1. Overview Theory Index of Refraction and Path Length Setup and Procedure Michelson Interferometer Filming the Pressure Gauge Results Analysis Sources of Error Refractive Index vs. Pressure 2011 Summer

2. Change in Path Length A difference in path length, ∆s, occurs when light travels through regions of differing indices of refraction A varying path length leads to a changing interference pattern (i.e. moving fringes) Using a Michelson Interferometer and a vacuum chamber, we can note the fringe shifts of an interference pattern as the pressure in the vacuum chamber equalizes with that of the room. When counting fringes, each fringe that passes is equivalent to a change in path length of one wavelength, so the total change is the wavelength multiplied by the number of fringes, m The total path difference divided by twice the length of the vacuum chamber is equal to the difference between the indices of refraction of air and vacuum. Because the interference pattern observed is the result of a phase shift, we are indirectly measuring the phase velocity of light in air. n vacuum L Vacuum chamber

3. Procedure After setting up the Michelson Interferometer, we placed the vacuum chamber between the beam splitter and a mirror on one of the arms We put 5-6 fringes on the grid paper and aligned one of the bold lines to the center of the fringes as reference A camera was set up next to the apparatus to film the pressure gauge as we let air back in The vacuum chamber was pumped down to ~200 Torr using a handheld mechanical pump Air slowly entered chamber again and we started the camera As the fringes passed the bold line, one partner made a sharp metallic sound (screwdriver on metal) that could be used in the video to determine when to record the pressure The room temperature, humidity, and pressure were also noted (*We could not measure RH or P) Interference Pattern Vacuum Chamber Beam Splitter HeNe Laser CameraPressure Gauge/ Vacuum Pump

4. Extracting Data We filmed the pressure gauge as air re-entered the chamber By making a sharp metallic sound when the fringes reached a certain position, we could determine when to record pressure information Having our data as a video file allows us flexibility in recording it We re-watched each trial several times and noted when to record pressure In slow motion we went to those times and recorded the pressure Recording the pressure gauge and fringes simultaneously would eliminate human response time error Used inHg to record pressure (better resolution on meter) then converted to Torr

5. Results Since we could not achieve perfect vacuum, we must use the y-intercept from our best fit line to determine the number of fringe shifts, m m λ (nm)L (m)TrialY-intercept of trendlinen air (measured)St. Dev. 632.80.038132.91.00027 Input233.31.00028 From Data332.51.00027 OutputAverage32.91.000270.000003

6. With temperature (ºC), ambient pressure (kPa) and relative humidity (%), we can calculate the theoretical value for n air We could not measure relative humidity or pressure, but the formula is still interesting to see Equation from the Engineering Metrology Toolbox As we could not take all of the required data, we do not have a value for n air Our percent error is statistical and not based on expected values Our value for n air is in an acceptable range It agrees with the previous theoretical value It is higher than previous experimental values, though they tended to have higher statistical error which could throw off the numbers somewhat Analysis Sourcen airσ% Theory (2007)1.00026 2011Su1.000270.0000031.2% 2007 A and B1.0002550.0000062.4% 2006 Group of 21.000240.0000041.7% 2006 Group of 31.000240.00002711.2%

7. Sources of Error Sources Projects in Optics. Newport Corporation Stone, Jack and Jay Zimmerman. “Index of Refraction of Air.” Engineering Metrology Toolbox. Accessed Oct. 1. 2007. http://emtoolbox.nist.gov/Wavelength/Documentation.asp Pressure gauge allows for only precision to about a quarter of an inHg Vibration in room made it difficult to precisely note fringe shift Fringes moved slightly (<1 fringe) between trials resulting in more spread in the value of m Reaction time between observing fringe shift and producing audio signal Could be minimized with a clicker or something involving less movement to produce the sound Could be eliminated all together with a setup that allows both the pressure gauge and fringes to be recorded simultaneously Recording Errors Was difficult to take readings and record information – Improved by Su11 by using camera and taking readings after recording audio signal for each fringe shift We removed 2006 problem of recording using time intervals instead of fringes – Su11 also recorded fringe shifts