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Announcements 11/9/12 Prayer Clement sick today, no office hours Lab 8 going on, due on Sat Nov 17 Lab 9 starts tomorrow, due on Sat Nov 17 …

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Announcements 11/9/12 Prayer Clement sick today, no office hours Lab 8 going on, due on Sat Nov 17 Lab 9 starts tomorrow, due on Sat Nov 17 Lab 10 starts tomorrow, due on Tues Nov 20 Exam 3 starts day after break Two facts you should know: eix eix eix eix cos x sin x 2 2i (They follow quickly from eix = cosx + i sinx) From warmup Extra time on? a. (nothing in particular) Other comments? a. (nothing in particular) Double slit diffraction Two slit interference From Wikipedia http://en.wikipedia.org/wiki/ Double-slit_experiment From warmup What is the purpose of S1 in the right figure? Some good thoughts: a. To make sure that the light sources at b and c are identical b. Is it to make sure that the point source of light is centered exactly between b and c and to make sure that b and c are coherent? c. That is the original ray. The two slits b and c split it up like a speaker splits up a single sound wave. Reminder: How did we do it with sound? An alternate method: Use a laser, then S1 not needed Double slit experiment aka “Young’s Double Slit” Essentially the same min as 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 Wait, which is correct? The Easy Part Maxima/minima Approximation #1: d is small enough that the two rays are parallel. Requires d L. Maxima: DPL = ? d sin m Minima: DPL = ? d sin m 12 From warmup Consider a two-slit interference pattern like those above. What do you suppose would happen if the entire setup were immersed in water? a. The bars would move together and get smaller because the wavelength decreases when you immerse it in water, therefore the distance between the bars is decreased. 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 factors First: what’s the phase shift for two waves oscillating in phase with a known DPL? Quick writing (w/o Approx. 1) 3.2 m two sources what is relative of sound, =1.2m phase shift, here? (in phase) 3.0 m f = ( DPL / ) 360 f = 2pDPL / f ( x, t ) A cos(kx t ) A cos(kx t 60 ) How to add? Intensity? What’s DPL? Clicker Vote: What should f = 2pDPL / we measure the phase shift relative to? a. The top slit b. The bottom slit c. Halfway between the two slits The Full Answer Etot = Etop slit + Ebottom slit f = 2pDPL / = [use whiteboard] I ~ |E|2 2p d I = [use whiteboard] I I 0 cos2 2 sin Plot of I(y) for I0=1, =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 2 2 p dy I I 0 cos tan 1 y / 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 2 L Max: cosx = 1 … d sin m Min: cosx = 0 … d sin (m 12 ) What you need to know Given on exam Not given on exam f 2p DPL d sin m DPL d sin (approx. #1) d sin m 12 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 2 L 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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