Interference in Waves

1
Interference in Waves

• SPH4U Grade 12 Physics
• Unit 2

2
Tribal Challenge!

• A ray of light travels from glass into water.
  Find the angle of refraction in water if the
  angle of incidence in glass is 30º.
• (nwater 1.33, and nglass 1.5)
• 3 points first team correct
• 1 point every correct answer after that

3
Tribal Challenge!

• A ray of light travels from glass into
  water. Find the angle of refraction in water if
  the angle of incidence in glass is 30º.
• (nwater 1.33, and nglass 1.5)
• Solution

Therefore, the angle of refraction in water is
34.3º.
4
Review

• When two waves cross paths and become
  superimposed, they interact in different ways.
  This interaction is called interference.
• Waves that build each other up have constructive
  interference.
• Waves that cancel each other out have destructive
  interference.

5
Review
Constructive Interference
Destructive Interference
6
Two Point Interference Pattern

• When we have two identical point sources that are
  side by side, in phase, and have identical
  frequencies, we can analyse the interference
  pattern that is produced to learn more about the
  waves.
• ripple tank simulation of two point source
  pattern http//www.falstad.com/ripple/

7
Two Point Interference Pattern
Antinodes
Nodes
Sources
8
Two Point Interference Pattern
Thin line trough

• In the diagram, crests are represented by thick
  lines and troughs are represented by thin lines.
  We get constructive interference then whenever a
  thick line meets thick line, or when a thin line
  meets a thin line. This constructive
  interference causes antinodes, shown by the red
  dots.

Thick line crest
9
Two Point Interference Pattern

• Destructive interference occurs whenever a thick
  line meets a thin line. These points form nodes,
  which are represented by a blue dot. The nodes
  and antinodes appear to stand still which makes
  this a standing wave pattern.

10
Two Point Interference Pattern

• The antinodes and nodes seem to all be located on
  lines. These are called antinodal lines and
  nodal lines, respectively. There is a central
  line in the pattern, the line that bisects the
  line segment drawn between the two sources. This
  is called the central antinodal line.

Central antinodal line
11
Two Point Interference Pattern

• The antinodes and nodes seem to all be located on
  lines. These are called antinodal lines and
  nodal lines, respectively. There is a central
  line in the pattern, the line that bisects the
  line segment drawn between the two sources. This
  is called the central antinodal line.

Central antinodal line
12
Two Point Interference Pattern

• The number of nodal lines increases when you do
  any of the following
• Increase frequency of the sources
• Decrease the wavelength of the waves
• Increase separation between the sources

13
Mathematical Analysis
1st nodal line, n1

• If we have a two point source interference
  pattern like this one we can analyse it
  mathematically in order to determine the
  wavelength of the waves.

2nd nodal line, n1
n3
The nodal lines are measured from the central
antinodal line outward.
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Mathematical Analysis

• Lets put a point P1 somewhere on the first nodal
  line. We can measure the path length between
  each source and this point. These are the blue
  and red lines.

A
P1
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Mathematical Analysis

• The path difference, ?s is the difference between
  the length of the blue and red lines. On the
  first nodal line, the path difference equals ½ ?.
  

P1
?s P1S1 P1S2 ½ ?
This equation works for points that are on the
first nodal line only
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Mathematical Analysis

• In general, we can find the path difference for a
  point on any nodal line using the equation below

P1
?s P1S1 P1S2 (n-½) ?
This equation works for points that are on the
nth nodal line, only if the wavelengths are large
enough or if the point P is not too far away from
the sources.
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Mathematical Analysis
P1

• If the point P1 is very far away compared to the
  distance between the sources, we can use this
  equation

?n
d
? wavelength n nth nodal line d
distance between S1 and S2 ?n angle between the
central line and the nth nodal line
18
Mathematical Analysis
P1
xn

