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: (They follow quickly from e ix = 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.A series of equal amplitude peaks, equally spaced b. b.A series of equal amplitude peaks, alternating between two spacing distances c. c.A series of alternating amplitude peaks, equally spaced d. d.A series of alternating amplitude peaks, alternating between two spacing distances

Two slit interference From Wikipedia Double-slit_experiment

Double slit experiment 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? aka “Young’s Double Slit” screen here max min max min intensity

Experimental challenge How do you get two points sources of light that are oscillating in phase with each other? a. a.How did we do it with sound? b. b.Options for light? (I can only think of two) c. c.What he did: Young's_Double_Slit_Interferometer Wait, which is correct?

How to solve the problem Complex numbers!! The light from each slit travels a different distance a. a.This creates a phase shift b. b.Incorporate the phase shift into e i  First: what’s the phase shift for two waves oscillating in phase with a known  PL?  = (  PL /  )  360   = 2  PL /

What’s  PL? Clicker Vote: What should we measure the path length relative to? a. a.The top slit b. b.The bottom slit c. c.Halfway between the two slits  = 2  PL / Approximation #1: d is small enough that the two rays are parallel. Requires d << L.

The Easy Part Maxima/minima Maxima:  PL = ? Minima:  PL = ?

The Full Answer E tot = E top slit + E bottom slit = [use whiteboard] I ~ |E| 2 I = [use whiteboard] Plot of I(y) for I 0 =1, =500 nm, L=1 m, d=1  m How did I turn  into y? Approximation #2: sometimes (not here!)  is small enough that  y/L. Requires y << L.  = 2  PL /

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

screen here max min max min intensity

screen here max min max min max min max

Maxima/minima, revisited Max: cosx =  1  … Min: cosx = 0  …

What you need to know 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 Given on exam Not given on exam Demo: Double slit experiment!