Transcript Course overview and Interference

Chapter 35: Interference
Water waves
General
Goals for Chapter 35
• To consider interference of waves in space
• To analyze two-source interference of
light
• To calculate the intensity of interference
patterns
• To understand interference in thin films
• To use interference to measure extremely
small distances
Introduction
• Why do soap bubbles
show vibrant color
patterns, even though
soapy water is colorless?
• What causes the
multicolored reflections
from DVDs?
• We will now look at
optical effects, such as
interference, that depend
on the wave nature of
light.
What was the most important discovery in physics this year ?
Two black holes merging 1.3 billion light years away
produce detectable gravitational waves.
What was the most important discovery in physics this year ?
What was the most important discovery in physics this year ?
How can one measure a relative displacement that is
only ~10-18m ?
Ans: Use interference
How will win the Nobel Prize in Physics this year ?
Rainer
Weiss
Kip Thorne
Ron Drever
2015: Takaaki Kajita, Art McDonald (UH affiliate faculty) for
neutrino oscillations. [Hope to mention this topic at the end of
this course in “modern physics”]
Wave fronts from a disturbance
• Figure 35.1 at the right
shows a “snapshot” of
sinusoidal waves spreading
out in all directions from a
source.
• Superposition principle:
When two or more waves
overlap, the resultant
displacement at any instant
is the sum of the
displacements of each of
the individual waves.
Constructive and destructive interference
• Figure 35.2 at the right
shows two coherent wave
sources.
• Constructive interference
occurs when the path
difference is an integral
number of wavelengths.
• Destructive interference
occurs when the path
difference is a half-integral
number of wavelengths.
Reminder
General
Antinodes
Nodes
Interfering Sources
Interfering Sources
Two-source (slit) interference of light
d sin   m (in phase, constructive)
d sin    m  12   (out of phase, destructive)
Notice the hyperbolae
Interference from two slits
•
Projection of two-slit interference onto a screen.
•
The linear dimension of the separation of fringes
depends on the angle and the distance from the
screen.
ym

R
ym
m
 sin  
R
d
m
ym  R
d
tan  
•
Here, R is distance to screen, d is separation of
slits, and m is the “order” of the fringe.
Two-slit interference
• Example 35.1: Given the measurements in the
figure, what is the wavelength of the light?
m
ym  R
d
l = ym d / mR = (9.49 ´10 m)(0.200 ´10 ) / (3)(1.00m)
-3
-9
= 633´10 m = 633nm
-3
Broadcast pattern of a radio station
•
Example 35.2: Radiation pattern of two radio towers, 400 m apart, operating
at 1500 kHz, oscillating in phase. In what directions is the intensity greatest?
8
3´10
m/s
c
l= f =
= 200m
3
1500 ´10 Hz
X
ml m(200m) m
sin(q ) =
=
=
d
400m
2
Þ q = 0, ±30 0 , ±90 0
400m
S1 -------------S2
Broadcast pattern of a radio station
•
Example 35.2: Radiation pattern of two radio towers, 400 m apart, operating
at 1500 kHz, oscillating in phase. In what directions is the intensity greatest?