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Understanding Diffraction: Key Concepts, Problems, and Laboratory Applications

This week's agenda covers fundamental aspects of diffraction, including problem-solving techniques and practical applications in laboratory settings. We will address topics such as the relationship between slit spacing and angle, constructive interference, and the impact of coherent monochromatic light. Key activities include a quiz on interference, a review session, and a bonus quiz focusing on basic diffraction formulas. Join us as we explore diffraction's nuances, challenge our understanding, and prepare for real-world applications in optics.

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Understanding Diffraction: Key Concepts, Problems, and Laboratory Applications

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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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