# Announcements 11/11/11

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Announcements 11/11/11  Prayer  Lab 8 going on, due on Sat Nov 19  Lab 9 starts tomorrow, due on Sat Nov 19  Lab 10 starts tomorrow, due on Tues Nov…
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Announcements 11/11/11  Prayer  Lab 8 going on, due on Sat Nov 19  Lab 9 starts tomorrow, due on Sat Nov 19  Lab 10 starts tomorrow, due on Tues Nov 22  Slinky (down to you, Thomas…) Two facts you should know: eix  eix cos x  2 eix  eix sin x  2i (They follow quickly from eix = cosx + i sinx) Reading Quiz  According to the book, a double-slit diffraction pattern (viewed on a screen far from the slits) is: 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 Two slit interference From Wikipedia http://en.wikipedia.org/wiki/ Double-slit_experiment 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? Wait, which is correct? a. How did we do it with sound? b. Options for light? (I can only think of two) c. What he did: http://en.wikipedia.org/wiki/ Young's_Double_Slit_Interferometer 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 Easy Part  Maxima/minima Maxima: DPL = ? d sin   ml Minima: DPL = ?   d sin   m  12 l The Full Answer  Etot = Etop slit + Ebottom slit f = 2pDPL / l = [use whiteboard]  I ~ |E|2  2p d  I = [use whiteboard] I  I 0 cos2   l 2 sin     Plot of I(y) for I0=1, l=500 nm, L=1 m, d=1 mm  How did I turn  into y?  Approximation #2: sometimes (not here!)  is small enough that   y/L. Requires y L. Plots 2p d 2  I  I 0 cos  sin    l 2  2  p dy I  I 0 cos     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 Maxima/minima, revisited 2 2p d  2  p dy  I  I 0 cos  sin   I  I 0 cos    l 2   lL   Max: cosx = 1  … d sin   ml  Min: cosx = 0  … d sin   (m  12 )l What you need to know Given on exam Not given on exam f  2p DPL l d sin   ml DPL  d sin  (approx. #1)  d sin   m  12 l  E  E0 eif1  eif2  ...    y L (approx. #2) 2 I~ E Demo: Double 2  p dy  2  2p d slit experiment!  I  I 0 cos   I  I cos 0 sin   l 2  lL     HW 32-4: Solve the three slit problem  Exam problem likely (possibly extra credit)  Disclaimer: This only works for very narrow slits  Lecture after next: wide slits
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