AP B Physics…
Interference & Diffraction
Topics
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Diffraction
Interference & Coherence of lasers
Destructive & Constructive Interference
Two-Slit Interference
Interference in Thin Films
Summary
Diffraction: creates many tiny
waves which may later interfer
Diffraction is the bending of
waves around boundaries
Huygens’ Principle
A wave behaves as if each point
on its wave-front is a source of
spherical wavelets
Interference and Coherence
Waves can interfere: that
is, combine together
to form complex
wave patterns
But interference is best
demonstrated using
coherent waves
Interference and Coherence
Coherence means that
waves have a phase
relationship that is
maintained for many
cycles
Laser light is coherent
Destructive and Constructive
Interference
Destructive interference occurs when
two interfering waves are completely out of phase.
Constructive interference occurs when
two interfering waves are in phase.
http://phet.colorado.edu/simulations/sims.php?sim=Wave_Interference
Two-Slit Interference
. Two light rays
start in phase,
but rb travels
longer to reach
point P
d
Constructive
 
interference
 occur
will
P
A
rA
y
r
rB


B

L
if the path difference Dr = rB – rA = m l, m=1,2,3


Two-Slit Interference
P
Destructive
interference
will occur
d
if
A


 
Dr = (m + ½)lB

=3/2,5/27/2

rA
y
r
rB




L
Two-Slit Math Proof
P
How does the
path difference
depend on
the angle d
q?
 
 that
Note
r = (rB + rA)/2
when d << r

A
rA
y
r
rB
q


B

L
Dr = rB  rA

Two-Slit Math Proof (sara?)
P
From
2r = rB + rA
rA





L

we obtain
2rDr = rB2  rA2
rB
q
d
and
Dr = rB – rA
y
r
Dr = rB  rA

which leads to Dr =d sin q
Two-Slit Interference
P
Small angles :
sin = tan = y/L
But also
Dr = d sin q
** Combine:
rA
d

l

y
r
rB
q



L
Dr = rB  rA

Dy/L= d/path where thepath = l if constructive
=l/2 if destructive
Two-Slit Interference Examplesneed at least 2 sources!
1. Two speakers for sound
(don’t sit on a node!)
2. Two barriers for light
to diffract (see black/white
fringes on a screen)
3. CD, DVD, rough surfaces
(multiple reflections overlap)
4. Diffraction grating (many slits)
slit size = d= 1mm/# lines
Applications: Storage Media
CDs
use infrared lasers
DVDsred lasers
Blu-ray
violet lasers
Gratings- forensics, spectroscopy
Two-Slit Interference: Intensity
FYI: Intensity depends on the square of the amplitude
ex. If the Electric field
of light doubles, the
intensity quadruples
surfing tip: a wave twice as high has 4x the energy!)
Two-Slit Interference: slit
width vs. laser wavelength
FYI: more diffraction happens if try to force a longer
wavelength (red vs. blue) through a smaller slit
more diffraction means lines are spread out,
not as intense, fewer of them
see web site:
http://phet.colorado.edu/en/simulation/wave-interference
Diffraction Grating
A device with multiple slits
is called a diffraction
grating
The greater the number of
slits the brighter and
narrower the maxima
The greater the number of
slits the greater the
contrast between the
maxima and regions
between them
Single-Slit Interference
Similar math to double slit, but just switch it:
constructive if path = a sinq = ml/2
Destructive if path =a sinq = ml


a is the slit width
Single-Slit Math Proof
Rays 1 and 3 differ in path length by
½ a sinq. So, if this equals ½ l there
will be destructive
interference
In general, the condition
for destructive interference
is a sinq = ml
Interference in Thin Films
Iridescent butterfly
http://www.microscopy-uk.org.uk
Interference in 1-2-3 Thin Film
1-2-3 means the refractive index
keeps increasing as the light penetrates
n=1 (air)
n=2 (film)
n=3 (main substance or substrate)
(not an example: soap bubbles, glass/air/glass wedge)
Interference in 1-2-3 Thin Film
Math: use the wavelength in the film:
If is the wavelength in air
then f = / in the film
n=1 (air)
n=2 (film)
n=3 (main substance or substrate)
Interference in 1-2-3 Thin Film
Same as double slit interference:
Bright , constructive if path = 1 wavelength
Only trick: two reflection so the film
thickness is only ½ wavelength
A
d
thin film
B
Interference in 1-2-3 Thin Film
example: for bright constructive reflection
if start with 400 nm light, n= 2 for film,
then wave = 200nm in the film
and the thickness is half of that
lair = 400nm
lfilm= 200 nm
d = ½ wave = 100nm
(d=1/4 wave = 50nm if want dark)
A
d
B
“staggered”Thin Films
Staggered means the refractive index of the film is largest
(opposite physics: d= ½ wavelength is darkest)
n=1 (air)
n=3 (film)
n=2 (main substance or substrate)
(example: soap bubbles, glass/air/glass wedge)
Summary
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Diffraction
 waves bend around edges and objects
 Creates numerous waves for interference
 Limits the size of resolvable objects
Interference
 Constructive or destructive overlap if 2
waves travel a different distance
 Slits, gratings, thin films
 Constructive if path difference is a full wave
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