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Understanding Double-Slit Diffraction

Learn about double-slit diffraction patterns and interference in this comprehensive guide for physics students. Discover key principles, experimental challenges, and how to predict maxima and minima. Explore Young's Double Slit experiment and solve problems using complex numbers. Get ready for your term project progress report!

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Understanding Double-Slit Diffraction

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  1. Announcements 11/12/10 • Prayer • Term project progress report due Saturday night • Still missing slinkies from: • Stephen Grant • Chris Read • Roger Brown • Tess Larson (She dropped the class; she’s just on the list here so I don’t forget about her) • Two mathematical facts we will use:

  2. Reading Quiz • According to the book, a double-slit diffraction pattern (viewed on a screen far from the slits) looks like: • A series of equal amplitude peaks, equally spaced • A series of equal amplitude peaks, alternating between two spacing distances • A series of alternating amplitude peaks, equally spaced • A series of alternating amplitude peaks, alternating between two spacing distances

  3. Water Waves Credit: next several slides from Dr. Durfee

  4. Water Waves

  5. Interference... A single source

  6. Interference... Two sources

  7. intensity screen here Double slit experiment aka “Young’s Double Slit” • Exactly the same as the two speaker demo • Goal: what’s the shape of that curve? How can we predict where the maxima & minima will be? min max min max

  8. Experimental challenge • How do you get two points sources of light that are oscillating in phase with each other? • How did we do it with sound? • Options for light? (I can only think of two) • What he did: Image credit: Wikipedia

  9. How to solve the problem • Complex numbers!! • The light from each slit travels a different distance • This creates a phase shift • Incorporate the phase shift into eif • First: what’s the phase shift for two waves oscillating in phase with a known DPL? f = ( DPL / l )  360 f = 2pDPL / l

  10. What’s DPL? f = 2pDPL / l • Clicker Vote: What should we measure the path length relative to? • The top slit • The bottom slit • Halfway between the two slits Approximation #1: d is small enough that the two rays are parallel. Requires d << L.

  11. The Answer f = 2pDPL / l • Etot = Etop slit + Ebottom slit = … • I ~ |E|2 I = … • Plot of I(y) for I0=1, l=500 nm, L=1 m, d=1mm • How did I turn q into y? • Approximation #2: q is small enough that qy/L. Requires y << L.

  12. Plots (approx. 1 and 2) (approx. 1 only)

  13. intensity screen here min max min max

  14. max min max min max min max screen here

  15. How to predict max/min • Max: cosx = 1  … • Min: cosx = 0  …

  16. What you need to know • How to solve the problem this way—works for any number/pattern of slits • Three slits on HW 32-5 • Potential problem like this on exam • This only works for very narrow slits (width << separation between slits) • The two formulas above (on notecard, unless you can quickly derive them) • Conditions for max/min (on notecard, unless you can quickly derive them) • How Young did his experiment

  17. Wrapping Up • Demo: Double-slit experiment The fast way to get these

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