Malus’ Law
Purpose: To measure the variation of the transmission of radio waves through 2 polarizers as the orientation angle between them is changed. This is a quantitative continuation of the “Polarized or Unpolarized” activity and should be done in this order.
http://en.wikipedia.org/wiki/Malus%27s_law#Malus.27_law_and_other_properties
Student Info:
1) Designed for Physics (Grades 11/12)
2) Prior Knowledge: “Polarized or Unpolarized” Activity, Graphing of Trig. Functions
3) Suggested Website:
http://scholar.hw.ac.uk/site/physics/topic6.html
Teacher Info:
1) Prior Knowledge: Polarization Activity and Graphing of Cosine Function
2) Vocabulary: Malus’ Law, intensity, electric field and crossed polarizers
3) Suggested Website:
http://en.wikipedia.org/wiki/Malus’s_law
Time Required:
1) Setup 20 min 2) Activity / Lab 20 min
3) Data Analysis 30 min 4) Discussion / Wrap Up 20 min
Materials Needed:
1) VSRT System (See Appendix I)
2) Single CFL set 2 feet from detectors next to each other (~2.5 inches center to center)
3) Polarizers (~2mm wide / ~2mm spacing) made from metallic tape (Cu or Al)
and Polarizer Holder marked at 10° Increments (or mounted to a protractor)
Procedure:
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Start VSRT System and verify operation without polarizers.
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Place both polarizers in the same orientation and verify signal level above 100K.
* Note: If the CFL/LNBF distance is changed, the signal level can be
adjusted near 100K, so the output is roughly the % transmission.
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Rotate one polarizer relative to the other (in front of separate detectors)
in 10° increments and record the Power in column #2 in the table below.
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Repeat until the polarizers are oriented at 90° (crossed) to each other.
Data Table:
Angle
[ ° ]
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* Power
[ K ]
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% Transmission
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Theoretical Transmission [ %] )
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% Difference
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0
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10
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20
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30
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40
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50
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60
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70
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80
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90
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Average % Diff. =
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* - See Basic VSRT Operation for discussion of Power [K]
Calculations:
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Calculate the % Transmission by dividing the Power at a certain angle by the Power at 0°. { Note: The results should be less than 100% }
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Compute the theoretical transmission by taking the cosine of the angle, then squaring it and multiplying by 100 for a percentage;
i.e. – Trans(theo) = cos ² *100%
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Calculate the % Difference = (% Transmission – Theoretical Transmission)
Theoretical Transmission
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Average the % Difference and place result in the shaded box on lower right.
Graphing:
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Setup the graph for the % Transmission (0% to 100%) vs. Angle (0° to 90°) adjusting the scale of the axes to maximize the size of the graph.
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Graph the measured transmission (2nd column) vs. angle and label it.
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Graph the theoretical transmission (3rd column) vs. angle and label it.
Questions:
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Is the graph of % Transmission vs. Angle linear? Why or Why Not?
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For which angles is there good agreement (<5% difference) between the measured transmission and the theoretical transmissions?
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Where is the % Transmission most sensitive to small changes in angle (few °)?
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Where is the % Transmission least sensitive to small changes in angle (few°)?
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Explain the answers for questions #3 & #4 based on the shape of the curves.
Additional Activities:
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Vary the polarizer slit widths and spacings to check these effects.
Note: The slit/spacing width needs to be ~ 1/10th the wavelength (~2.5mm).
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Try both polarizers in front of either LNBF. Does this also work? Why?
Sample Results:
Malus’ Law using 12GHz radio waves
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Right Polarizer - Horizontal
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I(max) =
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160
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Angle [°]
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Signal
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Fit=I(max)*cos²
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0
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162
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160
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10
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159
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155
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20
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126
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141
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30
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109
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120
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40
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86
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94
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50
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60
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66
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60
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55
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40
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70
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31
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19
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80
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18
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5
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90
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7
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0
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