lab 3 physics

8/11/2019 Lab 3 Physics

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Propagation of Light: Diffraction

One of the biggest things that most people do not quite understandabout light is its wave properties. The fact that it behaves as a wave and

is subjected to phenomenon known as diffraction can be hard to grasp.

Since light always seems to go straight its hard to imagine that it can

bend around corners or spread out upon reaching an obstacle or small

opening.

In this lab we studied the concept of beam divergence as a function

of distance then we collimated this beam to a point that we sent into aseries of diffraction gratings that split this beam into a different patterns

of intensities and such. We were able to measure the intensities as a

function of position and thus able to compare the graphs of the

intensities of certain gratings with each other. We also noted how these

patterns changed (if ever so slightly) upon changing the angle of

incidence on the gratings themselves and lastly we were able to

determine the spacing on an object like a CD that can be used asdiffraction grating.


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Introduction:

The Experiment:

Preliminary Measurements

Resistance () Voltage (mV) Uncertainty (mV) Vi/Vo

3 0.529 0.06 N/A

10 1.76 0.2 3.32703

30 5.47 0.4 3.1079

100 17.51 2.0 3.2011

300 52.55 4.0 3.00114

1000 174.28 3.0 3.31646

3000 355.8 1.0 2.04154

10000 385.6 0.4 1.08375

30000 392.25 0.6 1.01725

100000 393.03 0.4 1.00199

300000 393.53 0.5 1.00127

0

50

100

150

200

250

300

350

400

450

1 10 100 1000 10000 100000 1000000

SignalVoltage(mV)

Resistance (k)

Signal Change as a Function of Resistance


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Resistance () Voltage (mV) Uncertainty (mV) Vi/Vo

2000 317.06 4.0 N/A

4000 368.96 4.0 1.16369

6000 379.34 3.0 1.02813

8000 384.04 1.0 1.01239

300

320

340

360

380

400

1000 2000 3000 4000 5000 6000 7000 8000 9000

SignalVoltage(mV)

Resistance (k)

Signal Voltage vs Resistance

180

200

220

240

260

280

300

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8Sign

alVoltage(mV)

Resistance (k)

Signal Voltage vs Resistance


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Modulating the Light Beam

-

Resistance of 300

Polarizer Angle () Multimeter Voltage (mV) Oscilloscope Voltage (mV)

0 17.321 36.2

28 13.061 28.2

44 9.03 19.4

50 7.088 15.8

56 5.099 11.5

65 3.044 7.4

70 2.061 4.3

76 1.034 3.3

77 0.824 1.7

80 0.549 1.24

84 0.261 0.765

86 0.134 0.419

90 0.094 0.198

Polarizer Angle () Multimeter Voltage (mV) Oscilloscope Voltage (mV)

0 17.288 35.1

0.1

5.1

10.1

15.1

20.1

25.1

30.1

35.1

0 10 20 30 40 50 60 70 80 90

SignalVoltage(m

V)

Polarizer Angle ()

Signal vs Polarizer Angle

Multimeter

Voltage

(mV)

Oscilloscope

Voltage

(mV)

cos()^2


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28 13.102 26.2

44 8.857 18.1

50 7.028 14.2

56 5.215 10.7

65 3.148 6.6

70 2.054 4.4

76 1.024 2.2

77 0.803 1.8

80 0.51 1.22

84 0.236 0.705

86 0.115 0.43

90 0.082 0.21

- Multimeter Error

Voltage 1 (mV) Voltage 2 (mV) Percent Error Uncertainty (mV)

17.321 17.288 0.190520178 0.03

13.061 13.102 0.313911645 0.04

9.03 8.857 1.915836102 0.17

7.088 7.028 0.846501129 0.06

5.099 5.215 2.274955874 0.12

-4

1

6

11

16

21

26

31

36

0 10 20 30 40 50 60 70 80 90

SignalVoltage(mV)

Polarizer Angle ()


Multimeter

Voltage

(mV)

OscilloscopeVoltage

(mV)


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3.044 3.148 3.416557162 0.10

2.061 2.054 0.339640951 0.01

1.034 1.024 0.967117988 0.01

0.824 0.803 2.548543689 0.02

0.549 0.51 7.103825137 0.04

0.261 0.236 9.578544061 0.03

0.134 0.115 0.372622083 0

0.094 0.082 12.76595745 0.01

-

Oscilloscope Error

Voltage 1 (mV) Voltage 2 (mV) Percent Error Uncertainty (mV)

