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In a Michelson interferometer using a He-Ne laser (lambda = 633 nm in vacuum), one arm contains a 4 cm thick gas cell. Initially the cell is evacuated and the central fringe is bright. As the cell fills to atmospheric pressure, 43 bright-dark-bright fringe shifts are counted. Find 10000*(n - 1), where n is the refractive index of the gas.

1. 6.83
2. 8.63
3. 10.83
4. 4.63

Correct answer: 6.83

Solution

The number of fringe shifts equals the extra optical path divided by lambda: N = L*(n-1)/lambda. So n-1 = N*lambda/L = 43*633e-9/0.04 = 6.805e-4. Thus 10000*(n-1) = 6.80 ~ 6.83.

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