Effects of Breathing on an Interferometer

Susan GosseDaniel 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

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

0 10 20 30 40 50

Temperature (C)

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es

Δm ≈ 2

Temperature plays HUGE role

Max expected shift is 2 fringes21 ºC to 37

ºCEnough for

effect seen

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 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

ρ = densityΦ = gravitational potential energy/unit mass Є = internal energy/unit mass

Mass Conservation:

Energy Conservation:

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

Pressure vs. Fringes

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

95.00 97.00 99.00 101.00 103.00 105.00

Pressure (kPa)

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Looking at Pressure

Pressure can play big role

Would need ΔP = 1 kPa to shift ½ fringe

Doubtful we are creating this much change

Δm ≈ 0.5

Looking at Humidity

Relative Humidity vs. Fringes

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0 20 40 60 80

Relative Hum idity (%)

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Humidity plays small role

Even if we went from 0% to 70%, only 1/10th fringe Not

responsible for effect

Δm ≈ 0.1

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

)1)(7601(760

)151)(1()1(1

15760,15 T

ppnn T

Tp

Where

T = temperature

p = pressure

α = 0.00366

βT = (1.049 – 0.0157T)10-6

β15 = 0.8135X10-6

Dependence on PressureFringe Shifts vs. Pressure

Trial 1:y = -2.4783x + 62.273

R2 = 0.9983

Trail 2:y = -2.4178x + 61.623

R2 = 0.9987

0

10

20

30

40

50

60

70

0 5 10 15 20 25Fringe Shift

Pre

ssu

re (

cm o

f H

g)

Trail 1

Trail 2

Linear (Trail 1)

Linear (Trail 2)

Pressure vs. Fringes

Pressure vs. Fringe Shift

Trial 2:y = -0.4131x + 25.469

R2 = 0.9987

Trial 1:y = -0.4028x + 25.104

R2 = 0.9983

0

5

10

15

20

25

0 10 20 30 40 50 60 70

Pressure (cm of Hg)

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e S

hif

t

Trail 1

Trail 2

Linear (Trail 2)

Linear (Trail 1)

Pressure vs. Index of Refraction

Pressure vs. Index of Refraction

Trial 2:y = -3E-06x + 1.0003

R2 = 0.9987

Trial 1:y = -3E-06x + 1.0003

R2 = 0.9983

0.00E+00

5.00E-05

1.00E-04

1.50E-04

2.00E-04

2.50E-04

0 10 20 30 40 50 60 70 80 90 100

Pressure (kPa)

Ind

ex

of

Re

fra

cti

on

(n -

n(v

ac

))

Trial 1

Trial 2

Linear (Trial 2)

Linear (Trial 1)

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

vacair nnLm

2

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

• Rememberthe light passes through the chamber twice (factor of 2)

n

L

Pressure chamber

• ∆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

v

a

a

v

a

va w

w

wfL

wfL

c

cn

•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

Fringe Shift vs. Pressure y = -1.1145x + 30.003

R2 = 0.9994

0

5

10

15

20

25

30

0.0 5.0 10.0 15.0 20.0 25.0 30.0

Pressure (inHg)

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Index of Refraction in Air

• 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

• λ of HeNe laser: λ = 633nm

m = 2L(na-nv)/λ

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.