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 nm, and the vessel containing the gas is 25.0 cm long, what is the index of refraction of the gas?
A) 1.000111
B) 1.000222
C) 1.000445
D) 1.000889
E) 1.00178

Question

Quizplus · Accepted Answer

The change in optical path length is 2(n - 1)L, where n is the index of refraction of the gas, and L is the length of the vessel. The change in optical path length is also equal to mλ, where m is the number of fringes counted. Thus, 2(n - 1)L = mλ. Solving for n, we get n = 1 + mλ/2L. Plugging in the given values, we get n = 1 + 397(560 nm)/2(25.0 cm) = 1.000111.

A Michelson Interferometer Is Used to Measure the Index of Refraction