Faraday Rotation - University of Missouri

Physics 425L
Optics Laboratory
The Faraday Effect
Introduction
In 1845 Michael Faraday suspected that there were connections between light and electromagnetism.
He conducted a series of experiments which 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 Wikipaedia
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 β is given by β = νBd where ν is the Verdet
constant, B is the strength of the magnetic field and d is the thickness of the material.
In 1897 H. Becquerel found the empirical formula for the Verdet constant
€
e
dn
ν=
λ
2mc dλ
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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 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 with an attached voltmeter, and a rod of Schott SF-59 glass as a sample. These devices have
the following parameters.
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Total length of the solenoid: 20 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
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.
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1. You will be measuring the Verdet constant of the Schott SF-59 glass rod. This rod is very
fragile and VERY EXPENSIVE. It has already been placed in the center of the solenoid. Do
not remove it or otherwise disturb it!
2. Assemble the laser, the analyzer ring, and the detector as shown in the photograph.
3. Remove the soft wire connecting the plugs of the laser cable and immediately plug them into
the rear of the laser power supply. Save the soft wire. You will reconnect it to the plugs when
you disassemble the apparatus. The wire prevents static electricity from damaging the laser.
4. Plug the solenoid cables into the solenoid power supply.
5. 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.)
6. 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.
7. Make sure that the alignment plug is in the laser end of the solenoid.
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8. Connect the power cord of the laser power supply to the wall AC power. Align the laser beam
so that the it falls on the center of the alignment plug. Place a white card in front of the
detector. Remove the alignment plug
9. Now align the laser beam so that it falls on the center of the shadow of the detector aperture.
10. Turn the voltage setting knob of the solenoid power supply counterclockwise to maximum and
the current setting knob clockwise to minimum. Plug in the solenoid power supply and adjust
the current to 3 amperes. Turn off the power supply.
11. Turn on the multimeter and set it to DC millivolts. Remove the card from in front of the
detector.
Procedure
Part A
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 five replications.
Part B
1. Rotate the polarizer to 45 degrees from the maximum obtained in Part A. Repeat the steps of
Part A to obtain five replications starting from the 45 degree setting instead of the maximum.
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
• After 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. You might think of other variations.
• Why are we using SF-59 as opposed to another glass?
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