Transcript Wave Interactions - University of South Florida

Wave Interactions
Because everything on the E & M
Spectrum is a wave, it shares all
the wave properties defined in the:
“Wave Properties”
Section of this Module.
Significant Wave Interactions
Superposition
Phase angle/shift
Doppler Effect
Interference
Diffraction
Interference
Single slit applet
Interference
Single slit
Double slit
Multiple slit
Thin film
Interference
Single slit process
Any wave being made to force it’s
way around an obstacle will
disrupt it’s own wave form.
Interference
Single slit process
As a result the wave divides into
many wavelets of equal
wavelength as it passes the
obstruction.
Interference
Single slit process
Interference
Single slit process
If we follow the path of two rays to
a single point of intersection we
will find interference has taken
place.
Interference
Interference
Single slit process
As you know there are two kinds of
interference.
Constructive
Destructive
Interference
Single slit process
Constructive interference will
occur when the two waves arrive
at the common point in phase.
Interference
Single slit process
Waves in phase are at the same
point and are matching in their
displacement.
I.e. both up or both down.
Interference
Interference
Single slit process
Destructive interference will occur
when the two waves arrive at the
common point out phase.
Interference
Single slit process
Waves out of phase are at the
same point and are opposite in
their displacement.
I.e. one up and the other down.
Interference
Interference
Single slit process
As a result of both types of
interference we get the distinctive
pattern of Bright and Dark patches.
These patterns are referred to as
Fringe Patterns or Interference
patterns.
Interference
Interference
Single slit process
The Bright patches are
Constructive and are called
Maxima.
Interference
Single slit process
The Dark patches are Destructive
and are called Minima.
Interference
Interference
Single slit process
The Pattern turns out to be a
alternating Maxima and Minima
each separated by ½ a
wavelength.
Interference
Single slit process
This ½ a wavelength or (multiple)
is called the path difference for
Destructive Interference.

 n
2
Interference
Single slit process
When the path difference a full
wavelength or (multiple)
Constructive Interference occurs.
  n
Interference
Single slit process
There also exists a ray that goes
straight through the center of the
slit undisturbed.
Interference
Interference
Single slit process
If we measure on the fringe
pattern from the center out to any
integer number Minima this
distance is significant.
Interference
Interference
Single slit process
This distance is is called the
dispersion distance we refer to it
as Y in all our diagrams.
Interference
Y
Interference
Single slit process
This dispersion distance depends
on an integer number we call n.
Can can range from 0 ,1,2,3…
Interference
n=2
n=1
Y
n=-1
n=-2
Interference
Single slit process
The distance to the screen where
the pattern shows up is also
significant to us.
Interference
Single slit process
This distance is called L in all our
diagrams and equations.
Interference
n=2
n=1
Y
n=-1
L
n=-2
Interference
Single slit process
The width of the slit is also
significant to our calculations.
Interference
Single slit process
This width is called w in all our
diagrams and equations.
Interference
n=2
n=1
Y
w
n=-1
L
n=-2
Interference
Single slit process
The Angle of the dispersion is also
significant to our calculations.
Interference

Single slit process
This angle is called
in all our
diagrams and equations.
Interference
n=2
n=1

w
Y
n=-1
L
n=-2
Interference
Single slit process
Finally we have everything we
need to make a calculation.
Slit Width (w)
Length to pattern (L)
Integer number (n)
Wavelength ( )
Angle ( )

Interference
n=2
n=1

w
Y
n=-1
L
n=-2
Interference
Single slit process
Our calculation is for the
wavelength.
yw

