User:John Callow/Notebook/Junior Lab 307/2009/11/25

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Speed of light
I worked with Johnny Gonzalez for this lab

Link to my summary

Link to lab manual used

For the experimenter
There is voltages in the range of 1800-2400 to watch out for.

For equipment
The photomultiplier tube will fry if turned on while exposed to room light.

Don't exceed 200v for the LED.

Connect the cables to the correct inputs on the LED.

Equipment
(1) Tektronix TDS 1002 Oscilloscope

(1) Bertran 313B Power Supply

(1) Canberra 2058 Delay Module

(1) Ortec 567 TAC/SCA Module

(1) Harshaw NQ-75 NIM Bin

(1) Harrison Laboratories 6207A Power Supply

(1) Photomultiplier Tube

(1) LED circuit

(several) Long BNC Cables

Note - I forgot to take down the model numbers in lab but I'm pretty sure Tom used the same equipment so copied the numbers down from his lab book here.

Setup
Before turning anything on make sure the photomultiplier tube is not in view of any direct light. For our setup it was safely inside a large cardboard tube. Connect everything together as shown on page 68 of Professor Gold's manual. Turn on the power supply to the PMT set to around 1800 to 2000 V.

The Bertan power supply should be set to 2000 volts and then using the voltage adjust knob may be set up to 2400. The top polarity on this supply should be set to negative.

On the Ortec Time-Amplitude Converter our delay was set to 25 ns with the range set to 50ns and the multiplier to 1. This was probably a bit high but it definitely made sure the start signal from the LED arrived before the PMT stop signal. Changing this value didn't appear to have any effect on our calculating the slope which is what we used to find the speed of light.

The power supply for the LED should be set to 150-200 Vdc, making sure not to go above these values. Ours was set to about 180 volts.

With all of this setup properly the oscilloscope should be showing some readings. We used channel one for measuring the signal from the PMT and channel two for the signal from the TAC. If there is not signal the PMT may be rotated to see if that helps, and also the triggering levels may be changed. It is also helpful to the the oscilloscope to take an average of the signals otherwise they are too jumpy to read. I'm not sure exactly how the oscilloscope averages but I imagine it takes the readings over a few nanoseconds or so and then averages them. This shouldn't effect our data in any negative way if this is the oscilloscopes method, as it is pretty much how we would have taken the data had we been able to read them without using the oscilloscopes average function.

Methods
The major issue with this experiment is finding a way to cancel out the effects of time walk. Because the TAC trigger is held constant and a wave of larger amplitude will have a higher rate of rise it will trigger earlier than one with a smaller amplitude. To counter this problem, we used channel one to view the output from the PMT, chose a reasonable output level, and then would rotate the PMT so that for each measurement the output was always the same.

For taking the readings from the TAC itself, we found that the oscilloscope only seemed to measure with an accuracy of +-.08V so it would jump a lot. We decided to take somewhat of a guess at the value by watching the measurement for a bit and seeing which direction it would tend to jump. If it was generally split between going up and down from a value, we used the middle value. If it jumped up more than down we chose .04 above the middle. If down more than up, .04 below the middle. This method could be improved by actually counting the up jumps vs. down jumps and taking the average value over a minute or so, and theres probably a way to get the oscilloscope to do this on its own but we weren't sure so we just went with what felt like a good estimate.

Data
With this data we found a linear fit(using Linest on google docs) giving a slope of 148(3.1) cm/V with intercept of -959.7(21.9) or because every 10 Volts is equivalent to 50ns we have

$$ Speed of Light = 29.6(6) \frac{cm}{ns} $$



From the two graphs it looks like this is a pretty decent fit, most of the points are within a few sdem's of the line.

Analysis
The speed of light rounded to our equipments ability to measure is 30.0 cm/ns. From just typing into google "speed of light" google prints that it is 29.9792458 cm/ns so this rounding doesn't change the number by much. Either way, our experiment looks to be completely in agreement, being less than one sdem away from the accepted value. The percent error or difference between our best estimate and the accepted value is only 1.3% so that is also really close.

error
The main source of error is probably with the experiments setup itself. The method of just rotating the PMT to change the amplitude of it's output to try and keep this constant for each data point is fairly difficult and not anywhere near exact. I'm guessing more advanced equipment has a system built in to auto calibrate for time walk. Not exactly sure how this would be done, but maybe with a double trigger at two levels so the difference in rising speed between waves can be found and then exactly calculated when different waves would hit a specified value.

The other issue is with the accuracy of the oscilloscope and the output from the TAC. Even after using the average function the oscilloscope still jumped around a lot. Our visual method of averaging further may have helped to counter this problem a little, but if we had just taken the middle value each time rather than watch for a minute our measurements would almost always have come out exactly the same, and would have messed with our ability to find a proper sdem. Even with these problems we managed to measure the fastest stuff around using only a distance of about a meter.

questions from the lab manual
In the manual it asks whether we expect our measurements to be more accurate at a short or further distance. I'm guessing because of the speed of light and the distances being measured that the uncertainty principle does come into play. As we shrink the distance, we were also measuring smaller and smaller times. With the time differences being on the order of single nanoseconds it seemed reasonable for this to cause our short distances to be more uncertain. Our data also seems to support this, as at 30 cm the range had length of 8 where for the most part everywhere else was only 4.


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