A Michelson interferometer is used to measure the index of refraction of a gas by counting interference fringes as the gas is slowly leaked into a transparent vessel placed in one arm of the interferometer. The vessel initially contains a vacuum, and as the gas is let in, the number of bright fringes is counted-i.e., the number of times the central region of the screen changes from bright to dark and back to bright. Suppose the index of refraction of the gas is 1.0003 . If the wavelength of light used is $560 \mathrm{~nm}$, and the vessel containing the gas is $25 \mathrm{~cm}$ long, how many bright fringes will be observed?
A) $1.78 \times 10^{6}$
B) 133
C) $2.23 \times 10^{5}$
D) $4.47 \times10^{5}$
E) 134
F) 267

Question

Quizplus · Accepted Answer

The number of fringes observed is given by the formula $ N = \frac{2L(n-1)}{\lambda} $, where $ L $ is the length of the vessel, $ n $ is the index of refraction, and $ \lambda $ is the wavelength. Substituting the given values: $ N = \frac{2 \times 0.25 \times (1.0003 - 1)}{560 \times 10^{-9}} \approx 267 $.

A Michelson Interferometer Is Used to Measure the Index of Refraction