Measuring the Speed Measuring the Speed of Light!of Light!

Photonic partnersPhotonic partners::

David OrensteinDavid Orenstein

Anuta BezryadinaAnuta Bezryadina

Nathan BurdNathan Burd

OutlineOutline

Diagram of Experimental Setup Diagram of Experimental Setup w/Explanation of Experimental Setup w/Explanation of Experimental Setup

Theory of light propagationTheory of light propagation Theory of how a laser worksTheory of how a laser works Experimental ProcedureExperimental Procedure DataData AnalysisAnalysis ConclusionConclusion

Experimental SetupExperimental 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 PropagationThe Theory of Light PropagationLight is a self-perpetuating oscillation of electric and magnetic 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 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 a vacuum. It has both a wave and particle aspect as the energy of a quantum of light is a very small, but finite energy of a quantum of light is a very small, but finite value. A packet of light is called a photon and can interact value. A packet of light is called a photon and can interact with electrons. We use this “photoelectric” effect to our with electrons. We use this “photoelectric” effect to our advantage when we attempt to turn the light into a signal advantage when we attempt to turn the light into a signal we can read off of the oscilloscope. we can read off of the oscilloscope.

A A laserlaser is a device that controls the way that energized atoms release is a device that controls the way that energized atoms release photons. "Laser" is an acronym for photons. "Laser" is an acronym for light amplification by stimulated light amplification by stimulated emission of radiationemission of radiation, which describes very succinctly how a laser , which describes very succinctly how a laser works. Although there are many types of lasers, all have certain essential 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 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 an excited state. Typically, very intense flashes of light or electrical discharges pump the lasing medium and create a large collection of discharges pump the lasing medium and create a large collection of excited-state atoms (atoms with higher-energy electrons). It is necessary 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 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 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 three levels above the ground state. This increases the degree of population inversionpopulation inversion. The population inversion is the number of atoms . The population inversion is the number of atoms in the excited state versus the number in ground state. in the excited state versus the number in ground state.

Once the lasing medium is pumped, it contains a collection of atoms with Once the lasing medium is pumped, it contains a collection of atoms with some electrons sitting in excited levels. The excited electrons have some electrons sitting in excited levels. The excited electrons have energies greater than the more relaxed electrons. Just as the electron energies greater than the more relaxed electrons. Just as the electron absorbed some amount of energy to reach this excited level, it can also 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 release this energy. As the figure below illustrates, the electron can simply relax, and in turn rid itself of some energy. This relax, and in turn rid itself of some energy. This emitted energyemitted energy comes comes in the form of in the form of photonsphotons (light energy). The photon emitted has a very (light energy). The photon emitted has a very specific wavelength (color) that depends on the state of the electron's specific wavelength (color) that depends on the state of the electron's energy when the photon is released. Two identical atoms with electrons in energy when the photon is released. Two identical atoms with electrons in identical states will release photons with identical wavelengths. identical states will release photons with identical wavelengths.

How a Laser Works:

Emission and Population InversionEmission and Population Inversion

Diagram of He-Ne LaserDiagram 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 ProcedureExperimental Procedure To determine the speed of light, we looked at the difference To determine the speed of light, we looked at the difference

in time it took for the modulated signals to reach two in time it took for the modulated signals to reach two detectors by two different path lengths. detectors by two different path lengths.

We connected the modulated signal on the detector box to We connected the modulated signal on the detector box to both the laser and the oscilloscope. both the laser and the oscilloscope.

Then we connected detector A’s input to Channel A on the Then we connected detector A’s input to Channel A on the oscilloscope and did the same with detector B.oscilloscope and did the same with detector B.

We set up the beam splitter and mirror so that the mirror’s We set up the beam splitter and mirror so that the mirror’s distance behind the splitter was minimal. We then distance behind the splitter was minimal. We then determined the systematic error as the time difference determined the systematic error as the time difference between the very small path lengths should have been between the very small path lengths should have been negligible.negligible.

We then varied the distance of the mirror and beam splitter We then varied the distance of the mirror and beam splitter and determined the time difference for each change in and determined the time difference for each change in length.length.

DataData

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

AnalysisAnalysis

Final AnalysisFinal Analysis

We fitted the 5 points with Scientist linear We fitted the 5 points with Scientist linear relationship, y=ax + b (where y is time and x is relationship, y=ax + b (where y is time and x is distance)distance)

Scientist gave us values for a and bScientist gave us values for a and b

a: 3.5305 +/- 0.0437 ns/ma: 3.5305 +/- 0.0437 ns/m

b: -15.2 +/- 2.1 nsb: -15.2 +/- 2.1 ns

The speed of light is 1/a and we experimentally The speed of light is 1/a and we experimentally determined it to be:determined it to be:

c(experimental): (2.861 +/- 0.042)*10^8 m/sc(experimental): (2.861 +/- 0.042)*10^8 m/s

ConclusionConclusion

The speed of light traveling through the air The speed of light traveling through the air on the 1on the 1stst floor of Thornton Hall at SFSU floor of Thornton Hall at SFSU was determined to bewas determined to be

c(experimental): (2.861 +/- 0.042)*10^8 m/sc(experimental): (2.861 +/- 0.042)*10^8 m/s

Perhaps refinement of distance Perhaps refinement of distance measurements and better focusing of the measurements and better focusing of the dispersive laser light would yield a result dispersive laser light would yield a result closer to the expected value of closer to the expected value of

c: 2.99*10^8 m/sc: 2.99*10^8 m/s