1P33-

Class 33: Outline

Hour 1:

Interference

Hour 2:

Experiment 13: Interference

2P33-

Last time: Microwaves (mw)92 10 15mw mw

cf Hz cm

f

This time: Visible (red) light:14 54.6 10 6.54 10red red

cf Hz cm

f

How in the world do we measure 1/10,000 of a cm?

3P33-

We Use Interference

This is also how we know that light is a wave phenomena

4P33-

Interference: The difference between waves and bullets

No Interference:

if light were madeup of bullets

Interference: If light is a wave we see spreading and addition and subtraction

5P33-

Interference: The difference between waves and bullets

Link to interference applet

6P33-

InterferenceInterference: Combination of two or more waves to

form composite wave – use superposition principle.

Waves can add constructively or destructively

Conditions for interference:

1. Coherence: the sources must maintain a constant phase with respect to each other

2. Monochromaticity: the sources consist of waves of a single wavelength

7P33-

Demonstration:Microwave Interference

8P33-

Interference – Phase Shift

Look here as function of time

Consider two traveling waves, moving through space:

Look here as function of time

Constructive Interference

Destructive Interference

9P33-

Microwave Interference

Link to mpeg

10P33-

Interference – Phase Shift

What can introduce a phase shift?

1. From different, out of phase sources

2. Sources in phase, but travel different distances1. Thin films

2. Microwave Demonstration

3. Double-slit or Diffraction grating

11P33-

PRS Question:Interference

12P33-

Extra Path Length

In Phase Here

L

Constructive Interference

L m

Still in Phase Here

(m=0, ±1, ±2…)

13P33-

Extra Path Length

In Phase Here

L

12

Destructive Interference

L m

Not in Phase Here

(m=0, ±1, ±2…)

14P33-

Thin Film Interference - Iridescence

15P33-

Thin Film Interference - Iridescence

16P33-

Thin Film Interference

17P33-

Thin Film: Extra Path

d

Extra path length ~ 2d

12

2 Constructive2 Destructived md m

Oil on concrete, non-reflective coating on glass, etc.

18P33-

Phase Shift = Extra Path?

2

L

What is exact relationship between L & ?

sin( ) sin( )

2sin( ) sin( )

k x L kx k L

kx L kx

12

m

m

constructive

destructive

19P33-

Two Transmitters

20P33-

Microwave Interference

Link to mpeg

21P33-

Two In-Phase Sources: Geometry

:

sin

L d

d

Assuming

Extra path length

L d Assume

tan siny L L

1

2

sin Constructivesin Destructived md m

22P33-

Interference for Two Sources in Phase

(1) Constructive:

sin constructiveym

d d L

0,1...constructive

Ly m m

d

(2) Destructive: ( 1/ 2)m 1

0,1,...2destructive

Ly m m

d

m

23P33-

In-Class: Lecture Demo

From our lecture demo, we measure:L ~ 1.16 m; d ~ 0.24 m; ydestructive ~ ? m

Estimate the wavelength & frequency of our microwaves

10,1,...

2destructive

Ly m m

d

2destructiveLy d

For m = 0 (the first minimum):

Just Found:

24P33-

How we measure 1/10,000 of a cm

is smaller by 10,000 times.

But d can be smaller (0.1 mm instead of 0.24 m)

So y will only be 10 times smaller – still measurable

Question: How do you measure the wavelength of light?

Answer: Do the same experiment we just did (with light)

2destructiveLy d

First

25P33-

The Light Equivalent:Two Slits

26P33-

Young’s Double-Slit Experiment

Bright Fringes: Constructive interference

Dark Fringes: Destructive interference

27P33-

PRS QuestionDouble Slit Path Difference

28P33-

Lecture Demonstration:Double Slit

29P33-

Diffraction

30P33-

Diffraction Diffraction: The bending of waves as they pass by

certain obstacles

No spreading after passing though slits

Spreading after passing though slits

No Diffraction Diffraction

31P33-

Single-Slit Diffraction

1 3 2 4 sin2

ar r r r

Destructive interference:

sin 1, 2,...a m m

“Derivation” (Motivation) by Division:

Divide slit into two portions:

12sin

2

am

Don’t get confused – this is DESTRUCTIVE!

32P33-

Intensity Distribution

sin 1, 2,...a m m Destructive Interference:

33P33-

Putting it Together

34P33-

PRS Question:Two Slits with Width

35P33-

Two Slits With Finite Width aWith more than one slit having finite width a, we must consider

1. Diffraction due to the individual slit

2. Interference of waves from different slits

36P33-

Two Slits With Finite width aZero Order Maximum

First Order Maximum

sind sina First Diff. Minimum

37P33-

Lecture Demonstration:Double Slits with Width

38P33-

Babinet’s Principle

Case I: Put in a slit, get diffraction

Case II: Fill up slit, get nothing

Case III: Remove slit, get diffraction

By superposition, the E field with the slit and the E field with just the filling must be exact opposites in order to cancel: E Efilling slit

So the intensities are identical: I Ifilling slit

39P33-

Experiment 13: To DoDownload Excel File!

1. Single Slit – 4 different slits. Use known width a and zeroes ydestructive to Estimate wavelength of red light

2. Human Hair (Babinet says just single slit). Use red (from 1) and zeroes ydestructive to Estimate thickness of hair

3. Double Slit – 4 different slits. Use known spacing d and zeroes to Estimate wavelength of red light

4. CD Track Spacing (Diffraction Grating) Estimate track spacing