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Agenda

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  1. Agenda • Monday • Diffraction – Problems • How small? • How many? • Tuesday • Diffraction – Laboratory, Quiz on Interference • Wed • Review • Fri • Bonus Quiz

  2. Basic Diffraction Formula • Dx = ml (constructive) • Dx = (m+1/2)l (constructive) • m integer • Open question • What is Dx?

  3. Multiple Slits • Dx = ml (constructive) • Dx = (m+1/2)l (constructive) • m integer • Open question • Dx = dsinq

  4. Equation vs. Experiment Screen Coherent, monochromatic Light wavelength l m 3 2 1 0 -1 -2 -3 Slits (Turned perp.) Rectangular q d dsin(q) = ml

  5. Examine Situation for Given LaserMeans: l fixed Screen Coherent, monochromatic Light wavelength l m 3 2 1 0 -1 -2 -3 Slits (Turned perp.) q d dsin(q) = ml

  6. Range of possible d values?Given: l fixed Screen Coherent, monochromatic Light wavelength l m 3 2 1 0 -1 -2 -3 Slits (Turned perp.) q d dsin(q) = ml

  7. Range of possible d values?Given: l fixed dsin(q) = ml d = ml / sin(q) Anything related to range of d? Try big & small….

  8. Range of possible d values?Given: l fixed dsin(q) = ml d = ml / sin(q) How big can d be? Pretty big, m can range to infinity…. If d is big, what happens to angle? sin(q) = ml/d…. Large slit spacing, all diffraction squeezed together Interference exists – just all overlaps – beam behavior

  9. Large Distance(Assume large width…) Screen Coherent, monochromatic Light wavelength l Slits (Turned perp.) Slit one Slit Two d dsin(q) = ml

  10. Range of possible d values?Given: l fixed dsin(q) = ml d = ml / sin(q) How small can d be? Pretty small, m can be zero How about for anything but m = 0 Smallest  m =1 d = l/sin(q) d small when sin(q) big, sin(q) <= 1 smallest d for m=1 diffraction: d = l Replace: lsin(q)=ml sin(q) = m implies if d = l, three diffraction spots if d < l, no diffraction (m=0?)

  11. Range of possible d values?Given: l fixed Screen Coherent, monochromatic Light wavelength l m 1 0 -1 Slits (Turned perp.) d ~ l dsin(q) = ml

  12. What Happens? • Diffraction from spacing & width • Overlaying patterns, superposition • 3 slits, all same spacing • Very similar to two slits • Tons of slits, all same spacing • Refined interference. Focused maxima • Move screen farther away from slits • Bigger angle/distance on screen • Move light source, leave rest same • Nothing

  13. ResolutionWhen can you identify 2 objects? Screen Coherent, monochromatic Light wavelength l m 1 0 -1 Slits (Turned perp.) d ~ l w ~ l Not Here… dsin(q) = ml

  14. ResolutionWhen can you identify 2 objects?Begin with diffraction Diffraction of light through a circular aperture 1st ring (spot)  sin(q) = 1.22l/D Same setup idea as before

  15. ResolutionWhen can you identify 2 objects?Begin with diffraction Diffraction of light around a circular block 1st ring (spot)  sin(q) = 1.22l/D Same setup idea as before Things that might cause diffraction rings… Pits/dust on glasses Iris of your eye Telescope Lens Raindrops

  16. Pretty Picture Raindrop Moon What you see

  17. Headlights Resolved (barely) Unresolved

  18. Issue • How close must a car be before you can tell it is NOT a motorcycle. (assume both headlights work) • sin(q) = 1.22l/D Small Angle sin(q) ~ tan(q) ~ q [radians] 1.5 m q

  19. Issue • How close must a car be before you can tell it is NOT a motorcycle. (assume both headlights work) • q = 1.22l/D • q = y/L • What is D? Small Angle sin(q) ~ tan(q) ~ q [radians] 1.5 m = y q L

  20. Issue • How close must a car be before you can tell it is NOT a motorcycle. (assume both headlights work) • q = 1.22l/D • q = y/L • pupil: D ~ 5 mm • What is l? Small Angle sin(q) ~ tan(q) ~ q [radians] 1.5 m = y q L

  21. Issue • How close must a car be before you can tell it is NOT a motorcycle. (assume both headlights work) • q = 1.22l/D • q = y/L • pupil: D ~ 5 mm • lGREEN ~ 500 nm • Calculation Time Small Angle sin(q) ~ tan(q) ~ q [radians] 1.5 m = y q L

  22. Issue • How close must a car be before you can tell it is NOT a motorcycle. (assume both headlights work) • q = 1.22l/D • q = y/L • y/L = 1.22l/D • L/y = D/(1.22l) • = 500 nm D = 5 mm Small Angle sin(q) ~ tan(q) ~ q [radians] 1.5 m = y q L

  23. Issue • How close must a car be before you can tell it is NOT a motorcycle. (assume both headlights work) • q = 1.22l/D • L/y = D/(1.22l) • L = Dy/(1.22l) = 12km ~ 7 miles • Little far, but not crazy far • aberrations blur image more here • = 500 nm D = 5 mm Small Angle sin(q) ~ tan(q) ~ q [radians] 1.5 m = y q L

  24. Agenda Monday Diffraction – Problems Tuesday Diffraction – Laboratory, Quiz on Interference Wed Review Fri Bonus Quiz

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