A Michelson Interferometer Is Used to Measure the Index $560 \mathrm{~nm}$

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, 397 bright fringes are counted. That is, the central region of the screen changes from bright to dark and back to bright 397 times. If the wavelength of light used is $560 \mathrm{~nm}$ , and the vessel containing the gas is $25.0 \mathrm{~cm}$ long, what is the index of refraction of the gas?

A) 1.00178
B) 1.000111
C) 1.000889
D) 1.000445
E) 1.000222