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Announcements 3/21/11

Learn about the double-slit interference phenomenon in physics, the mathematical facts behind it, and how to predict the diffraction pattern. Explore the experimental challenges and approximations involved in this fascinating topic.

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Announcements 3/21/11

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  1. Announcements 3/21/11 • Prayer • Two labs this week (telescope, interferometer) • Two mathematical facts you should know: (They follow quickly from eix = cosx + i sinx)

  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. Interference... A single source

  4. Interference... Two sources

  5. 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

  6. 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

  7. 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

  8. 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.

  9. 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.

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

  11. intensity screen here min max min max

  12. max min max min max min max screen here

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

  14. What you need to know • How to solve the problem this way—works for any number/pattern of slits • You analyze three slits for HW 32-4 • Could be 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)

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

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