(4-29) em waves
TRANSCRIPT
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Physics 104
Lecture 12
Electromagnetic Waves(Interference & Diffraction)
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Communiversity
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Princeton Nursery SchoolMay 5th
Liberty Science CenterMay 11th
Foundation AcademyMay 12th
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Final Exam Announcement
Friday, May 16th
1:30pm-4:30pm
McDonnell A01, A02 and Jadwin A10
Closed book, Closed notes No calculators or electronic devices
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Remember:
Exam 4 is a take-home (45min.)available onlinestarting at noon on Friday May 2nd.
Due by NEXT Friday May 9that noonuse the
PHY 104 return box in Jadwin Hall on the 1st Floor
near the Entrance
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Superposition Principle
Superposition principle states that the
total electric or magnetic field due to two
sources is the sum of the individual
fields:
EM waves consist of propagating E andB fields.
The E and B fields of two sources add
according to the superposition principle.
E total = E1 + E2 +...
Btotal =
B1 +
B2 +...
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Interfering waves withunequal amplitudes: EB=.9EA
ConstructiveA and B in phase Wave A
Wave B
Wave A+B
DestructiveA and B outof phase 1/2
cycle (180o)
Wave A
Wave B
Wave A+B
t
t
E
E
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Coherence
Two or more waves can produce interference effects.
To get a consistent interference effect, the two
waves must be coherent.
Coherent means that the phase difference between the
waves is constant.
Two incandescent light bulbs do not produce coherent
waves, since the light in each is produced by atoms
radiating independently and randomly.6
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Question
150 nm
nm600=
Q1. Is the interference between
the reflected beams:
A) Constructive
B) Destructive
C) Somewhere in between
D) Not enough information
given.
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Producing coherenceand phase shifts.
Single light source,
split into two beams.
Single light source,reflected off two surfaces.
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Speed of light intransparent media v = c/n
Speed of light in vacuum = c = 0f0
Speed of light in media is less than c:
vc
n
c
n index of refraction : n > 1
vc
n0f0
nf
But frequency depends on the oscillating charthat produced the EM wave.
f f0
0n 9
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Phase shift due to reflections
Reflections can produce phase shifts:
1) Reflection from less dense medium off more densemedium (hard reflection):
phase shift is equivalent to /
2) Reflections from more dense medium off less dense
medium (soft reflection):
phase shift is 0
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Thin film interference
Example:
n1
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Q2. What is condition fordestructive interference?
n1< n2> n3
Ray 1 has phase shift of /.
Ray 2 has no phase shift.
(A) 2 twater = 0,
2 twater = / / water= /n
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Thi Fil I f i
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Thin-Film Interference insoap bubble
Gravity makes the
bubble thin at the top
and thick at the bottom.
Why is it black at the
top?
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Phasing in an Antenna Array
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Huygens Principle
Each point on a
primary waveform
serves as the sourceof spherical
secondary wavelets
that advance with a
speed and frequencyequal to those of the
primary wave.
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2-slit interference waterwaves
By passing water waves
through narrow slits,
one generates sphericalwavelets emanating
from each slit.
The two wavelets then
interfere.
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Interference-path difference
Path length differences
are a common source of
phase shifts.
Phase difference: 2 r
wherer = path difference
and= wavelength 17
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Interference fromTwo (Very Narrow) Slits
md =sin
)(sin2
1+= md
Interference maxima:
Interference minima:18
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Microwave zone plate
In this demo you see vividly how microwaves can
interfere, depending on their path difference.
Each zone plate corresponds to a different path length
from the source to the detector.
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Microwave zone plate demo
The zone plate with some
of the zones removed.The microwave detector is
shown in front of the plate.
The source is behind the plate.
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Zone plate
Source Detector
L1L1
L2 L2
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Zone plate condition forinterference
Source Detector
L1 L1L2 L2
Constructive: 2L1-2L2=
Destructive: 2L1- 2L2= /
/
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Single Slit Diffraction
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Pin Hole Camera (Airy Spot)
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Point
Source
Pin
Hole
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What about a solidsphere?
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Q3. What will happen if we shine laser light
at a solid sphere?
a) Will create a solid black shadow
b) Some light will appear on the screen directly
on the axis of the laser beam
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Poisson Point
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Point
Source
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Poisson Point
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Single Slit Diffraction
L
y=tan
=sina
But since
sintan
a
Ly
=
The narrower the slit,
the wider the diffraction
pattern.
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D bl lit I t f
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Double-slit Interferencewith Diffraction
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In general, one observes the combined effects of two-slit
and single-slit interference. Here d = 5a.
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Diffraction Grating (N slits)
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Atomic Line Spectra
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Single Photon Counting
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3000 photons 10,000 photons
100,000 photons 1M photons
4 M photons 30 M photons
How aboutInterference?