4.1 Alignment & Polarization

1. Turn on the power supply for the laser and set the voltage to about 2.5 V for now.
2. Set the oscilloscope for the expected 0-5 V signal. If you use a large value for sec/div and set the trigger to ‘auto’, the signal from the detector should scroll through the screen.
3. Adjust the position and angle of the laser, solenoid, and detector such that you are getting the maximum voltage output from the detector as measured on the oscilloscope. Your laser beam should be very straight relative to the optical track, with the beam going through the center (or just below the center) of the solenoid and hitting the detector at the center of its lens. You may need to make small adjustments to the angle and position of the detector and/or laser to maximize the signal. If the signal ever goes above 4.5 V, turn down the laser voltage and continue adjusting to reach the maximum signal possible.
4. Add the polarizer before the solenoid. Loosen the screw that holds the polarizer and rotate it (without taking it out of the holder). Does turning it change the signal at the detector? Why or why not? Turn the polarizer until the signal is a maximum. Turn down the diode laser voltage if the signal goes above 4.5 V.
5. Add the second polarizer after the solenoid, set the angle to 0 and rotate the inner ring polarizer until the signal is a minimum (you can zoom in on the scope to make sure it really is the minimum). We’ll say that the polarizer is oriented horizontally. Now ONLY use the outer ring to rotate the polarizer.
6. Check that you see a maximum in the signal at 90, and that the signal at 45 is 1-2 V. In fact, if you smoothly rotate the polarizer while looking at the oscilloscope, you should see a sinusoidal function.

4.2 Malus’ Law

1. Starting from 90, record the detector signal each 5 until about -45 (i.e. the other side of zero). You can use the cursor on the scope or use a small value for sec/div and have the scope display the near-instantaneous detector signal.
2. Plot your data. You don’t have to fit it right now, but it should at least look sinusoidal.
3. If we want a maximum change in polarization in order to get the largest signal possible, what polarization angle should we be starting from?
4. You will use these measurements to determine the fractional change in the signal as a function of polarization angle.

4.3 DC Current

1. CAREFULLY slide the glass rod into the solenoid. DO NOT TOUCH THE ENDS OF THE ROD! Use the cotton swabs to slide the glass rod roughly centered in the solenoid. Look at the beam after the solenoid using a piece of paper to make sure it isn’t hitting the edge of the glass rod. Check that the detector output is around 1-2 V. You may have to adjust the detector position since the laser beam may deflect slightly off the faces of the glass rod.
2. Plug the grey cable from the solenoid into the solenoid DC power supply (red to red and black to black). Add an ammeter to the circuit to precisely monitor the DC current.
3. Set the polarization angle to 45.
4. Record the detector output.  Set the current from the DC power supply to 0-1 A. Record the detector output before and after the current change. Then rotate the polarizer to bring the signal back to its original value. Record the rotated angle and the solenoid current. Take as many points in the 0-1 A range as you think you need. Note that it can be hard to precisely read the angle of the polarizer better than about 0.3 degrees.
5. You will use these measurements and the Malus curve data to determine the Verdet constant of the glass sample.

4.4 AC Current

Take a minute to look at the oscilloscope controls and remind yourself how to trigger the `scope and use the measure and acquire functions.

1. Turn off the solenoid DC power supply. Plug the solenoid into the grey box that outputs the amplified AC current (the box furthest to your right) (red to red and black to black). Add a multimeter in series to measure the AC current. Use the BNC cable to measure the voltage across the solenoid with channel 2 of the oscilloscope AND as the reference signal for the lock-in amplifier.
2. Turn on the function generator. Set the frequency to some prime number between 200 and 250 Hz. Set the amplitude to 50 mVpp (peak-to-peak voltage).
3. Turn on the power supply for the current amplifier. Use the leftmost voltage knob to turn the voltage up to 30 V (DO NOT GO HIGHER THAN THAT!). Do not adjust the current.
4. Connect the output of the detector to channel 1 of the oscilloscope.  Set the oscilloscope to trigger off of channel 2.
5. Slowly increase the amplitude setting of the function generator until it’s at about 450 mV peak to peak. Adjust the oscilloscope settings so that you can see both channel 1 and channel 2. Use as small a V/div as you can for the detector signal so that the amplitude of the oscillations is as large as possible. You can use 50 mV/div or better if your signal is less than 2 V.
6. If the signal is noisy, use the `acquire’ menu on the scope to average many traces together – 64 usually does the trick.
7. Use the `measurement’ menu to determine the mean value of the oscilloscope signal and its peak-to-peak amplitudes.  You are interested in the fractional change in the signal since you are ALWAYS interested in normalizing your data.  And this way you can compare signals measured with different load resistances and to the Malus curve data.
8. Take measurements for as many values of AC current as you need to be confident in a linear fit of the data.  Use as low an AC current as you can while still confidently measuring the amplitude on the scope.
9. Estimate the phase difference between the reference and detector signals.  You will need this value to set up the lock-in amplifier.
10. Disconnect the photodiode and use the multimeter to measure the resistance of the oscilloscope.  Do not change the sensitivity of the oscilloscope, since that changes the internal resistance.

Now for the lock-in amplifier:

1. Measure the internal resistance of the current channel (marked by an `I’) on the lock-in amplifier.  What factor do you expect the signal to decrease by?
2. Take a minute to look at the front panel of the lock-in amplifier and locate the controls and signal displays that you need.
3. Unplug the detector signal from the oscilloscope and plug it into the `I’ input.
4. Adjust the scale of the lock-in amplifier until you aren’t overloaded (OVLD light isn’t red or blinking). Your signal will likely be in the range of 0.1 to 10 mV.
5. Set the timescale of the output filter to something small so that the signal updates quickly. The millisecond range should work well.
6. Hold down the ‘fine’ phase option to vary the phase. You should see the signal increase and decrease as you cycle from -180 to +180 degrees.
7. Now you will find the phase angle at which the reference and detection signals are perfectly out of phase (i.e. 90 apart).  Set the phase of the lock-in to what you measured on the oscilloscope plus 90.  Then make small adjustments to the phase until you have minimized the signal (you will need to increase the sensitivity to be sure you’re really near zero).  Then add back and re-set the sensitivity.  This is the phase you will operate at.  We did all that because it is easier to find a minimum than it is to find a maximum.
8. Increase the amplitude of the output from the function generator to 450 mV.  Record the output signal of the lock-in amplifier. You may need to adjust the sensitivity. Use a relatively long time constant for the filter to remove even more noise – usually 1-3 seconds works well.  Note that the lock-in amplifier is reporting the root-mean-square amplitude.
9. Record the AC current from the multimeter. Note that the multimeter is using root-mean-square as the definition of the amplitude.
10. With those values, you should be able to determine the Verdet constant and see if it agrees with your `scope measurements.

4.5 Liquid Sample

1. Check that the glass cylinder is full of water.  Air bubbles will deflect the laser light and air has a different Verdet constant than water.
2. Carefully use the cotton swab sticks to remove the glass rod from the solenoid and place it in its holder.
3. CAREFULLY slide the glass cylinder holding distilled water into the solenoid. DO NOT TOUCH THE FACES OF THE CYLINDER.
4. You will likely need to adjust the lock-in sensitivity settings, but you should have a decidedly non-zero amplitude measurement.
5. Collect data at various amplitudes from the function generator – enough to be confident in the slope of a resulting linear fit.
6. Collect data at as small an amplitude on the function generator until you can no longer confidently determine the output voltage or you hit 50 mV on the function generator.
7. You can now determine the Verdet constant of water.