Effects of Breathing on an Interferometer

1
Effects of Breathing on an Interferometer

• Susan Gosse
• Daniel Freno
• Junior Lab II

2
Breath Affects Interference Fringes

• We see roughly ½ of a fringe shift when someone
  breaths on air in the interferometer
• Theories as to why
• Different temperature results in different nair
• Bernoulli pressure changes result in different
  index of refraction (nair) for air
• Water vapor from breath changes nair
• Higher CO2 content changes nair
• Stellar Aberration effects due to wind velocity
• Assumptions
• Path length of 5 cm
• Temperature between 21 ºC (normal) and 37 ºC
• Humidity between 35 (normal) and no more than
  70
• Pressure possibly lowered from 98 kPa not much
  though

3
Simplified Equation with T, p, RH

• p pressure in kPa
• t temperature in Celsius
• RH relative humidity in percent (ranges from 0
  to 100)
• Valid ONLY for wavelength 633 nm
• Agrees with full Ciddor equation within 5 x 10-5
  for
• 90 kPa lt p lt 110 kPa
• 0 lt RH lt 70
• 350 µmol/mol lt CO2 concentration lt 550 µmol/mol
• Dependence approximately linear for pressure,
  humidity
• Stronger, more complicated dependence for
  temperature

4
Looking at Temperature

• Temperature plays HUGE role
• Max expected shift is 2 fringes
• 21 ºC to 37 ºC
• Enough for effect seen

?m 2
5
Bernoulli on Compressible Fluids

• Based on mass conservation and assumption of no
  heat transfer, Bernoullis equation says that as
  velocity increases, pressure decreases (with
  caveats)

Picture from http//en.wikipedia.org/wiki/Bernoull
i's_principle
6
Bernoullis Equation

• The amount of material entering V1 equals the
  amount entering V2
• The energy entering V2 equals the amount leaving
  V1
• Assumes no heat transfer, viscous flows, etc.
• Energy is sum of
• kinetic energy
• gravitational energy
• internal energy of fluid
• p dV work energy

Mass Conservation
Energy Conservation
? density F gravitational potential
energy/unit mass ? internal energy/unit mass
7
Bernoullis Equation

• Thus the result as pressure goes down, velocity
  goes up
• Assuming level height (dropping gravity term)
  microscopically
• When velocity increases, it means that a greater
  proportion of each molecules energy is directed
  in the forward direction
• Less energy is directed outward in other
  directions
• Pressure is a result of this outward motion
• Thus less pressure

8
Looking at Pressure

• Pressure can play big role
• Would need ?P 1 kPa to shift ½ fringe
• Doubtful we are creating this much change

?m 0.5
9
Looking at Humidity

• Humidity plays small role
• Even if we went from 0 to 70, only 1/10th
  fringe
• Not responsible for effect

?m 0.1
10
CO2 Effects

• The Engineering Metrology Toolbox website
  suggests that CO2 effects are negligible compared
  to other effects
• Closed rooms typically have concentration of 450
  µmol/mol (µmol/mol ppm parts per million)
• 300 µmol/mol is lowest concentration likely to be
  found normally
• 600 µmol/mol is highest likely to find in an
  indoor setting
• Using the Ciddor calculator with standard values
  and varying CO2 concentrations from 300 to 600
  µmol/mol
• n 1.000261742 for 300 µmol/mol
• n 1.000261783 for 600 µmol/mol
• ?n 4.1 x 10-8
• ? fringes 0.01
• Caveat that extreme range could exceed equation
  limits of validity

11
Aberration Effects

• A perpendicular velocity added by the breath
  could cause the light to travel a longer path
  length
• Similar to stellar aberration
• Unlikely since very slow velocity compared to
  speed of light

http//en.wikipedia.org/wiki/Aberration_of_light
12
Conclusion

• Most likely, effect of ½ fringe shift is due to
  temperature
• Can easily account for this difference and more
• Pressure could be cause, but unlikely since need
  1 kPa change
• Would have to be further tested to determine
• Humidity and CO2 are NOT the causes
• Aberration is unlikely due to low velocity of
  breath

13
Dependence on Temp, Pressure
Where T temperature p pressure a
0.00366 ßT (1.049 0.0157T)10-6 ß15
0.8135X10-6
14
Dependence on Pressure
15
Pressure vs. Fringes
16
Pressure vs. Index of Refraction
17
Experimental Results for nair

• Trial one nair 1.00021
• Trial two nair 1.00021
• Theory tells us that nair 1.00026 this small
  discrepancy may be due to measurement
  inaccuracies, or possibly to the effect of the
  glass plates

18
Feynman Sprinkler
19
Index of Refraction Calculator
20
Index of Refraction Calculator
21
Optical Path Length

• The length traveled by light with the index of
  refraction of the medium taken into account
• s 2nL
• s is the optical path length, n is the index of
  refraction and L is the length of the vacuum
  chamber
• Remember?the light passes through the chamber
  twice (factor of 2)

• ?s 2?nL ? CHANGE in Optical Path Length
• Shift of m number of fringes? ?s 2?nL ? ?n
  ?s/2L
• If ?s is one wavelength, then m is one fringe
• ?n ?/2L ? ?n m?/2L ? m 2?nL/ ?

22
Index of Refraction Theory

• na index of refraction
• cv speed of light in vacuum
• ca speed of light in air
• f frequency of light
• L length of chamber
• wv no. wavelengths passing through chamber in
  vacuum
• wa no. wavelengths passing through chamber in
  air

• L/wv is equal to the wavelength of the laser
• wa is found by adding measured number of fringes
  passed to wv

23
Index of Refraction in Air
m 2L(na-nv)/?

• m is the number of fringes that have gone past
  while returning to 1 atm from vacuum
  m 30.003
• L is the length of the vacuum chamber L 3.81
  cm
• nv 1
• ? of HeNe laser ? 633nm

We extrapolated our line to zero pressure and the
number of fringes there (y-intercept) is our
m. Using this equation for all 5 sets of our
data, we calculated an average value for
na1.00024.
According to the above equation, from the
American Handbook of Physics, where P is the
pressure inside the chamber and T is the
temperature of the room, na1.00028.