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 n air  Bernoulli pressure changes result in different index of refraction (n air ) for air  Water vapor from breath changes n air  Higher CO 2 content changes n air  “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 for  90 kPa < p < 110 kPa  0 % < RH < 70%  350 μmol/mol < CO 2 concentration < 550 μmol/mol  Dependence approximately linear for pressure, humidity  Stronger, more complicated dependence for temperature

Looking at Temperature Δm ≈ 2  Temperature plays HUGE role  Max expected shift is 2 fringes  21 ºC to 37 ºC  Enough 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

Bernoulli’s Equation  The amount of material entering V 1 equals the amount entering V 2  The energy entering V 2 equals the amount leaving V 1  Assumes no heat transfer, viscous flows, etc.  Energy is sum of  kinetic energy  gravitational energy  internal energy of fluid  p dV work energy ρ = density Φ = 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

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  Humidity plays small role  Even if we went from 0% to 70%, only 1/10 th fringe  Not responsible for effect Δm ≈ 0.1

CO 2 Effects  The Engineering Metrology Toolbox website suggests that CO 2 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 CO 2 concentrations from 300 to 600 μmol/mol  n = for 300 μmol/mol  n = for 600 μmol/mol  Δn = 4.1 x  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

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 CO 2 are NOT the causes  Aberration is unlikely due to low velocity of breath

Dependence on Temp, Pressure Where T = temperature p = pressure α = β T = (1.049 – T )10 -6 β 15 = X10 -6

Dependence on Pressure

Pressure vs. Fringes

Pressure vs. Index of Refraction

Experimental Results for n air  Trial one : n air =  Trial two: n air =  Theory tells us that n air = – this small discrepancy may be due to measurement inaccuracies, or possibly to the effect of the glass plates

Feynman Sprinkler

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) 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 n a = index of refraction c v = speed of light in vacuum c a = speed of light in air f = frequency of light L = length of chamber w v = no. wavelengths passing through chamber in vacuum w a = no. wavelengths passing through chamber in air L/w v is equal to the wavelength of the laser w a is found by adding measured number of fringes passed to w v

Index of Refraction in Air m is the number of fringes that have gone past while returning to 1 atm from vacuum: m = L is the length of the vacuum chamber: L = 3.81 cm n v = 1 λ of HeNe laser: λ = 633nm m = 2L(n a -n v )/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 n a = 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, n a =