A Michelson Interferometer is used to measure the refractive index of a gas. The

Question

A Michelson Interferometer is used to measure the refractive index of a gas.  The gas is allowed to flow into a gas cell of length "L" placed in one arm of the Interferometer, in which the light of wavelength "" circulates.

a) If "N" fringes are counted as the cell is filled from vacuum to atmospheric pressure, derive an expression for the index of refraction of the gas based on the given quantities.

b) How many fringes of 588nm light would count if CO2 (n=1.00045) were used and if the cell were 11cm long?

Explanation / Answer

N1 = L / y where N1 is number of wavelengths y in distance L (air) N2 = L n / y where N2 is the number of wavelengths (gas) N = N2 - N1 = L/y (n - 1) b) N = .11 / 5.88 * 10E-7) * .00045 = 84 fringes a) n = N y / L + 1 For our example n = 84 * 5.88 * 10E-7 / .11 + 1 = .00045 + 1

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