 w sin 
nL
Interference
Single slit process
Or our calculation is for the Path
Difference.
w
  sin 
2
Interference
Single slit process
Or our calculation is for the
position of the Minima.
nL
y
w
Interference
Single slit applet
Diffraction
Double slit
Diffraction
Double slit process
Any wave being made to force it’s
way around two obstacles will
disrupt it’s own wave form at least
twice.
Diffraction
Double slit process
As a result the wave divides into
many wavelets of equal
wavelength as it passes through
each of the obstructions.
Diffraction
Double slit process
Diffraction
Double slit process
If we follow the path of any two
rays to a single point of
intersection we will find
interference has taken place.
Diffraction
Diffraction
Double slit process
As you know there are two kinds of
interference.
Constructive
Destructive
Diffraction
Double slit process
Constructive interference will
occur when the two waves arrive
at the common point in phase.
Diffraction
Double slit process
Waves in phase are at the same
point and are matching in their
displacement.
I.e. both up or both down.
Diffraction
Diffraction
Double slit process
Destructive interference will occur
when the two waves arrive at the
common point out phase.
Diffraction
Double slit process
Waves out of phase are at the
same point and are opposite in
their displacement.
I.e. one up and the other down.
Diffraction
Diffraction
Double slit process
As a result of both types of
interference we get the distinctive
pattern of Bright and Dark patches.
These patterns are referred to as
Fringe Patterns or Interference
patterns.
Diffraction
Diffraction
Double slit process
The Bright patches are
Constructive and are called
Maxima.
Diffraction
Double slit process
The Dark patches are Destructive
and are called Minima.
Diffraction
Diffraction
Double slit process
The Pattern turns out to be a
alternating Maxima and Minima
each separated by ½ a
wavelength.
Diffraction
Double slit process
This ½ a wavelength or (multiple)
is called the path difference for
Destructive Interference.

 n
2
Diffraction
Double slit process
When the path difference a full
wavelength or (multiple)
Constructive Interference occurs.
  n
Diffraction
Double slit process
There also exists a ray that goes
straight through the center of each
slit undisturbed.
Diffraction
Diffraction
Double slit process
If we measure on the fringe
pattern from the center out to any
integer number Maxima this
distance is significant.
Diffraction
Diffraction
Double slit process
This distance is is called the
dispersion distance we refer to it
as Y in all our diagrams.
Diffraction
Y
Diffraction
Double slit process
This dispersion distance depends
on an integer number we call n.
Can can range from 0 ,1,2,3…
Diffraction
n=2
n=1
Y
n=0
n=1
n=2
Diffraction
Double slit process
The distance to the screen where
the pattern shows up is also
significant to us.
Diffraction
Double slit process
This distance is called L in all our
diagrams and equations.
Diffraction
n=2
n=1
Y
n=0
L
n=1
n=2
Diffraction
Double slit process
The distance of the slit separation
is also significant to our
calculations.
Diffraction
Double slit process
This distance is called d in all our
diagrams and equations.
Diffraction
n=2
n=1
Y
n=0
d
L
n=1
n=2
Diffraction
Double slit process
The Angle of the dispersion is also
significant to our calculations.
Diffraction

Double slit process
This angle is called
in all our
diagrams and equations.
Diffraction
n=2
n=1
Y
d
n=0

L
n=1
n=2
Diffraction
Double slit process
Finally we have everything we
need to make a calculation.
Slit Separation (d)
Length to pattern (L)
Integer number (n)
Wavelength ( )
Angle ( )

Diffraction
n=2
n=1
Y
d
n=0

L
n=1
n=2
Diffraction
Double slit
Diffraction
Double slit process
Our calculation is for the
wavelength.
yd

 d sin 
nL
Diffraction
Double slit process
Or our calculation is for the Path
Difference for constructive is.
  d sin   n
Diffraction
Double slit process
Or our calculation is for the Path
Difference for destructive is.
1
  d sin   (n   )
2
Diffraction
Double slit process
Or our calculation is for the
position of the Minima.
nL
y
d
Diffraction
Double slit
Interference & Diffraction
Multiple slit
Interference
Thin film
Interference, cont.
Constructive
Interference, cont.
Destructive
Interference, cont.
Wave cancellation


Sound
Light
Interference, cont.
Wave cancellation

Sound
Interference, cont.
Wave cancellation

Light
Diffraction & Interference of light,
cont
Geometry of the solution
Formulas…
Patterns
Path difference
Phase difference
Wavelength dependency
Diffraction & Interference of light,
cont
Geometry of the solution
Diffraction & Interference of light,
cont
Formulas…
Diffraction & Interference of light,
cont
Patterns
Diffraction & Interference of light,
cont
Path difference
Diffraction & Interference of light,
cont
Phase difference
Diffraction & Interference of light,
cont
Wavelength dependency