A laboratory wants to measure the refractive index of nitrogen gas using a Michelson…
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 laboratory wants to measure the refractive index of nitrogen gas using a Michelson interferometer with an evacuable cell of length ℓ in one arm and a stabilised helium-neon laser of vacuum wavelength λ=632.8 nm. The cell is filled from vacuum to 1 atm at 20 ∘C, where nitrogen has n−1=2.8×10−4 at this wavelength. The beam crosses the cell twice (once each way), so the fringe count as the cell fills is N=2(n−1)ℓ/λ. The group can read the fringe position to the nearest twentieth of a fringe, δN=0.050, and the target precision on n−1 is δ(n−1)=1.0×10−6.
((a)) Choose the minimum cell length ℓ that meets this precision target.
((b)) For that cell length, state the total number of fringes N counted over the full evacuation-to-atmosphere fill, and confirm that resolving to a twentieth of that count meets the stated precision.