36.2 35.1 3.038674033 1.01

28.2 26.2 7.092198582 2.00

19.4 18.1 6.701030928 1.30

15.8 14.2 10.12658228 1.60

11.5 10.7 6.956521739 0.80

7.4 6.6 10.81081081 0.80

4.3 4.4 2.325581395 0.103.3 2.2 33.33333333 1.10

1.7 1.8 5.882352941 0.10

1.24 1.22 1.612903226 0.02

0.765 0.705 7.843137255 0.06

0.419 0.43 2.625298329 0.01

0.198 0.21 6.060606061 0.01

- Resistance of 2000


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Angle () Voltage Multi. (mV) Uncertainty (mV) Voltage Oscill.(mV) Uncertainty (mV)2

0 162.8 2.0 328 4.0

27 140.14 4.0 284 2.0

36 120.06 3.0 244 3.0

43 100 1.0 202 2.0

49 80.06 4.0 164 4.0

55 60.03 2.0 124 2.0

61 40 3.0 82 3.0

71 20 1.0 41 4.0

76 9.82 0.5 20 1.0

80 5.04 0.4 11 0.7

84 2.44 0.6 5 0.886 1.25 0.2 3 0.1

90 0.84 0.3 1 0.3

- Resistance 5000

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90

SignalVoltage(m

V)

Polarizer Angle ()


Voltage

Multi.

(mV)

Voltage

Oscil.(mV)


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Polarizer Angle () Voltage Multi. (mV) Uncertainty (mV) Voltage Oscill.(mV) Uncertainty (mV)

0 185.68 3.0 372 2.0

46 160 1.0 325 3.0

53 140.32 3.0 284 3.0

57 120.5 2.0 254 1.0

60 100.11 2.0 205 2.0

66 69.84 1.0 144 1.0

75 29.83 1.0 63 1.0

79 15.16 0.7 33 0.8

82 7.41 0.8 16 0.5

85 3.1 0.2 7 0.2

87 1.56 0.25 4 0.1

90 0.87 0.05 2 0.05

Calibrating the Polarizing Attenuator

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90

SignalVoltage(mV)

Polarizer Angle ()


Voltage

Multi. (mV)

Voltage

Oscill.(mV)


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cos()^2 Voltage 1 (mV) Extinction Ratio 1 Voltage 2 (mV) Extinction Ratio 2

1 17.321 1 17.288 1

0.779596 13.061 0.75406 13.102 0.75787

0.51745 9.03 0.52133 8.857 0.51232

0.413176 7.088 0.40921 7.028 0.40652

0.312697 5.099 0.29438 5.215 0.301650.178606 3.044 0.17574 3.148 0.18209

0.116978 2.061 0.11899 2.054 0.11881

0.058526 1.034 0.0597 1.024 0.05923

0.050603 0.824 0.04757 0.803 0.04645

0.030154 0.549 0.0317 0.51 0.0295

0.010926 0.261 0.01507 0.236 0.01365

0.04866 0.134 0.00774 0.115 0.00665

0 0.094 0.00543 0.082 0.00474

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

ExtinctionRatio(T/T

max)

Cos () ^2

Cos () ^2 vs Extinction Ratio

Extinction

Ratio 1

Extinction

Ratio 2


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cos()^2 Voltage 1 (mV)

Extinction Ratio

1 Voltage 2 (mV)

Extinction Ratio

2

1 36.2 1 35.1 1

0.779596 28.2 0.77901 26.2 0.74644

0.51745 19.4 0.53591 18.1 0.51567

0.413176 15.8 0.43646 14.2 0.404560.312697 11.5 0.31768 10.7 0.30484

0.178606 7.4 0.20442 6.6 0.18803

0.116978 4.3 0.11878 4.4 0.12536

0.058526 3.3 0.09116 2.2 0.06268

0.050603 1.7 0.04696 1.8 0.05128

0.030154 1.24 0.03425 1.22 0.03476

0.010926 0.765 0.02113 0.705 0.02009

0.04866 0.419 0.01157 0.43 0.01225

0 0.198 0.00547 0.21 0.00598

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

ExtinctionRatio(T/T

max

Cos () ^2

Cos () ^2 vs Extinction Ratio

Extinc

tion

Ratio

1

Extinc

tion

Ratio

2


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Resistance () Max. Intensity (mV) Min. Intensity (mV) Background (mV) Extinction Ratio

100 17.77 0.021 0.0047 0.001182

200 35.62 0.046 0.014 0.001291

500 39 0.102 0.036 0.002615

800 142.3 0.18 0.06 0.001265

1000 177.16 0.19 0.15 0.001072

0.0016

0.008

0.04

0.2

1

5

25

125

0 200 400 600 800 1000 1200

SignalVoltage(m

V)

Resistance (k)

Signal vs Resistance

Max. Intensity (mV)

Min. Intensity (mV)

Background (mV)

lab 3 physics

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