In Michelson's interferometer the yellow sodium line composed of two wavelengths `lambda_(1) = 589.0 nm` and `lambda_(2) = 589.6nm` was used. In the process of translational displacemnet of one of the mirrors the interference pattern vanished periodically (why?). Find the displacement of the mirror between two successive appearances of the sharpest pattern.

Explanation

Interference pattern vanishes when the maxima due to one wavelength mingle with the minima due to the other. Thus
`2 Delta h = k lambda_(2) = (k + 1) lambda_(1)`
where `Deltah =` displacement of the mirror between the sharpest patterns of rings
Thus `k (lambda_(2) - lambda_(1)) = lambda_(1)`
or `k = (lambda_(1))/(lambda_(2) - lambda_(1))`
So `Deltah = (lambda_(1)lambda^(2))/(2(lambda_(2) - lambda_(1))) = (lambda^(2))/(2Delta lambda) = 2.9 mm`.