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…)

cos2

ix ixe ex

sin2

ix ixe ex

i

Two facts you should know:

(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 spacedb. A series of equal amplitude peaks, alternating between

two spacing distancesc. A series of alternating amplitude peaks, equally spacedd. 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

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

inte

nsity

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:

http://en.wikipedia.org/wiki/Young's_Double_Slit_Interferometer

Wait, which is correct?

How to solve the problem

Complex numbers!! The light from each slit travels a different

distancea. This creates a phase shiftb. Incorporate the phase shift into ei

First: what’s the phase shift for two waves oscillating in phase with a known PL? = ( PL / ) 360

= 2PL /

What’s PL? Clicker Vote: What

should we measure the path length relative to?

a. The top slitb. The bottom slitc. Halfway between the

two slits

= 2PL /

Approximation #1: d is small enough that the two rays are parallel. Requires d << L.

The Easy Part

Maxima/minima

Maxima: PL = ?

Minima: PL = ?

sind m

12sind m

The Full Answer

Etot = Etop slit + Ebottom slit

= [use whiteboard]

I ~ |E|2

I = [use whiteboard]

Plot of I(y) for I0=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.

= 2PL /

20

2cos sin

2

dI I

Plots

20

1

2cos sin

2

tan /

dI I

y L

2

0 cosdy

I IL

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

screen here

max

min

max

min

inte

nsity

screen here

max

min

max

min

max

min

max

Maxima/minima, revisited

Max: cosx = 1 …

Min: cosx = 0 …

20

2cos sin

2

dI I

20 cos

dyI I

L

sind m

12sin ( )d m

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

20

2cos sin

2

dI I

20 cos

dyI I

L

Given on exam Not given on exam

sind m

12sind m

2 PL

(approx. #2)y L

PL sin (approx. #1)d

1 20 ...i iE E e e 2

~I E Demo: Double slit experiment!