A more demanding measurement is wanted: the refractive index of helium gas

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Interference and diffraction · Interference and diffraction

Optics and Photonics, Ch Two-beam interference and interferometry

Problem

A more demanding measurement is wanted: the refractive index of helium gas, for which n−1=3.6×10−5n-1 = 3.6\times10^{-5} at 1 atm and λ=632.8\lambda = 632.8 nm (the vacuum wavelength of the stabilised helium-neon laser used). A Michelson interferometer with an evacuable cell of length ℓ\ell in one arm gives a fringe count N=2(n−1)ℓ/λN = 2(n-1)\ell/\lambda as the cell fills from vacuum to 1 atm. Electronic (photodiode) fringe interpolation lets the group resolve δN=0.010\delta N = 0.010 of a fringe, and the target precision is δ(n−1)=1.0×10−8\delta(n-1) = 1.0\times10^{-8}. ((a)) Choose the minimum cell length ℓ\ell that meets this precision target. ((b)) State the total fringe count expected for that cell length as it fills from vacuum to 1 atm, and comment on whether this length is a practical bench dimension.

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