Announcements 3/21/11 Prayer Two labs this week (telescope,

interferometer) Two mathematical facts you should know:

(They follow quickly from eix = cosx + i sinx)

cos2

ix ixe ex

sin

2

ix ixe ex

i

Reading Quiz

According to the book, a double-slit diffraction pattern (viewed on a screen far from the slits) looks like:

a. A series of equal amplitude peaks, equally spaced

b. A series of equal amplitude peaks, alternating between two spacing distances

c. A series of alternating amplitude peaks, equally spaced

d. A series of alternating amplitude peaks, alternating between two spacing distances

Interference... Interference...

A single source

Interference... 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

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:

Image credit: Wikipedia

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 Answer

Etot = Etop slit + Ebottom slit

= …

I ~ |E|2

I = …

Plot of I(y) for I0=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.

= 2PL /

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

How to predict max/min

Max: cosx = 1 …

Min: cosx = 0 …

20

2cos sin

2

dI I

20 cos

dyI I

L

brightsind m

1dark 2sin ( )d m

What you need to know

How to solve the problem this way—works for any number/pattern of slits

a. You analyze three slits for HW 32-4b. 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)

20

2cos sin

2

dI I

20 cos

dyI I

L

Wrapping Up

Demo: Double-slit experiment

20

2cos sin

2

dI I

20 cos

dyI I

L

max : sind

m

1min : sin

2

dm

max :dy

mL

1min :

2

dym

L

The fast way to get these