Faraday Rotation by Teachspin: Experiments

Faraday Rotation

Faraday Rotation This experiment is appropriate for sophomore, junior, or senior students taking physics. The more advanced students can be challenged to measure small Verdet constants in liquid as well as solid samples. They can also study the theoretical model that Van Baak presents. This "simple" experiment has some wonderful surprises. We guarantee that!

The angle of rotation (α) of the plane of polarization of a light wave for a transparent material of length l in a magnetic field B is given by: α = νlB

The symbol ν is defined as the Verdet constant. For the SF-59 glass rod sold with the TeachSpin apparatus, the Verdet constant for 650 nm light is 23 rad/Tm.

The “standard” strategy for measuring this rotation is to place a linear polarizer on each end of the solenoid containing the transparent material and cross them at 90°. The light source (laser in our case) is at one end and a detector is at the opposite end. With the magnetic field off and the polarizers “crossed” (at 90° to one another) there is “extinction,” giving no (or very small) signal output from the detector. Putting current through the solenoid creates a magnetic field parallel to the light beam. This field produces a rotation of the polarization of the light which increases the light at the detector.

The polarizer in front of the detector is now rotated until extinction is again achieved. The angle of rotation of the polarizer is measured. This rotation angle can be measured as a function of magnetic field, length of sample, and wavelength of light. It depends on all three.

Although finding the angle of rotation by recreating “extinction” is conceptually straight forward, it is a very poor experimental strategy (as the student can discover and as we realized when developing this unit). First of all, for small angle Faraday rotation, the change in optical transmissions is zero to the first order when the polarizers are set at 90°. The maximum change in transmission, for a given small change in the angle of polarization, occurs when the polarizers are arranged at 45°. It is therefore more effective to set the polarizers at 45°, determine the transmission, apply the magnetic field and rotate the polarizers to return the transmission to the initial level. The analysis and experimental measurement of the optimum arrangement of the polarizers is a good exercise for the students. It will give them better insights into both these measurements and the calculus of differentials.

Fig. 2: Intensity Change as a function of angle for a coil current of 1 ampere.

TeachSpin’s Signal Processor / Lock-In Amplifier (or any commercial lock-in) can be used with the FR1-A to measure extremely small Faraday Rotations in a variety of materials. In these experiments an AC magnetic field is used so that the Faraday rotation is “coded” (modulated) at the AC frequency. Students can easily observe tiny rotations with this setup as well as easily determine the “best” relative angle of the two polarizers to observe the small rotation. They can compare these measurements with their theoretical analysis.