Today 1/22
Light Interference: read Text 27.1,2
HW: 1/22 Handout
“Interference (more than one frequency)”
due Friday 1/24
Today:
Questions? Example Problem
Young’s Double Slit experiment
Peer Guidance Center
Begins Wed afternoon Wit 209
A little review
Waves
Two types, transverse and longitudinal
Wave speed depends only on the medium
Period, Frequency, Amplitude--just like SHM
v = f
Interference
Superposition-- adding waves
It’s all about Path Length Difference, , and..
Sources “in” or “out” of “Phase”
Example:
What is the lowest frequency
of sound that will produce
destructive interference here?
PL1 = 2.0m
Two sources
emit in phase
PL2 = 2.2m
Young’s Double Slit (like two
speakers)
Wave
crests
c
d
c
d
c
d
c
d
c
Wave
troughs
Single
frequency
source

In phase at
the slits
Dark and
bright
“fringes” on
a screen
Young’s Double Slit (like two
speakers)
Wave
crests
Wave
troughs
Single
frequency
source

In phase at
the slits
Does the
pattern
expand or
contract
when:
-the slits
move closer
together?
-the
wavelength
increases?
Always true for any interference
problem
Sources
In Phase:
Constructive if PLD = m
Destructive if PLD = (m + 1/2)
PLD = “path length difference”
Sources Out Constructive if PLD = (m + 1/2)
Destructive if PLD = m
of Phase:
m = 0, 1, 2, 3,… (I used “n” the other day)
Two slit geometry (screen far away)
PLD = d sin (d = slit separation)
d

d
PLD
(close

enough)

Screen
Two slit geometry
PDL = d sin (d = slit separation)
d

Screen
d sin = m constructive interference
d sin = (m+ 1/2) destructive interference
When the sources (slits) are “in phase”
A simpler picture
Two slits very close together (d)
Screen
very

far
away
d sin = m constructive interference (L)
d sin = (m+ 1/2) destructive interference
When the sources (slits) and “in phase”
The m’s
0 “zeroth order” fringe
1 “first order” fringe
2 “second order” fringe
d sin = m
d sin = (m+ 1/2)
m=2
m=1
m=1
m=0
m=0
m=0
m=1
m=1
m=2
Distance between fringes, y
tan  = y/L

L
m=2
m=1
m=1
y m=0
m=0
m=0
m=1
m=1
m=2
Example:
m=2
m=1
m=1
m=0
5mm

m=0
2m
m=0
m=1
m=1
Light with a wavelength of 500 nm passes
m=2
through two closely spaced slits and forms an
interference pattern on a screen 2m away. The distance
between the central maximum and the first order bright
fringe is 5 mm. What is the slit spacing? The light is in phase
at the slits.
tan  = 5mm / 2m
 = 0.14°
d sin  = m = 1(500 nm)
d = 0.2 mm
Example:
Twin radio antennas broadcast in phase at a frequency of
93.7 MHz. Your antenna is located 150 m from one tower and
158 m from the other. How is the reception, good or bad?
vwave = c = 3108 m/s
PLD = 8 m
v=f
m
0
1
2
3
4
Does this equal some m or some (m + 1/2) ?
 = 3.2m
m
0
3.2m
6.4m
9.6m
12.8m
Make two lists
(m + 1/2)
1.6m
4.8m
8.0m
11.2m
14.4m
The condition is met for
destructive interference.
Reception at that
location is bad.