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Chapter15
Section 1 Interference
Objectives
• Describe how light waves interfere with each other to produce bright and
dark fringes.
• Identify the conditions required for interference to occur.
• Predict the location of interference fringes using the equation for double-slit
interference.
What is interference
• Wave interference is the phenomenon that occurs when two waves meet
while traveling along the same medium. The interference of waves causes the
medium to take on a shape that results from the net effect of the two
individual waves upon the particles of the medium
• Interference takes place only between waves with the same wavelength. A
light source that has a single wavelength is called monochromatic.
Types of wave interference
• This type of interference is sometimes called constructive interference.
Constructive interference is a type of interference that occurs at any
location along the medium where the two interfering waves have a
displacement in the same direction. In this case, both waves have an upward
displacement; consequently, the medium has an upward displacement that is
greater than the displacement of the two interfering pulses. Constructive
interference is observed at any location where the two interfering waves are
displaced upward. But it is also observed when both interfering waves are
displaced downward
Constructive interference example
In this case, a sine pulse with a maximum displacement of -1 unit
(negative means a downward displacement) interferes with a sine
pulse with a maximum displacement of -1 unit. These two pulses
are drawn in red and blue. The resulting shape of the medium is a
sine pulse with a maximum displacement
Types of Interference
• Destructive interference is a type of interference that occurs at any
location along the medium where the two interfering waves have a
displacement in the opposite direction. For instance, when a sine pulse with a
maximum displacement of +1 unit meets a sine pulse with a maximum
displacement of -1 unit, destructive interference occurs. This is depicted in
the diagram below.
Example of destructive interference
Combining Light Waves
• Waves must have a constant phase difference for interference to be observed.
• Coherence is the correlation between the phases of two or more waves.
– Sources of light for which the phase difference is constant are said to be
coherent.
– Sources of light for which the phase difference is not constant are said to
be incoherent.
Demonstrating Interference
• Interference can be demonstrated by passing light through two narrow
parallel slits.
• If monochromatic light is used, the light from the two slits produces a series
of bright and dark parallel bands, or fringes, on a viewing screen.
Conditions for interference
Demonstrating Interference
• The location of interference fringes can be predicted.
• The path difference is the difference in the distance traveled by two beams
when they are scattered in the same direction from different points.
• The path difference equals
dsin.
Demonstrating
Demonstrating interference
• The number assigned to interference fringes with respect to the central bright fringe
is called the order number. The order number is represented by the symbol m.
• The central bright fringe at q = 0 (m = 0) is called the zeroth-order maximum, or the
central maximum.
• The first maximum on either side of the central maximum (m = 1) is called the firstorder maximum.
Equations
• Equation for constructive interference
d sin  = ±m m = 0, 1, 2, 3, …
The path difference between two waves =
an integer multiple of the wavelength
• Equation for destructive interference
d sin  = ±(m + 1/2) m = 0, 1, 2, 3, …
The path difference between two waves =
an odd number of half wavelength
Interference example
• The distance between the two slits is 0.030 mm. The second-order bright fringe (m = 2) is
measured on a viewing screen at an angle of 2.15º from the central maximum. Determine
the wavelength of the light.
Solution
Interference
1. Define
Given: d = 3.0  10–5 m
m=2
 = 2.15º
Unknown:  = ?
Diagram:
Solution
Interference
2. Plan
Choose an equation or situation: Use the equation for constructive
interference.
d sin  = m
Rearrange the equation to isolate the unknown:
d sin

m
Solution
3. Calculate
Substitute the values into the equation and solve:
3.0  10


–5

m  sin2.15º 
2
  5.6  10 –7 m  5.6  102 nm
  5.6  102 nm
Problem
Two slits are 0.05 m apart. A laser of
wavelength 633nm is incident to the slits.
A screen is placed 2m from the slits.
a) Calculate the position of the first and second bright fringe.
b) What is the maximum number of destructive interference spots there can be on
either side of the central maximum?
videos
• Let’s watch some videos
Homework
• DO problems 1-4 in your book pg. 567
Closure
• Today we learned about interference
• Next class we are going to continue with chapter 15