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Microwave ExperimentsMicrowave ExperimentsFred, Geoff, Lise,and PhilFred, Geoff, Lise,and Phil
Intensity vs. AngleIntensity vs. Angle
Meter (*1) for Horn Source Spread - Probe
-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
-60 -40 -20 0 20 40 60
Angle (Degrees)
Me
ter
(*1)
S
Probe
Basic OpticsBasic Optics
ReflectionReflection– AnglesAngles– Standing WavesStanding Waves
Speed of light: c=Speed of light: c==(freq*(x/nodes)*2)=(freq*(x/nodes)*2) 10.5 ± .1 Ghz10.5 ± .1 Ghz -> -> 3.01E8±.03E8 m/s 3.01E8±.03E8 m/s (typical)(typical)
Angle of Incidence vs. Angle of Reflection
y = 1.0007x - 2.0397R2 = 0.991
0
20
40
60
80
100
0 50 100Incidence Angle (Degrees)
Reflected
Expected
Linear(Reflected)
MS S
Probe: CountNodes in x
x
IntensityIntensity
Point Source: I~1/rPoint Source: I~1/r22
Our Source: I~1/rOur Source: I~1/r
Meter vs. Distance y = 42.393x + 106.07R2 = 0.9614
0
1000
2000
3000
4000
5000
0 20 40 60 80 100 120
R (cm)
r
MS
Refraction Through a PrismRefraction Through a Prism
Use prismUse prism See handout for experiment diagramSee handout for experiment diagram Measure the angle of maximum intensityMeasure the angle of maximum intensity Using this angle and Snell’s Law, Using this angle and Snell’s Law,
calculate the index of refraction of the calculate the index of refraction of the PrismPrism
n = 1.46n = 1.46
PolarizationPolarization
Polarization: Direction of E-fieldPolarization: Direction of E-field Our source and receiver are polarizedOur source and receiver are polarized
– Only projection of E onto polarization of Only projection of E onto polarization of receiver is detected: Ereceiver is detected: Ereceivedreceived~ cos (~ cos ())
Intensity ~ cos Intensity ~ cos 22(())Meter vs. Source Angle
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 50 100 150 200
Angle (Degrees)
Meter (M)Cos^2(Receiver)
Source Polarization
ReceivedSignal
Receiver Polarization
S M
InterferenceInterference
Path DifferencePath Difference– Wave is Wave is f(kx-f(kx-t)t)– Implies Phase Diff.Implies Phase Diff.
=k=k= (2= (2//) f (z/d)=f sin() f (z/d)=f sin())
Effect of Effect of – E~sin(E~sin(kx-kx-t-.5 kt-.5 k) + ) + sin(sin(kx-kx-t+.5 kt+.5 k) = ) =
22sin(sin(kx-kx-t) cos(.5 kt) cos(.5 k))– I~EI~E22
– I~ cosI~ cos22(.5 k(.5 k) = cos) = cos22(.5 k (.5 k f sin(f sin())))
d
f
z
d>>f -> sin()->tan()So = f (z/d)
Double Slit InterferenceDouble Slit Interference Diffraction EffectsDiffraction Effects
– Intensity from each source varies as Intensity from each source varies as sinsin22(()/)/22, where , where =.5 k w sin(=.5 k w sin(), w=slit ), w=slit widthwidth
– So I~ sinSo I~ sin22(.5k (.5k sin(sin() w) w) cos) cos22(.5k (.5k sin(sin() f) f) /(.5 ) /(.5 k k sin(sin() w) w))22
PredictionPrediction– Black: DiffractionBlack: Diffraction– Blue: Diff. + InterferenceBlue: Diff. + Interference
I
f = 2 w
Double Slit ResultsDouble Slit Results
ResultsResults– Envelope and InterferenceEnvelope and Interference– Limit of Resolution of Angle?Limit of Resolution of Angle?
Meter for Double Slit Interference
-0.5
0
0.5
1
1.5
2
2.5
3
-100 -50 0 50 100
Phi (Degrees)
M
S
MirrorExtension
Single Slit DiffractionSingle Slit Diffraction
Used various slit widths and measured Used various slit widths and measured intensity verses angleintensity verses angle
sin(sin() = n) = n/a
S
MirrorExtension M
a
Single Slit DiffractionSingle Slit Diffractionslit width = 7
0
5
10
15
20
25
30
35
-15 5 25 45 65 85
angle (degrees)
inte
ns
ity
(mA
)
slit width = 13
0
5
10
15
20
25
30
-15 5 25 45 65 85
angle (degrees)
inte
ns
ity
(mA
)
slit width = 3
0
5
10
15
20
25
30
-15 5 25 45 65 85
angle (degrees)
inte
nsi
ty (
mA
)
Lloyd’s MirrorLloyd’s Mirror PremisePremise
– Two ways to reach Two ways to reach detectordetector
Off of mirror or straight lineOff of mirror or straight line
– Path difference implies Path difference implies interferenceinterference
2*(Distance Between 2*(Distance Between Maxima)=Maxima)=
ResultsResults– Wavelength:Wavelength:
2.5 ± .7 cm2.5 ± .7 cm
– c=2.6E8 m/s ± .3E8 m/sc=2.6E8 m/s ± .3E8 m/s
Meter vs. Mirror Separation
0.300.350.400.450.500.550.60
0.0 5.0 10.0 15.0 20.0 25.0
Mirror Separation (cm)
Met
er (
*30)
S M
Fabry-Perot InterferometerFabry-Perot Interferometer
Changing the interference pattern Changing the interference pattern between two partial reflectors allows us between two partial reflectors allows us to measure the wavelength.to measure the wavelength.
See handout for experiment diagramSee handout for experiment diagram (d2 – d1)/M = (d2 – d1)/M = We measured We measured = 2.62 = 2.62 0.1 and and
= 3 = 3 0.1
Michelson Interferometer
Setup– Beam Splitter– Path Difference->Interference
Results– Wavelength=
S
M
Fiber OpticsFiber Optics
Using tube filled with styrene pellets, we Using tube filled with styrene pellets, we noticed higher transmission levelsnoticed higher transmission levels
Although very sensitive to positioning, Although very sensitive to positioning, the signal was rather constant with the signal was rather constant with different curvaturesdifferent curvatures
Bragg DiffractionBragg Diffraction Bragg’s law give us a way to measure Bragg’s law give us a way to measure
distances between crystal planesdistances between crystal planes d sind sin = n = n /2 where d is the distance /2 where d is the distance
between crystal planesbetween crystal planes
http://www.physics.sfsu.edu/~bland/courses/490/labs/d2/braggthy.html
Bragg Diffraction
-2
0
2
4
6
8
10
0 10 20 30 40 50
grazing angle (degrees)
Me
ter
(*1)
Frustrated Total Internal Frustrated Total Internal ReflectionReflection
SetupSetup Is there any transmission to 2?Is there any transmission to 2?
S
M
12
Meter vs. prism spearation
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
-5 0 5 10 15 20
Prism Separation (cm)
Me
ter
(*33
)
LensesLenses
meter vs. distance
0
0.05
0.1
0.15
0.2
0.25
0.3
0 10 20 30 40 50 60
position (cm)
me
ter
rea
din
g (
*30)
-3 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 375
77
79
81
83
Meter (*1)
Parallel Position (cm)
Perpendicular Position (cm)
-3 -1.5 -0.5 0.5 1.5 2.5
75
79
83
00.050.10.150.2
0.25
0.3
0.35
Meter (*1)
Parallel Position (cm)
Perpendicular Position (cm)
S