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

cos2

ix ixe ex

sin

2

ix ixe ex

i

Two facts you should know:

(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 identicalb. 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

Essentially 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

Wait, which is correct?

The Easy Part

Maxima/minima

Maxima: PL = ?

Minima: PL = ?

sind m

12sind m

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

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

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

First: what’s the phase shift for two waves oscillating in phase with a known PL?

Quick writing (w/o Approx. 1)

= ( PL / ) 360

= 2PL /

3.2 m

3.0 m

two sourcesof sound, =1.2m

(in phase)

what is relative phase shift, here?

( , ) cos( ) cos( 60 )f x t A kx t A kx t

Intensity?How to add?

What’s PL?

Clicker Vote: What should we measure the phase shift relative to?

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

the two slits

= 2PL /

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

12

sin ( )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!