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 = e 2mc λ dn dλ 8/13/13 Page 1 of 1
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. Setup 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 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 8/13/13 Page 2 of 2
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. 2. 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. 3. Assemble the laser, the analyzer ring, and the detector as shown in the photograph. 4. 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. 5. 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 8/13/13 Page 3 of 3
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? 8/13/13 Page 4 of 4
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 2.0426 435.8 2.01557 480 1.98899 486.1 1.98604 546.1 1.96349 587.6 1.955 589.3 1.9521 632.8 1.94324 643.8 1.94131 656.3 1.93927 706.5 1.93218 852.1 1.91856 1014 1.90974 1060 1.90788 1529.6 1.89599 1970.1 1.88887 2325.4 1.8835 8/13/13 Page 5 of 5