1. Measuring the Speed of Light Jack Young Rich Breazeale Ryan Phelan

2. Table of Contents Reasons to Perform This Experiment Reasons to Perform This Experiment Properties of the He-Ne Laser Properties of the He-Ne Laser Experimental Setup and Procedure Experimental Setup and Procedure Data Data Data Analysis Data Analysis Results Results Conclusion Conclusion

3. Reasons to Perform This Experiment To find out if the measured value agrees with theory To find out if the measured value agrees with theory The speed of light c is an important constant found in many physics formulas The speed of light c is an important constant found in many physics formulas It is the connection between matter and energy E=mc 2 It is the connection between matter and energy E=mc 2

4. Properties of the He-Ne Laser Population inversion Population inversion Stimulated Emission Stimulated Emission Monochromatic light Monochromatic light Coherent light Coherent light Collimated light Collimated light

5. Population Inversion Electrons accelerated in an electric field collide with the helium atoms in the gas. This excites helium from the ground state to the 2s and 3s long- lived, metastable excited states. Electrons accelerated in an electric field collide with the helium atoms in the gas. This excites helium from the ground state to the 2s and 3s long- lived, metastable excited states. Collision of the excited helium atoms with the ground-state neon atoms results in transfer of energy to the neon atoms, exciting them into the 2s and 3s states. This is due to a coincidence of energy levels between the helium and neon atoms. Collision of the excited helium atoms with the ground-state neon atoms results in transfer of energy to the neon atoms, exciting them into the 2s and 3s states. This is due to a coincidence of energy levels between the helium and neon atoms. The Neon now has a population inversion, more electrons in its higher energy states than in the ground state. The Neon now has a population inversion, more electrons in its higher energy states than in the ground state. The population inversion causes the electrons in the 3s state to spontaneously drop to a lower energy state, releasing photons which are coherent and monochromatic (633nm). The population inversion causes the electrons in the 3s state to spontaneously drop to a lower energy state, releasing photons which are coherent and monochromatic (633nm).

6. Stimulated Emission When a Neon atom absorbs a 632.8 nm photon and its population is inverted (many electrons in the 3p state), the incident photon is reemitted and in many cases one or more electrons will drop from the 3p to the 2p state, resulting in the emission of another 632.8 nm photon. When a Neon atom absorbs a 632.8 nm photon and its population is inverted (many electrons in the 3p state), the incident photon is reemitted and in many cases one or more electrons will drop from the 3p to the 2p state, resulting in the emission of another 632.8 nm photon. The photons produced in this “stimulated emission” will all be coherent (in phase). The photons produced in this “stimulated emission” will all be coherent (in phase). Each photon produced can be absorbed by another Neon atom to stimulate the emission of more coherent photons. Each photon produced can be absorbed by another Neon atom to stimulate the emission of more coherent photons. This “pumping” of the laser medium leads to a chain reaction of stimulated emissions This “pumping” of the laser medium leads to a chain reaction of stimulated emissions

7. Coherence Coherence arises from the stimulated emission process. Since a common stimulus triggers the emission events which provide the amplified light, the emitted photons are "in step" and have a definite phase relation to each other. Coherence arises from the stimulated emission process. Since a common stimulus triggers the emission events which provide the amplified light, the emitted photons are "in step" and have a definite phase relation to each other. Non-coherent light Coherent light

8. Collimation The mirrors at each end of the laser tube are parallel so the laser light reflected from them is nearly perfectly parallel to the tube. The mirrors at each end of the laser tube are parallel so the laser light reflected from them is nearly perfectly parallel to the tube. This results in a collimated beam. This results in a collimated beam.

9. Experimental Setup

10. Experimental Procedure We measured the phase of each modulated laser beam and found the temporal difference between them. We measured the phase of each modulated laser beam and found the temporal difference between them. This difference indicated the different times the two beams took to reach the detector box. This difference indicated the different times the two beams took to reach the detector box. Based on the path length difference and the phase difference, we were able to determine the speed of the laser beam. Based on the path length difference and the phase difference, we were able to determine the speed of the laser beam.

11. Data Run Path length difference Phase difference #1: Hallway 97.54 m 290.7 ns #2: Hallway 55.07 m 145.0 ns #3: Hallway 31.70 m 90.1 ns #4: Hallway 13.11 m 19.9 ns #5: Tabletop 1.17 m -15.2 ns

12. Data Analysis

14. Using Scientist, we calculated the slope of the graph of phase difference vs. path length difference. Using Scientist, we calculated the slope of the graph of phase difference vs. path length difference. Scientist calculated the slope at 3.168 (ns/m) and the standard deviation at 0.043 (ns/m). Scientist calculated the slope at 3.168 (ns/m) and the standard deviation at 0.043 (ns/m). This standard deviation is 1.3688% the slope value. This standard deviation is 1.3688% the slope value. We inverted this slope to get our measured speed and determined the standard deviation. We inverted this slope to get our measured speed and determined the standard deviation. We also determined the delay in the equipment’s circuitry by determining the y-intercept on the time vs. distance graph. We also determined the delay in the equipment’s circuitry by determining the y-intercept on the time vs. distance graph.

15. Results The calculations give us: 3.16 (+/-0.04) x 10 8 m/s The calculations give us: 3.16 (+/-0.04) x 10 8 m/s Scientist found the “y-intercept” to be at Scientist found the “y-intercept” to be at T = –18.37 ns This is the delay due to circuitry This is the delay due to circuitry

16. Conclusion Our measurement of the speed of light is about four standard deviations away from the accepted value Our measurement of the speed of light is about four standard deviations away from the accepted value Something is wrong with our data or, more likely, our error analysis Something is wrong with our data or, more likely, our error analysis We probably could have achieved better results if our distance measurements were more accurate We probably could have achieved better results if our distance measurements were more accurate It sucks to do experiments in the hallway It sucks to do experiments in the hallway