Class 33: Outline
Hour 1:
Interference
Hour 2:
Experiment 13: Interference
P33- 1
Last time: Microwaves (mw)
f mw = 2 × 10 Hz λmw
9
c
= = 15 cm
f
This time: Visible (red) light:
f red = 4.6 × 10 Hz λred
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
and addition and subtraction
P33- 4
Interference: The difference
between waves and bullets
http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizati
ons/light/08-waves2d/08-waves320.html
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
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 = mλ (m=0, ±1, ±2…)
⇓
Constructive Interference
P33- 12
Extra Path Length
∆L
In Phase Here
Not in Phase Here
∆L = ( m + ) λ
(m=0, ±1, ±2…)
⇓
Destructive Interference
1
2
P33- 13
Thin Film Interference Iridescence
Image courtesy of John M. Sullivan, University of Illinois and Technical University of Berlin.
P33- 14
Thin Film Interference Iridescence
•Bubbles
•Butterfly Wings
•Oil on Puddles
P33- 15
Thin Film: Extra Path
Extra path length ~ 2d
2d = mλ
⇒ Constructive
2d = ( m + 12 ) λ ⇒ Destructive
d
Oil on concrete, non-reflective coating on glass, etc.
P33- 16
Phase Shift = Extra Path?
What is exact relationship between ∆L & φ?
sin(k ( x + ∆L )) = sin(kx + k ∆L)
= sin(kx +
φ
=
λ 2π
∆L
2π
λ
∆L) ≡ sin(kx + ϕ )
⎧ m constructive
=⎨
1
m
+
destructive
2
⎩
P33- 17
Two Transmitters
P33- 18
Microwave Interference
P33- 19
Two In-Phase Sources: Geometry
Assuming L d :
Extra path length
δ = d sin (θ )
Assume L d λ
y = L tan θ ≈ L sin θ
δ = d sin (θ ) = mλ
δ = d sin (θ ) = ( m + 12 ) λ
⇒ Constructive
⇒ Destructive
P33- 20
Interference for Two
Sources in Phase
(1) Constructive:
δ = mλ
δ
mλ yconstructive
sin θ = =
=
d
d
L
yconstructive = m
λL
d
δ = (m + 1/ 2)λ
1 ⎞ λL
⎛
= ⎜m+ ⎟
m = 0,1,...
2⎠ d
⎝
m = 0,1...
(2) Destructive:
ydestructive
P33- 21
In-Class: Lecture Demo
Just Found:
1 ⎞ λL
⎛
ydestructive = ⎜ m + ⎟
m = 0,1,...
2⎠ d
⎝
For m = 0 (the first minimum):
ydestructive = λ 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- 22
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 = λ L
2d
λ 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- 23
The Light Equivalent:
Two Slits
P33- 24
Young’s Double-Slit Experiment
Bright Fringes: Constructive interference
Dark Fringes: Destructive interference
P33- 25
PRS Question
Double Slit Path Difference
P33- 26
Lecture Demonstration:
Double Slit
P33- 27
Diffraction
P33- 28
Diffraction
Diffraction: The bending of waves as they pass by
certain obstacles
No Diffraction
No spreading after
passing though slits
Diffraction
Spreading after
passing though slits
P33- 29
Single-Slit Diffraction
“Derivation” (Motivation) by Division:
Divide slit into two portions:
a
δ = r1 − r3 = r2 − r4 = sin θ
2
Destructive interference:
a
δ = sin θ = ( m + 12 ) λ
2
a sin θ = mλ
m = ±1, ± 2,...
Don’t get confused – this is DESTRUCTIVE!
P33- 30
Intensity Distribution
Destructive Interference: a sin θ = mλ
m = ± 1, ± 2,...
P33- 31
Putting it Together
P33- 32
PRS Question:
Two Slits with Width
P33- 33
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- 34
Two Slits With Finite width a
Zero Order Maximum
First Diff. Minimum
a sin θ = λ
First Order Maximum
d sin θ = λ
P33- 35
Lecture Demonstration:
Double Slits with Width
P33- 36
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- 37
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 λred (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- 38