Physics307L F09:People/Ozaksut/Notebook/070912
Speed of Light
see comment
Photos
Setup
=DAY 1= 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 Oscilloscope showed a maximum amplitude of 100mV.
A few comments from Koch
- 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.
- 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.
- 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.
Notes
--Anne Ozaksut 15:46, 19 September 2007 (EDT) The basic idea of our lab setup 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 clear 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?)) The PMT takes about two nanoseconds to process photons into an electric current.
We want to detect the speed of light, or the distance between our emitter (LED) and detector (PMT) divided by the time between emission by LED and absorption by PMT. We will take multiple measurements at different distances because the speed we measure should be independent of how far apart our apparatuses are. Because we are dealing with very fast moving photons, 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 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 error we might add to the equation. i.e. 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 in air, we need to factor in that time when we add delay cables to our system.
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 something to consider when we figure out where to add delay cables to our system and how long they need to be.
To reiterate: 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 (F=L/4pid^2), the processed PMT current will have a larger amplitude. This 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 triggering amplitude sooner. To reduce this systematic error, we take advantage of the light polarizers attached to the LED and PMT 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 considered eliminating the time-to-amplitude converter (TAC) in addition to the delay box from our system in order to reduce systematic error, but we decided to test the apparatuses during the first half of DAY 2 of the lab, and if the apparatuses worked the way we expected, we would include them in our system. If the apparatuses didn't work correctly, we would hook up the LED output directly to the our oscilloscope with one cable of length L1, and hook up our PMT directly to our oscilloscope with one cable of a greater effective length (factoring in PMT delay), and then try to measure the time between wavefronts on the oscilloscope. This is definitely not ideal though, because our oscilloscope might not be able to make such fast detections very precisely.
DAY 2
--Anne Ozaksut 17:49, 24 September 2007 (EDT) editing notes by --Matthew Depaula 17:27, 19 September 2007 (EDT) The delay box was removed from our setup since last week's lab, so we began today's lab by testing the TAC. We specified a 50mV/ns conversion on the TAC because we knew the total length of our cardboard tube was between 5 and 15 feet, and we would most likely be taking our measurements at small distance increments nearer the PMT in order to get strong signals from the TAC. Therefore, our (delta time)'s would be about 1 ns each, and we could detect 50mV increments well on the oscilloscope. We added a cable to the PMT-oscilloscope connection in order to add the sufficient delay we would have gotten from the delay box. Instead of testing the TAC by taking two PMT-stop measurements at different LED distances (because this would necessitate adjusting the polarizers), we took two PMT-stop measurements at the same LED distance but added a delay cable to the PMT-stop the second time, and measured the difference in TAC amplitude on the oscilloscope. We did get clear TAC signals each time, and we estimated the delay from the cable to be about the same as in air, and the change in measured amplitude on the oscilloscope was reasonable. From this, we concluded that not only was our TAC working correctly, but our LED signal and PMT signal were both strong and both of these were setup correctly. --Anne Ozaksut 17:49, 24 September 2007 (EDT)In retrospect, if we were to really test the TAC, we would need to know the resistance of the cables we were using. We are using a significant amount of cable in our system, and because we are trying to measure the speed of light in a distance of between 5 and 15 feet, and we have more than 15 feet of cable on either end of our system, and more than that, we have different lengths of cable on either end, even a speed of propagation in the cable as close to c as 5c/6 would significantly alter our data. Also, there would not be any experimental error in factoring in that property because it is a fixed property of the cable, printed on the side of the cord.
Data
We start by connecting the LED to the start port on the TAC and the PMT to the stop port. We connect the TAC to Channel 1 on the oscilloscope, and because we have to maintain constant PMT amp, we use a T-connector on the TAC stop and attach a cable to the oscilloscope, so that we may watch both the PMT and the TAC signal simultaneouly. Although we added a delay to the PMT-to-oscilloscope, it doesn't matter, because we only care about the amplitude. 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 to obtain the following values of TAC amp at different distances:
- 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.
