Measuring the Speed of Light! Photonic partners: David Orenstein Anuta Bezryadina Nathan Burd

Outline Diagram of Experimental Setup w/Explanation of Experimental Setup Theory of light propagation Theory of how a laser works Experimental Procedure Data Analysis Conclusion

Experimental Setup Modulated light emerges from the laser, encounters the beam splitter where it then travels by two paths of different lengths to the photocell detector. Each beam enters its own detector and is interpreted by the oscilloscope, which shows two waves nearly superposed on one another. I have separated the signal generator and the photocell detector for clarity, while in the actual setup they were part of the same component in our system.

The Theory of Light Propagation Light is a self-perpetuating oscillation of electric and magnetic fields that travels linearly with a speed of 2.99*10^8 m/s in a vacuum. It has both a wave and particle aspect as the energy of a quantum of light is a very small, but finite value. A packet of light is called a photon and can interact with electrons. We use this “photoelectric” effect to our advantage when we attempt to turn the light into a signal we can read off of the oscilloscope.

How a Laser Works: A laser is a device that controls the way that energized atoms release photons. "Laser" is an acronym for light amplification by stimulated emission of radiation, which describes very succinctly how a laser works. Although there are many types of lasers, all have certain essential features. In a laser, the lasing medium is “pumped” to get the atoms into an excited state. Typically, very intense flashes of light or electrical discharges pump the lasing medium and create a large collection of excited-state atoms (atoms with higher-energy electrons). It is necessary to have a large collection of atoms in the excited state for the laser to work efficiently. In general, the atoms are excited to a level that is two or three levels above the ground state. This increases the degree of population inversion. The population inversion is the number of atoms in the excited state versus the number in ground state. Once the lasing medium is pumped, it contains a collection of atoms with some electrons sitting in excited levels. The excited electrons have energies greater than the more relaxed electrons. Just as the electron absorbed some amount of energy to reach this excited level, it can also release this energy. As the figure below illustrates, the electron can simply relax, and in turn rid itself of some energy. This emitted energy comes in the form of photons (light energy). The photon emitted has a very specific wavelength (color) that depends on the state of the electron's energy when the photon is released. Two identical atoms with electrons in identical states will release photons with identical wavelengths.

Emission and Population Inversion

Diagram of He-Ne Laser Accelerated electrons strike bound electrons in the Helium, which are then excited and then “jump” to a Neon atom creating population inversion. As these electrons fall to a lower energy level they emit photons at the specific wavelength of 632.8 nm. These emerge from the end of the laser as collimated light: a laser beam.

Experimental Procedure To determine the speed of light, we looked at the difference in time it took for the modulated signals to reach two detectors by two different path lengths. We connected the modulated signal on the detector box to both the laser and the oscilloscope. Then we connected detector A’s input to Channel A on the oscilloscope and did the same with detector B. We set up the beam splitter and mirror so that the mirror’s distance behind the splitter was minimal. We then determined the systematic error as the time difference between the very small path lengths should have been negligible. We then varied the distance of the mirror and beam splitter and determined the time difference for each change in length.

Data Set 1: Change in length = zero ave. time diff. = -12.8 ns Set 2: Change in length = 10.14 m ave. time diff. = 21.8 ns Set 3: Change in length = 20.7 m ave. time diff. = 57.8 ns Set 4: Change in length = 36.88 m ave. time diff. = 110 ns Set 5: Change in length = 98.3 m ave. time diff = 334.2 ns

Analysis

c(experimental): (2.861 +/- 0.042)*10^8 m/s Final Analysis We fitted the 5 points with Scientist linear relationship, y=ax + b (where y is time and x is distance) Scientist gave us values for a and b a: 3.5305 +/- 0.0437 ns/m b: -15.2 +/- 2.1 ns The speed of light is 1/a and we experimentally determined it to be: c(experimental): (2.861 +/- 0.042)*10^8 m/s

c(experimental): (2.861 +/- 0.042)*10^8 m/s Conclusion The speed of light traveling through the air on the 1st floor of Thornton Hall at SFSU was determined to be c(experimental): (2.861 +/- 0.042)*10^8 m/s Perhaps refinement of distance measurements and better focusing of the dispersive laser light would yield a result closer to the expected value of c: 2.99*10^8 m/s