Overview

OverviewTheory

Index of Refraction and Path Length

Setup and Procedure

Michelson Interferometer

Filming the Pressure Gauge

Results

Analysis

Sources of Error

Refractive Index vs. Pressure2011 Summer

Change in Path Length

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• 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.

nvacuum

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Vacuum chamber

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 LaserCamera Pressure Gauge/

Vacuum Pump

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

Fringe Number vs Pressure (Torr)

y = -0.043x + 32.9

y = -0.044x + 33.3

y = -0.042x + 32.50

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25

0 100 200 300 400 500 600 700

Pressure (Torr)

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e N

um

ber

Trial 1 Torr (actual pres.)



Linear (Trial 1 Torr (actual pres.))



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) Trial Y-intercept of trendline n air (measured) St. Dev.632.8 0.038 1 32.9 1.00027

Input 2 33.3 1.00028 From Data 3 32.5 1.00027

Output Average 32.9 1.00027 0.000003

• With temperature (ºC), ambient pressure (kPa) and relative humidity (%), we can calculate the theoretical value for nair

• 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 nair

• Our percent error is statistical and not based on expected values

• Our value for nair 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

Source n air σ %

Theory (2007) 1.00026

2011Su 1.00027 0.000003 1.2%

2007 A and B 1.000255 0.000006 2.4%

2006 Group of 2 1.00024 0.000004 1.7%

2006 Group of 3 1.00024 0.000027 11.2%

Sources of Error

SourcesProjects 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

Overview

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