Class 33: Outline
Hour 1:
Interference
Hour 2:
Experiment 13: Interference
P33- 1
Last time: Microwaves (mw)
f mw  2 10 Hz mw
9
c
  15 cm
f
This time: Visible (red) light:
f red  4.6 10 Hz red
14
c
5
  6.54 10 cm
f
How in the world do we
measure 1/10,000 of a cm?
P33- 2
We Use Interference
This is also how we know that
light is a wave phenomena
P33- 3
Interference: The difference
between waves and bullets
No Interference:
if light were made
up of bullets
Interference: If light is
a wave we see spreading
P33- 4
and addition and subtraction
Interference: The difference
between waves and bullets
Link to interference applet
P33- 5
Interference
Interference: 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
P33- 6
Demonstration:
Microwave Interference
P33- 7
Interference – Phase Shift
Consider two traveling waves, moving through space:
Look here as function of time
Constructive
Interference
Look here as function of time
Destructive
Interference
P33- 8
Microwave Interference
Link to mpeg
P33- 9
Interference – Phase Shift
What can introduce a phase shift?
1. From different, out of phase sources
2. Sources in phase, but travel different
distances
1. Thin films
2. Microwave Demonstration
3. Double-slit or Diffraction grating
P33- 10
PRS Question:
Interference
P33- 11
Extra Path Length
L
In Phase Here
Still in Phase Here
L  m (m=0, ±1, ±2…)

Constructive Interference
P33- 12
Extra Path Length
L
In Phase Here
Not in Phase Here
L   m   
(m=0, ±1, ±2…)

Destructive Interference
1
2
P33- 13
Thin Film Interference Iridescence
P33- 14
Thin Film Interference Iridescence
P33- 15
Thin Film Interference
P33- 16
Thin Film: Extra Path
Extra path length ~ 2d
2d  m
 Constructive
2d   m  12    Destructive
d
Oil on concrete, non-reflective coating on glass, etc.
P33- 17
Phase Shift = Extra Path?
What is exact relationship between L & ?
sin(k  x  L )  sin(kx  k L)
 sin(kx 


 2
L
2

L)  sin( kx   )
 m constructive

1
 m  2 destructive
P33- 18
Two Transmitters
P33- 19
Microwave Interference
Link to mpeg
P33- 20
Two In-Phase Sources: Geometry
Assuming L d :
Extra path length
  d sin  
Assume L
d

y  L tan   L sin 
  d sin    m
  d sin     m  12  
 Constructive
 Destructive
P33- 21
Interference for Two
Sources in Phase
(1) Constructive:
  m

m yconstructive
sin   

d
d
L
yconstructive  m
L
d
  (m  1/ 2)
1  L

 m 
m  0,1,...
2 d

m  0,1...
(2) Destructive:
ydestructive
P33- 22
In-Class: Lecture Demo
Just Found:
1  L

ydestructive   m  
m  0,1,...
2 d

For m = 0 (the first minimum):
ydestructive   L
2d
From our lecture demo, we measure:
L ~ 1.16 m; d ~ 0.24 m; ydestructive ~ ? m
Estimate the wavelength & frequency of our
microwaves
P33- 23
How we measure 1/10,000 of a cm
Question: How do you measure
the wavelength of light?
Answer: Do the same
experiment we just did (with light)
First ydestructive   L
2d
 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
P33- 24
The Light Equivalent:
Two Slits
P33- 25
Young’s Double-Slit Experiment
Bright Fringes: Constructive interference
Dark Fringes: Destructive interference
P33- 26
PRS Question
Double Slit Path Difference
P33- 27
Lecture Demonstration:
Double Slit
P33- 28
Diffraction
P33- 29
Diffraction
Diffraction: The bending of waves as they pass by
certain obstacles
No Diffraction
Diffraction
No spreading after
passing though slits
Spreading after
passing though slits
P33- 30
Single-Slit Diffraction
“Derivation” (Motivation) by Division:
Divide slit into two portions:
a
  r1  r3  r2  r4  sin 
2
Destructive interference:
a
  sin    m  12  
2
a sin   m
m  1,  2,...
Don’t get confused – this is DESTRUCTIVE!
P33- 31
Intensity Distribution
Destructive Interference: a sin   m
m   1,  2,...
P33- 32
Putting it Together
P33- 33
PRS Question:
Two Slits with Width
P33- 34
Two Slits With Finite Width a
With 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
P33- 35
Two Slits With Finite width a
Zero Order Maximum
First Diff. Minimum
a sin  
First Order Maximum
d sin  
P33- 36
Lecture Demonstration:
Double Slits with Width
P33- 37
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:
Efilling   Eslit
So the intensities are identical:
I filling  I slit
P33- 38
Experiment 13: To Do
Download 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
P33- 39