Announcements 11/12/10

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Announcements 11/12/10  Prayer  Term project progress report due Saturday night  Still missing slinkies from: a. Stephen Grant b. Chris Read c. Roger…
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Announcements 11/12/10  Prayer  Term project progress report due Saturday night  Still missing slinkies from: a. Stephen Grant b. Chris Read c. Roger Brown d. 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: eix  eix eix  eix cos x  sin x  2 2i Reading Quiz  According to the book, a double-slit diffraction pattern (viewed on a screen far from the slits) looks like: a. A series of equal amplitude peaks, equally spaced b. A series of equal amplitude peaks, alternating between two spacing distances c. A series of alternating amplitude peaks, equally spaced d. A series of alternating amplitude peaks, alternating between two spacing distances Water Waves Credit: next several slides from Dr. Durfee Water Waves Interference... A single source Interference... Two sources Double slit experiment aka “Young’s Double Slit”  Exactly the same as min the two speaker demo max min max  Goal: what’s the shape of that curve? How can we predict where the maxima & minima will be? intensity screen here Experimental challenge  How do you get two points sources of light that are oscillating in phase with each other? a. How did we do it with sound? b. Options for light? (I can only think of two) c. What he did: Image credit: Wikipedia How to solve the problem  Complex numbers!!  The light from each slit travels a different distance a. This creates a phase shift b. 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 What’s DPL?  Clicker Vote: What should f = 2pDPL / l we measure the path length relative to? a. The top slit b. The bottom slit c. Halfway between the two slits Approximation #1: d is small enough that the two rays are parallel. Requires d L. The Answer  Etot = Etop slit + Ebottom slit f = 2pDPL / l =…  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. Plots 2p d 2  I  I 0 cos  sin q   l 2  2  p dy I  I 0 cos   q  tan 1  y / L  l L  (approx. 1 only) (approx. 1 and 2) min max min max intensity screen here max min max min max min max screen here How to predict max/min 2 2p d  2  p dy  I  I 0 cos  sin q  I  I 0 cos    l 2   lL   Max: cosx = 1  … d sinqbright  ml  Min: cosx = 0  … d sinqdark  (m  12 )l What you need to know 2  2p d  2  p dy  I  I 0 cos  sin q  I  I 0 cos    l 2   lL   How to solve the problem this way—works for any number/pattern of slits a. Three slits on HW 32-5 b. 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 Wrapping Up 2p d2  2  p dy I  I 0 cos  sin q  I  I 0 cos    l 2   lL  d dy max : sin q  m max : m l lL d 1 dy 1 min : sin q  m  min :  m l 2 lL 2 The fast way to get these  Demo: Double-slit experiment
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