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