Question

3. A Michelson interferometer is used to measure the refractive index of a gas. The gas is allowed to flow into a glass tube of length L, placed in one arm of the interferometer a. (5 pts) With the tube filled with glass, a shift of N fringes is observed in the resulting interference measurement. Find the index of refraction for the gas in terms of N, L and the wavelength (5 pts) How many fringes would be counted if we used a gas with index n-1.00045 for a 1 cm long tube, and a sodium light with 589 nm wavelength? (5 pts) How about if we wanted to now measure a strange gas mixture with n 100001. Can you do the measurement with the given setup? Explain if you can, or what you need to change in order to be able to measure properly. b. c.

Answer 1

"a) Let the wavelength of right side used be 'lambda' The interface pattern obtained at the screen are normally bright and dark concentric circles ""If the optical path length of one beam changes by one wavelength base to the gas tube of length 'L' then interface paper i.e., shifted by one fringe"". \r\n Optical path length of beam travelling through gas tube of refractive index (of gas) 'n' and length 'L' = nL optical path length of beam travelling through air of same length = L But light of beam traverser the path in both arms twice due to refraction so, total path difference is, delta = (n L - L) times 2 delta = 2L (n - 1) -(1) If 'N' fringes are shifted, then the path difference should be N times lambda, i.e., delta = 2L (n - 1) = N lambda"

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