Download Physics 476LW Advanced Physics Laboratory The Faraday Effect

Physics 476LW
Advanced Physics Laboratory
The Faraday Effect
Introduction
In 1845 Michael Faraday suspected that there were connections between light and electromagnetism.
He conducted a series of experiments that he hoped would demonstrate that in fact light and
electromagnetic radiation were related. Experiments with static electricity failed but when he passed
light through flint glass in a magnetic field he discovered that the plane of linearly polarized light was
rotated (see fig. 1). The purpose of this experiment is to measure the Faraday rotation of light under
various conditions.
Figure 1 from Wikipedia
Theory
Read the relevant section in an optics textbook (e.g. Introduction to Optics by Pedrotti, Pedrotti and
Pedrotti) and research other sources of information concerning the theory of Faraday rotation.
The rotation due to a magnetic field may be expressed in terms of e/m, the ratio of the charge of an
electron to its mass. According to the theory of Lorentz, an electron moving in its orbit about an atomic
nucleus will change its frequency of revolution which in turn leads to a rotation of the plane of
polarized light through the affected object. The angle of rotation, β in radians is given by β = νΒd
where ν is the Verdet constant, B is the strength of the magnetic field in millitesla and d is the thickness
of the material in centimeters.
In 1897 H. Becquerel found the empirical formula for the Verdet constant
ν=
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dn
λ
2mc dλ
Advanced Physics Laboratory - Faraday Rotation
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€
that Larmor derived theoretically in 1900. These facts allow us to calculate e/m by using the Verdet
constant measured in this experiment.
The Experiment
Apparatus
The apparatus for these experiments consist of a Hall effect probe, a fixed wavelength polarized laser
light source, a power supply for the laser, a magnetic solenoid, a power supply for the solenoid, an
analyzing polarizer, a detector and voltmeter, and a rod of Schott SF-59 glass as a sample. These
devices have the following parameters.
•
•
•
•
•
Total length of the solenoid and mounts: 20.5 cm
DC resistance of the solenoid: 2.6 ohm
B field near the center of the solenoid: 0.0111 T/A
Length, d, of the glass rod: 10 cm
Wavelength of the laser light: 650 nm
Setup
Figure 2. Faraday Rotation Apparatus
There are a number of delicate items involved in this experiment. Be sure that you read and understand
all of the instructions for this experiment before proceeding.
1. To assure ourselves that the magnetic field of the solenoid is nearly uniform over the range
where the sample is to be positioned we first map the magnetic field in the solenoid. Turn the
voltage setting knob of the solenoid power supply clockwise to maximum and the current
setting knob counterclockwise to minimum. Plug in the solenoid power supply and adjust the
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2.
3.
4.
5.
current to 3 amperes. Turn off the power supply. Plug the power supply into the solenoid and
turn it back on. Using the Hall effect probe take voltage reading at 1 cm intervals for the entire
length of the solenoid. The Hall probe has a calibration factor of 0.0089 T/A. Use this to map
the magnetic field strength of the solenoid. You might take measurements from each end and
average the two readings. Turn off the power supply.
The Schott SF-59 glass rod is very fragile and VERY EXPENSIVE. Handle it with care.
Carefully load the rod in its foam sleeve into the solenoid and center it using the padded rod.
Assemble the laser, the analyzer ring, and the detector as shown in the photograph.
Remove the wire connecting the plugs of the laser cable and immediately plug them into the
rear of the laser power supply. Save the wire. You will reconnect it to the plugs when you
disassemble the apparatus. The wire prevents static electricity from damaging the laser.
Plug the solenoid cables into the solenoid power supply.
Figure 3. Plug to meter from detector
6. Plug the detector cables into the multimeter. The plug with the small protrusion is the ground
and it goes into the COM socket. (See figure above.)
7. Set the load resistor switch on the detector to 1. WARNING: Do NOT set the load resistor
switch to any setting other than 1. Doing so can burn out the detector.
8. Make sure that the alignment plug is in the laser end of the solenoid.
9. Connect the power cord of the laser power supply to the wall AC power. Align the laser beam
so that it falls on the center of the alignment plug. Place a white card in front of the detector.
Remove the alignment plug
10. Now align the laser beam so that it falls on the center of the shadow of the detector aperture.
11. Turn on the multimeter and set it to DC millivolts. Remove the card from in front of the
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detector.
Procedure
Figure 4. Removal of alignment plug.
Because ambient light entering the detector will skew the results it is best to cover the detector and
analyzer with the black shroud. The analyzer can be adjusted through the opening in the side of the
shroud.
Part A - Maximum Extinction Method
1. Rotate the analyzing polarizer until the multimeter shows zero voltage. Note the angle reading
on the polarizer.
2. Turn on the power supply.
3. The voltage reading should rise. The change will be small. Rotate the analyzing polarizer until
the voltage reading returns to zero. Note the angle.
4. Turn off the power supply.
5. Repeat Experiment steps 1, 2, 3, and 4 four times for a total of ten replications.
Part B - Return to Fixed Intensity Method
1. Rotate the polarizer to 45 degrees from the maximum extinction obtained in Part A. For this
experiment repeat the steps of Part A but now adjust the analyzer angle so that the detector
output returns to the value found before the magnetic field is turned on. Repeat this ten times.
Analysis
1. One of the two methods of collecting data is better. Which one is it and why?
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2. Use your data to calculate the Verdet constant of the SF-59 glass rod.
3. Use your data to calculate the ratio e/m for the electron. You will need the SF-59 information
at the end of this lab manual.
Extensions
• When you have finished the above, if you have time and interest, try other variations of the
experiment. For example, you might use different currents, or use the maximum voltage reading
instead of zero. If you vary the current over 3 A, you will need to take care that the solenoid does not
overheat. You might think of other variations.
• Why are we using SF-59 as opposed to another glass?
For the SF-59 glass rod sold with the TeachSpin apparatus, the Verdet constant for 650 nm light is 23
rad/Tm.
Schott SF-59 Glass Data
Wavelength (nm)
Refractive Index at Wavelength
404.7
435.8
480
486.1
546.1
587.6
589.3
632.8
643.8
656.3
706.5
852.1
1014
1060
1529.6
1970.1
2325.4
2.0426
2.01557
1.98899
1.98604
1.96349
1.955
1.9521
1.94324
1.94131
1.93927
1.93218
1.91856
1.90974
1.90788
1.89599
1.88887
1.8835
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