Measuring the Speed of Light on a Nanosecond Time Scale

Transcription

1 WJP, PHY381 (2009) Wabash Journal of Physics v4.0, p.1 Measuring the Speed of Light on a Nanosecond Time Scale Bradley C. Vest, Thomas Warn, and M.J. Madsen Department of Physics, Wabash College, Crawfordsville, IN (Dated: December 17, 2009) The speed of light can be measured using the introductory-level physics equation x/ t. We used a pulsing LED light and a PMT to measure the speed of light and also show that we can accurately calibrate a nanosecond time scale. Our result for the speed of light was (3.19 ±.24) 10 8 m/s (95% CI), which agrees with the currently accepted value of m/s.

2 WJP, PHY381 (2009) Wabash Journal of Physics v4.0, p.2 As cosmic rays enter into the Earth s atmosphere, muon are spawned. Our planet is constantly bombarded with muons. Moving near the speed of light c with the average lifetime of 2.2 µs, muons make the trip from about 15 km above sea level to the surface in about 50 ns, relative to its frame [2]. Armed with this information, the next task is to detect the muons to measure their velocity. Scintillators are substances that glow when particles, such as muons, interact with its particles. As a muon enters the scintillator, it will interact with the scintillator s molecular structure causing the muon to decay into a muon-neutrino, electron, and anti-electron-neutrino. Two branches of photons are emitted during this process: the first with the initial interaction of the muon and scintillator, and the second when the decay product electron interacts with the scintillator [1]. Setting up two scintillators, one at a fixed position near a muon emitter and the other such that it can be placed at varying positions. Measuring the time difference that it takes for a muon to go through the near scintillator and the farther one. We can accurately measure the muon velocity; however because muons travel so quickly, a nanosecond timescale is required to make accurate measurements of the muon s velocity. In this letter we offer a method to easily measure the speed of light, resulting in a calibration technique to accurately measure muon lifetimes on a nanosecond timescale. We use a modified setup described in the Lupinski and Paudel paper [1], which measured muon velocities. We used a 4 m PVC tube that was spray painted black to reduce reflections. At one end of the tube is a LED attached to a PVC cap. The LED is driven by a signal generator at 3.3 MHz, through the circuit in FIG. 1. Because of the PMT s hypersensitivity to light, the LED s intensity was limited by the current through the LED; however, as the distance between the PMT and the LED changed, we needed a way to adjust the intensity, so we integrated a potentiometer into the circuit. See FIG. 2. On the other end of the tube is a Burle 8850 Photomultiplier Tube (PMT), which we ran at 1.5 kv. The typical transit time for the PMT is 42 ns. The peak quantum efficiency of our PMT is about 20%, but at the wavelength of the LED it was < 1%. The PMT s hypersensitivity to light allows for easy detection the light pulses from the LED. The PMT is not attached to the tube, allowing us to slide the PMT inside the tube for calibration purposes. An oscilloscope was connected to both the signal generator and the PMT. We collected data from the PMT by placing it at a known distance from the LED inside the tube and then

3 WJP, PHY381 (2009) Wabash Journal of Physics v4.0, p.3 12 V Square wave function generator Global Specialties Instruments 20 MHz Sweep/Function Generator Silicon NPN Transistor NTE311 10k Pot LED FIG. 1. The circuit used to drive the LED. The high frequency driver was used so we could easily turn down the frequency and see the flash to be sure it was working. The 10 kω potentiometer allowed us to adjust the brightness of the light as we moved the PMT. measured the difference in time from the signal generator s pulse to the PMT s detection pulse. We then moved the PMT further away from the LED and again measured the time difference, repeated for a total of 12 data points. The pulse from the PMT moved farther away from the driver pulse with respect to time, as the PMT moved farther from the LED, and pulses at different distances occurred at different times with respect to the driver pulse as seen in Fig 3. As the PMT moved farther from the LED the distance between the peaks on the oscilloscope increased. The timing between pulses was measured using a Tektronix- 100MHz digital oscilloscope using the signal generator pulse as a reference time for the signal pulses from the PMT. The time delay is proportional to the PMT s distance from the LED; using the accepted value of the speed of light, m/s [3], we expected to observe 1ft 1ns. For every foot we move the PMT, the peak should shift 1ns. The time pulse, taken from the 50% value of the normalized data, was plotted with its associated distance from the LED. A linear curve fit was used to fit the data. The slope of the fitted line is the speed of light (3.19 ±.24) 10 8 m/s (95% CI) as seen in Fig 4, which agrees with the accepted value. This will ultimately help in future experiments with

4 WJP, PHY381 (2009) Wabash Journal of Physics v4.0, p.4 a) x 0 x1 x 2 x 3 LED PMT b) Reference Pulse A t 0 t 1 t 2 FIG. 2. a) The PMT was moved down a PVC tube and the time it took for the pulse to reach the PMT was recorded with reference to the high frequency driver. b) The leading edge of the peak was used as the reference point for the time scale. It moved with respect to its distance from the LED. measuring the muon velocity knowing that we were able to accurately measure on a nano second time scale. The error bars come from being able to measure the time at the 50% value with a 95% CI. Just by moving the PMT and scintillator bar a foot at a time, the muon velocity should be able to be measured if another PMT and scintillator bar stay stationary for a reference time. [1] Lupinski, L, Paudel, R. Measuring the Muon Lifetime. Wabash Journal of Physics. (2009). [2] Duarte, M.G, Cambell, S. L. The Mean Life and Speed of Cosmic-Ray Muons. MIT. (2008). [3] Aliaga, Diego, Beard, Chris, Castilow, Jacob, Madsen, M. J. Measuring the Speed of Light Using a Time-of-ight by Pulsing a HeNe Laser with an Acousto-Optical Modulator. Wabash Journal of Physics. (2009).

5 WJP, PHY381 (2009) Wabash Journal of Physics v4.0, p Normalized Peak Height m 5.43 m 30 cm time steps time (s) FIG. 3. All the curves were normalized so that they could be plotted next to each other and compared. This also made it easy to find a reference point to identify the time. We used the 50% mark,.5 on a 0 to 1 scale which we created. 5.5 Speed of Light Distance (m) FIG. 4. A graph of the distance between the PMT and LED with respect to time. The linear fit for our data is given by y = x. The error was estimated to be a 95% confidence interval. The error is in being able to calculate the time by looking at the 50% value. The time offset makes the y-intercept arbitrary. Our result agrees with the accepted value of the speed of light.