Effects of Breathing on an
Interferometer
Susan Gosse
Daniel Freno
Junior Lab II
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
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 < p < 110 kPa
 0 % < RH < 70%
 350 μmol/mol < CO2 concentration < 550 μmol/mol
 Dependence approximately linear for pressure, humidity
 Stronger, more complicated dependence for temperature
Looking at Temperature
Temperature vs. Fringes
0.5
0.0
-0.5
Fringes
-1.0
-1.5
0
10
20
30
Δm ≈ 2
-2.0
40
50
 Temperature
plays HUGE
role
 Max expected
shift is 2
fringes
 21 ºC to 37
ºC
 Enough for
effect seen
-2.5
-3.0
-3.5
-4.0
Temperature (C)
Bernoulli on Compressible Fluids
 Based on mass conservation and assumption of no heat
transfer, Bernoulli’s equation says that as velocity
increases, pressure decreases (with caveats)
Picture from http://en.wikipedia.org/wiki/Bernoulli's_principle
Bernoulli’s Equation
Mass Conservation:
Energy Conservation:
 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




ρ = density
Φ = gravitational potential energy/unit mass
Є = internal energy/unit mass
kinetic energy
gravitational energy
internal energy of fluid
p dV work energy
Bernoulli’s 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 molecule’s 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
Looking at Pressure
Pressure vs. Fringes
6.0
5.0
4.0
3.0
Fringes
2.0
1.0
Δm ≈ 0.5
0.0
95.00
-1.0
97.00
99.00
101.00
-2.0
-3.0
-4.0
Pressure (kPa)
103.00
105.00
 Pressure can
play big role
 Would need
ΔP = 1 kPa to
shift ½ fringe
 Doubtful we
are creating
this much
change
Looking at Humidity
 Humidity plays
small role
 Even if we
went from 0%
to 70%, only
1/10th fringe
Relative Humidity vs. Fringes
0.06
0.04
Fringes
0.02
Δm ≈ 0.1
0.00
0
20
40
-0.02
-0.04
-0.06
Relative Hum idity (%)
60
80
 Not
responsible
for effect
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
Δn = 4.1 x 10-8
Δ fringes = 0.01
Caveat that extreme range could exceed equation limits of
validity
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
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
Dependence on Temp, Pressure
p(1  pT )(1  15 )
nTp  1  (n15, 760  1)
760(1  76015 )(1  T )
Where
T = temperature
p = pressure
α = 0.00366
βT = (1.049 – 0.0157T)10-6
β15 = 0.8135X10-6
Dependence on Pressure
Fringe Shifts vs. Pressure
70
Trial 1:
y = -2.4783x + 62.273
R2 = 0.9983
Pressure (cm of Hg)
60
Trail 1
Trail 2:
y = -2.4178x + 61.623
R2 = 0.9987
50
40
30
20
10
0
0
5
10
15
Fringe Shift
20
25
Trail 2
Linear (Trail 1)
Linear (Trail 2)
Pressure vs. Fringes
Pressure vs. Fringe Shift
25
Trial 1:
y = -0.4028x + 25.104
R2 = 0.9983
Fringe Shift
20
Trial 2:
y = -0.4131x + 25.469
R2 = 0.9987
15
10
5
0
0
10
20
30
40
Pressure (cm of Hg)
50
60
70
Trail 1
Trail 2
Linear (Trail 2)
Linear (Trail 1)
Pressure vs. Index of Refraction
Pressure vs. Index of Refraction
Trial 1:
y = -3E-06x + 1.0003
R2 = 0.9983
2.50E-04
Trial 2:
y = -3E-06x + 1.0003
R2 = 0.9987
Index of Refraction
(n - n(vac))
2.00E-04
Trial 1
Trial 2
Linear (Trial 2)
1.50E-04
Linear (Trial 1)
1.00E-04
5.00E-05
0.00E+00
0
10
20
30
40
50
60
Pressure (kPa)
70
80
90
100
Experimental Results for nair
m 
2 Lnair  nvac 

 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
Feynman Sprinkler
Index of Refraction Calculator
Index of Refraction Calculator
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)
Pressure chamber
n
L
• ∆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 = λ/2L  ∆n = mλ/2L  m = 2∆nL/ λ
Index of Refraction: Theory
•na = index of refraction
 fL 
 
cv  wv  wa
na  

ca  fL  wv
 
 wa 
•cv = speed of light in vacuum
•ca = speed of light in air
•f = frequency of light
•L = length of chamber
•L/wv is equal to the wavelength
of the laser
•wa is found by adding measured
number of fringes passed to wv
•wv = no. wavelengths
passing through chamber in
vacuum
•wa = no. wavelengths
passing through chamber in
air
Index of Refraction in Air
Fringe Shift vs. Pressure
m = 2L(na-nv)/λ
• L is the length of the vacuum
chamber: L = 3.81 cm
• nv= 1
• λ of HeNe laser: λ = 633nm
30
25
20
Fringes
• m is the number of fringes that
have gone past while returning
to 1 atm from vacuum:
m = 30.003
y = -1.1145x + 30.003
R2 = 0.9994
15
10
5
0
0.0
5.0
10.0
15.0
20.0
25.0
30.0
Pressure (inHg)
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
na=1.00024.
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, na=1.00028.