User:Kirstin Grace Harriger/Notebook/Physics 307L/Speed of Light Lab

Concepts

 * Time Walk: When the Time Amplitude Converter (TAC) triggers at a fixed voltage, the time at which it triggers will be later for smaller amplitude pulses than for larger ones. This means it detects the larger amplitude pulses sooner than it should. In our set up, as the light source is moved closer to the Photomultiplier tube (PMT), the amplitude of the signal sent by the PMT increases. The effect of this is that at each progressively closer measurement, the PMT generates a larger amplitude pulse than at the measurement before, and hence the pulse output by the PMT triggers the TAC sooner than it should for the amount of distance traveled by the light. This is called time walk, and it is an important source of systematic error in particle physics. To make up for this, a polarizer is attached to the PMT that allows us to to adjust the amplitude manually in order to keep it constant for each measurement.


 * Photomultiplier Tube (PMT): When the photocathode on the PMT is struck by photons from the LED, the photoelectric effect causes electrons to be dislodged and the they travel through a series of accelerating electrodes called diodes. The diodes multiply the current caused by the initial photons because each diode is at a higher potential than the last and more electrons are released than were incident. The is called secondary emission, and there must be vacuum inside the photomultiplier tube for it to work. The net current is output by the PMT and can be read with the oscilloscope.

Safety Concerns

 * High voltages are used in this experiment, so extra caution should be taken to check all connections.


 * The Photomultiplier tube is light sensitive and should be kept in the dark.


 * The power supply is charged after it is turned off, so wait for the capacitor to fully discharge, say 5 minutes, before handling. The power supply also has active connections on the back, so in order to move it, you have to turn it off.

Equipment

 * Tektronix Oscilloscope (Model TDS 1002)
 * Bertan Power Supply (Model 215, 3000V, 5mADC)
 * Canberra Delay Module (Model 2058)
 * Ortec TAC/SCA Module (Model 567)
 * Harshaw NIM Bin (Model NQ-75)
 * Harrison Laboratories Power Supply (Model 6207A, 160V, 0.2A)
 * Photomultiplier Tube (PMT)
 * LED circuit
 * BNC Cables

Procedure
The LED circuit and photomultiplier tube were already set up in a long cardboard tube, so we connected the rest of our equipment to them as follows:


 * 1) we put the Betran power supply, Canberra delay module, and the Ortec TAC/SCA into a chassis
 * 2) we connected the "A" connection of the photomultiplier tube (PMT) to the top input of the delay module
 * 3) we connected the output of the delay module to a BNC T-splitter (one side connected to the channel 1 input on the oscilloscope and the other to the "Stop" input of the Time-Amplitude Converter (TAC))
 * 4) we connected the "Start" input of the TAC to the cable attached to the LED
 * 5) we connected the power cable for the LED to the Harrison PSU
 * 6) we connected the output of the TAC to the channel 2 input of the oscilloscope
 * 7) we connected the "-HV" connection of the photomultiplier tube (PMT) to the Bertan Power Supply (PSU).

Then we adjusted the settings on the equipment as follows:


 * 1) for the Bertan power supply we set the voltage to 2000V, the offset to 400V, and the polarity to negative
 * 2) for the delay module we set the delay to 20ns
 * 3) for the TAC we set the range to 100ns, the multiplier to 1, the start and stop switches to "Anti", and the output switch to "Out"
 * 4) for the Harrison power supply we set the voltage to 190V.

We turned the set up on and measured the time delay between the release of light and the detection of light by measuring the difference in voltage between two delay settings on he delay module. The two signals were fed into the TAC, and the the delay between the two was converted into a voltage that could be read on the oscilloscope. The signal in the wires is not instantaneous. We had to induce a delay on the signal from the PMT because the wires connecting it to the oscilloscope were significantly shorter than the ones connected to the LED. We used the delay we measured to match the signals, and remove any systematic error induced by the cables.

After we found the delay, we measured the voltages from the photomultiplier tube at 20cm increments between 0 and 100cm. We measured the voltages on the oscilloscope and used the averaging function to keep the signal from fluctuating. We adjusted the polarizer attached to the PMT for each measurement to keep the amplitude of the pulse sent by the PMT constant. We watched the oscilloscope while adjusting the polarizer to gauge the amplitude in order to do this.

This is our set up. The oscilloscope is on the right, and the chassis is on the left. The long tube behind contains the PMT with the polarizer at the end behind the chassis, and the LED taped onto some meter sticks, so we can move it closer and farther from the PMT inside the long tube, on the other end.

This is the Chassis containing, from left to right: the Ortec TAC/SCA Module, the Canberra Delay Module, and the Bertan Power Supply.

This is the LED circuit that is at the end of the meter sticks.

This is the oscilloscope reading.

Data
These are the results from our 5 Trial Sets. The average velocities for each distance are at the bottom of this spreadsheet.

Analysis
This is a linear fit model for the voltage as a function of the distance based on the average values of the velocity over our 5 Trial Sets. The graph was created with MATLAB 7.8 which uses a least squares method. (Steve Koch 00:35, 13 October 2010 (EDT):including the matlab code would be very good practice)



The equation for the linear fit is $$y = .0032x + 0.8205$$, so the slope is .0032 V/cm.

I took the uncertainty in this slope to be +/- the voltage point farthest from the linear fit subtracted from linear fit value for distance corresponding to that voltage point, all divided by the distance for that point.

$$+/-(0.94 - 0.9468)/40 = +/- 0.00017$$ V/cm.

Inverting the slope, the slope plus the uncertainty, and the slope minus the uncertainty gives the average velocity, the minimum velocity, and the maximum velocity respectively. Average Velocity: $$1/0.0032 = 312.5$$ cm/V Minimum Velocity: $$1/0.00337 = 296.7359$$ cm/V Maximum Velocity: $$1/0.00303 = 330.0330$$ cm/V

From our initial measurement of the difference in voltage between two delay settings, we calculated the time delay to be 0.1 V/ns. This can be used to covert cm/V to cm/ns. Average Velocity: $$312.5 * 0.1 = 31.25$$ cm/ns Minimum Velocity: $$296.7 * 0.1 = 29.67$$ cm/ns Maximum Velocity: $$330 * 0.1 = 33$$ cm/ns

The accepted value from Wikipedia for the speed of light is 29.98 cm/ns.

Error in our experiment could have come from using a meter stick to take distance measurements, by miscalibrations in our set up, or by time walk. Human error could have come from adjusting the polarizers, doing the amplitude matching by eye, or in reading the distance.

Resources

 * 1) Alexandra Andrego's Speed of Light Lab
 * 2) Prof. Gold's Lab Manual

Collaboration

 * 1) Brian Josey