Transcript Wave Superposition Constructive Interference 2 or more waves

Superposition of Waves
• Principle of superposition: The displacement of
a medium caused by two or more waves is the
algebraic sum of each wave.
• Waves pass each other so the original wave
continues unaltered.
• Interference is the result of the superposition of
two or more waves.
Wave Superposition
Constructive
Interference
2 or more
waves adding
together to
make a larger
wave
Wave Superposition
The blue wave below represents the sum of the 2 other waves.
Constructive
Destructive
Interference
Interference
Antinodes
Nodes
Wave Superposition
Student Excel SHM lab plus superposition
• Wave front can be created by connecting
Sound
waves
travel
in
all
directions
similar point on the waves


Double Slit
Light Rays
L5LL1 2
0
 L
L6L2
3
4
L5
L64L2
LL3 1
2
d
1
d
0
d
dSin  m
Double Slit
4
d
3
d
2
d
1
d
0
d
1
2d
m
Sin 
d
3
2d
5
2d
7
2d

2
L1  0  L2
L5

2
2
d
L3  1  L4
LL16
L2
L3 L5  2L4  L6
2
1
d
0
d
Single Slit
0
d
4
d
3
d
2
d
1
d
1
2d
3
2d
5
2d
7
2d
dSin  (m  12 )
d
dSin  m
xm
tan  
L
xm
d
 m
L

m L
xm 
d
o
For small angles (θ<15 )
xm
sin   tan  
L
L
xm
Waves at Boundaries
Low Density Medium
High Density Medium
Note: Both amplitudes get smaller
Reflected pulse
Transmitted pulse
Waves at Boundaries
High Density Medium
Low Density Medium
Transmitted pulse
Reflected pulse
Does the frequency of a wave change as it moves into a new medium?
Does the velocity of a wave change as it moves into a new medium?
c
c
n1
n1
n2
n2
v 
v 
Does the wavelength of a wave change as it moves into a new medium?
v f
2 f  nc
1 f  nc
2
1
f  2cn2  2cn2
n11
2 
n2
Thin film Interference
Soap bubble
Part of the incident light is reflected on the top surface
Part of the light is transmitted and is reflected at the lower
surface
The lower wave travels the extra distance ABC
If the path length ABC is a multiple of λ there will
constructive interference
C
A
Oil
B
Water
Part of Incident wave is reflected and part
is transmitted
Reflected wave: from less dense to more dense
is reflected 180 degrees out of phase
T

4
• In the time it takes the incident wave to travel a distance
T (1/4λ), the reflected wave also travels 1/4λ.
• In the time it takes the transmitted wave to travel back to
the original boundary, the reflected wave also travels
1/4 λ
Identify the phase for wave 1
Inverting or Non-inverting
Identify the path length and phase for wave 2
1  
2  (
2T

)2  
C
A
Oil
B
Water
For constructive interference the phase difference must
be a multiple of 2π
For destructive interference the phase difference must be
an odd multiple of π
2  1  (m  0)2
(m  1, 2,3...)
2  1  (m  12 )2
(m  0,1,3...)
1  
2  (
2T

)2  
C
A
Oil
B
Water
A laser shines on a pair of identical glass microscope slides that form
a very narrow edge. The waves reflected from the top and the
bottom slide interfere. What is the interference pattern from top
view?
1  0
2  (
2T

)2  
As you move closer to the left edge, T goes to zero.
What is the phase difference between the two waves at the edge?
1  0
Destructive interference
2T
22 ( 0 )2
  

Polarization
 Sometimes it is desirable to block all but one
orientation of incoming light.
 For instance, you can wear polarizing sun glasses in
order to reduce glare.
 Think “Stars and Bars” in order to understand how
polarization works.
Stars and Bars
 Imagine you are behind bars. A Ninja comes along and
decides to throw stars at you. Are you safe from his stars?
 As you saw, the first two stars would not hit you. Why?
 Were you safe from the third star? Why?
 The first star was horizontally polarized. The second was
“other” polarized. Therefore, they could not make it through
the vertical bars.
 The third star was vertically
polarized; therefore, it was
able to pass through the
vertical bars and nail you!
Cross Polarization
 Watch the wave below. What is its polarization?
Why?
 Would it be able to pass through if we rotated one
polarizer by 90 degrees? Why?
 Explain what happened.
Polarization
 Watch the animations below. Which wave is
horizontally polarized? Why?
 Which one is vertically polarized? Why?