Announcements 3/21/11 Prayer Two labs this week (telescope, interferometer) Two mathematical 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) looks like: 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

Interference... A single source

Interference... Two sources

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: Image credit: Wikipedia

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 Answer E tot = E top slit + E bottom slit = … I ~ |E| 2 I = … Plot of I(y) for I 0 =1, =500 nm, L=1 m, d=1  m How did I turn  into y? Approximation #2:  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

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

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

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