Physics307L:People/Ozaksut/Notebook/070912

Speed of Light

Speed of Light Lab

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Steven J. Koch 02:20, 13 September 2007 (EDT):Great work in the lab today. This is a pretty complicated setup (given the simple concept), especially since none of us really have used the NIM-bin stuff before. I think you ran out of time before recording the final stuff at the end, and it would be important to record those kind of notes right away. I will sketch out a few of them. I do realize that it's tough to take notes while you are racing to get the experiment working at all, but it's a good habit to get into. In general, the description you do have is great.

--Matthew Depaula 17:27, 19 September 2007 (EDT) DAY 2 We began the lab by testing the delay due to the cables. We hooked the LED up to the start on the TAC and then split the signal with a T-connector to the stop on the TAC. We split the stop on the TAC with a cable to CH2 and then we hooked the TAC up to CH1. Because we connected the cable from the stop to the oscilloscope rather than from the start, we are relying only on the change in the TAC amplitude to determine the delay time of the cable. We used the cursor to measure the first input amplitude of the 3.5 ft cable, and we read 280mV. Then, we added cable and took a second measurement: total cable length 5.5 ft, amplitude 580mV. so the difference in cable length is 60cm, and the change in amplitude is 300mV.

We estimated the delay to be about 1ns per foot, and we got clear signals on the oscilloscope when we did this: the LED gives clear signals, and the TAC can interpret clear signals in the start and stop inputs. Then, we wanted to test our PMT signal, so we did the same thing: we weren't sure if the signal was stable. Turns out it was stable enough.

Data

We start by attaching all cables correctly as demonstrated by the Lab Manual. The LED was connected to the start port on the TAC, and the PMT cable connected to the stop port. We have the TAC signal entering Channel 1 on the oscillioscope. We have a T-connector on the stop, so that we may watch both the PMT and the TAC signal simultaneouly. The purpose of this is to obtain stability in the amplitude shown by the PMT. We have the PMT amplitude maximized at -3.72V, and will keep it at this value to obtain an accurate time walk. We used the measure function for the following values.

• Trial 1: 2.32+_ .004 V (We are not going to use this value)
• Trial 1(b): 4.88 +_ .04 V (TAC scale {TACs} 50ns); Meter Stick Reads 0.6 cm
• Trial 2: 4.84 +_ .04 V ;Meter Stick Reads 20 cm (Delta of 19.4cm)
• Trial 3: 4.60 +_ .04 V ;meter stick reads 60 cm (Delta of 40 cm)
• Trial 4: 4.36 +_ .04 V ;Meter stick reads 110 cm (Delta of 50 cm)
• Trial 5: 4.08 +_ .04 V ;Meter stick reads 140 cm (Delta of 30 cm) (4.2 +_ .04 V)

We tried running the PMT signal through a 5ns delay and noticed a net change of 1.6 V in the TAC output. With a 10 ns delay we recorded a value of 7.88 V. No delay is 6.04 V, 5 ns delay is 6.92 V, close to a 1 V net change, which is what we would expect based on our TAC settings.

Setup

We connected the green Light Emitting Diode (LED light) to a power supply at 200V, and also to the "start" input on the Time to Amplitude Converter (TAC). Then, we connected the Photo Multiplier Tube (light detector) located at the end of a dark tube to reduce ambient light, from the anode to a delay thing and then to the "stop" input on the TAC. The polarizer on the front of the LED lets us maintain a constant amplitude (340mV) of light as we move the LED closer to the detector. We wanted to measure the LED pulse and detected pulse independently first, so we connected the LED directly to the oscilloscope and the detector to the delay and then to the oscilloscope. We kept getting fuzzy signals or weird bumps in the signals, so we added terminators to the end of the cords to try to reduce the resonance. We first had our LED set at 9m from the detector, and when we pushed it in 2m, we noticed the signal from the detector became sharper.

We decided to start from scratch to obtain more precise measurements. This time we pulled the LED to the outer edge of the tube without exposing the PMT to ambient light. We re-polarized the detector until the Oscillioscope showed a maximum amplitude of 100mV.

