A Michelson Interferometer Is Used to Measure the Index of Refraction

Multiple Choice

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