• Note that due to trigonometry, you can also find
  ?n using basic trigonometry

L
?n
d
? wavelength n nth nodal line d
distance between S1 and S2 ?n angle between the
central line and the nth nodal line
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Mathematical Analysis
P1
xn

• This of course implies the following equation to
  be true

L
?n
d
? wavelength n nth nodal line d
distance between S1 and S2 ?n angle between the
central line and the nth nodal line
20
Example 1

• Two identical point sources 5.0cm apart,
  operating in phase at a frequency of 8.0Hz,
  generate an interference pattern in a ripple
  tank. A certain point on the first nodal line is
  located 10.0cm from one source and 11.0cm from
  the other. What is the wavelength of the waves?

21
Example 1

• Two identical point sources 5.0cm apart,
  operating in phase at a frequency of 8.0Hz,
  generate an interference pattern in a ripple
  tank. A certain point on the first nodal line is
  located 10.0cm from one source and 11.0cm from
  the other. What is the wavelength of the waves?

22
Youngs Double Slit Experiment

• Youngs Double Slit experiment, conducted at the
  end of the 1700s, is famous because it showed
  that light created an interference pattern that
  resembled the interference of water waves in a
  ripple tank.

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Youngs Double Slit Experiment

• Videos
• Derek Owens http//www.youtube.com/watch?vAMBcg
  VlamoU
• Dr. Quantum
• http//www.youtube.com/watch?vQ1YqgPAtzho

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Youngs Double Slit Experiment

• The experiment showed that light coming from the
  two slits interfered with itself to create
  constructive and destructive interference.

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Youngs Double Slit Experiment

• Where we have constructive interference we get
  brighter bands of light, and where there is
  destructive interference we get bands of
  darkness.

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Youngs Double Slit Experiment

• People had tried to do this experiment prior to
  Young, but their attempts had failed because the
  sources they had used were too far apart, and
  were out of phase with each other.

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Youngs Double Slit Experiment

• Young fixed these problems by using one source,
  the sun, and then splitting that light using a
  screen to make two sources. He also made the
  holes for S1 and S2 very close together. This
  allowed an interference pattern to be visible
  even though the wavelength of light is very
  small. (about 400-800 nano meters).

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Youngs Double Slit Experiment

• The fact that light passing through the two slits
  acted like point sources that created circular
  waves, was further evidence of diffraction
  (bending) of light.
• The experiment as a whole was strong evidence of
  the wave nature of light. At this point the wave
  theory could explain all properties of light
  except for propagation through a vacuum.

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Youngs Double Slit Experiment

• The experiment also provided a way to measure the
  wavelength of light, using the same equations we
  just derived for a two point source interference
  pattern.
• In youngs experiment, a nth order dark fringe
  would be at a location

30
Youngs Double Slit Experiment

• We can also use the following equation to
  calculate the wavelength of light in Youngs
  experiment
• ?x is the distance between adjacent dark lines
• L is the distance from the two sources of light
  to the screen
• d is the distance between the two sources of
  light
• ? is the wavelength of light

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Example 2

• You are measuring the wavelength of light from a
  certain single-colour source. You direct the
  light through two slits with a separation of
  0.15mm, and an interference pattern is created on
  a screen 3.0m away. You find the distance
  between the first and the eighth consecutive dark
  lines to be 8.0cm. At what wavelength is your
  source radiating?

32
Example 2

• You are measuring the wavelength of light from a
  certain single-colour source. You direct the
  light through two slits with a separation of
  0.15mm, and an interference pattern is created on
  a screen 3.0m away. You find the distance
  between the first and the eighth consecutive dark
  lines to be 8.0cm. At what wavelength is your
  source radiating?

33
Homework

• Prepare for tomorrows lab
• Read Section 9.3 9.5
• Make additional notes to supplement the lesson
  notes. Complete the following questions
• What is Poissons Bright spot? How did its
  discovery help to solidify the scientific view
  that light behaved like a wave?
• Pg. 468 2,3
• Pg. 484 2, 4, 5