--Anne Ozaksut 15:46, 19 September 2007 (EDT) The basic idea of our lab is we have an LED which emits green light pulses at a frequency proportional to the amount of power we use to power it, and a Photo Multiplier Tube (PMT) which detects the light pulses. A photomultiplier tube takes incoming photons and allows them to excite material inside the tube which will knock out electrons. These electrons will knock out more electrons in the next dynode (block of material), which will knock out more electrons in the next dynode etc. The anode at the end of the chain of dynodes collects all the multiplied electrons, and this is the output current. It’s a negative current pulse because I=Q/t and Q is a bunch of negatively charged electrons hitting the anode per time. The PMT multiplies at a constant rate, so we know that the output current is directly proportional to the amount of incoming light it receives. This is the useful information we get from the PMT. The reason we don’t just detect the light signal is… we need to use an oscilloscope to make our measurements and the photons from the LED might not be detectable as a wave because the LED is far from the scope and there’s a lot of resonance or photon absorption in the cardboard tube?? The PMT just makes the wave clearer to detect? Anyway, we want to detect the speed of light, or the time it takes our LED pulse to reach our detector divided by the time between emission (by LED) and absorption (by PMT). We are dealing with really fast moving stuff though, so we need to get rid of all the systematic error we can. First, we attach a cable of length L1 from the oscilloscope to the emitter. When the emitter emits a light pulse into the vacuum which is our cardboard tube, the emitter will also emit an electric pulse into the fixed-length cord which resists current a little more than vacuum resists current. This is a constant value we add to the equation. (so, even if our cord length = the distance from emitter to detector, the detector would detect a signal before the oscilloscope detects the emission.) Secondly, it takes our PMT a couple nanoseconds to work its magic, and since light travels at approximately 1 nanosecond per foot, we need to factor in that time when we calculate the speed of light. This is also a constant value we add to our equation. Thirdly, our oscilloscope isn’t connected directly to the PMT- it is connected by another cable composed of the same material as the first cord, of fixed length L2. This is also a constant value that we will add to the equation. (so, if the LED emits light at t=0, and the PMT receives light at t=t1=distance travelled times the speed of light, our oscilloscope will read t to be t1 + a couple nanoseconds + the length of the cord L2*the speed of propagation in the cord.) (also, if the LED emits light at t=0, our oscilloscope will read t=0+the length of the cord L1*the speed of EM propagation in the cord.) The idea is we will measure the difference in time between the emission and detection of the light pulse and divide it by the distance we separate the emitter and detector by, and repeat this many times at different distances, and we’ll plot the data and the slope of the curve should be the speed of light. Because we’re using an oscilloscope which has to trigger the pulse waves in order to tell us anything, we need to make sure we maintain a constant # of photons hitting the PMT at any distance, because if we have detect a huge # of photons at a short distance (L=E/4piR^3), our detected wave will have a huger amplitude, which is not a problem in itself, except that the wave will be triggered sooner because triggering occurs at a fixed value of amplitude, and therefore the huger amp wave grows to max amp faster and will hit that fixed amp sooner. To reduce this systematic error, we take advantage of the light polarizer attached to the LED by rotating the detector with respect to the polarized light in order to maintain a constant amplitude (constant # of photons detected by the PMT per time) no matter the distance of the emitter to the detector. We WOULD use a time-to-amplitude converter (TAC) to help us analyze the signals, but this would add a lot of connectors which we think might add some undefined systematic or mechanical error to our experiment that we can do without. Instead of hooking up the systematically delayed emitter cable to the TAC start and the systematically delayed detector cable +added fixed delay (through the delay machine, because our emitter cable is longer than all the detector cable/PMT delay combined) to the TAC stop and allowing the TAC to emit a signal whose amplitude is proportional to the time difference between the start and stop, and then measure the TAC amplitude when we do our measurements at all kinds of distances and then plot the results to find the speed of light, we would rather just hook up the systematically delayed emitter cable to the oscilloscope CH1 and the systematically delayed detector cable + added fixed delay to CH2, and then measure the time between peak amplitudes of each individual pulse and plot that vs our distances to determine the speed of light. Additionally, we don’t trust the delay machine because of last week’s results, so we are going to add that additional fixed delay on the emitter’s side by just lengthening the cord a sufficient amount.

A few comments from Koch

1. It's not clear the delay module works. The signal straight out of PMT looks smooth, but running it through the delay module makes it wiggly as all hell.
2. As a default, if Monday people can't make more progress, some estimations of pulse delays can be made with the oscilloscope alone. However, because of the limited bandwidth of the scope, I'm not sure this is possible. Maybe if we are clever.
3. We also couldn't figure out how to get the TAC to work. It didn't seem to be responding to the "stop" signal at all (possibly because the delay module is not working)? This did seem to be working, though, for Antonio and Brian.