Michelson\'s interferometer played an important role in improving our understand

Question

Michelson's interferometer played an important role in improving our understanding of light, and it has many practical uses today. For example, it may be used to measure distances precisely. Suppose the mirror labelled 1 in the figure below is movable. If the laser light has a wavelength of 639.0 nm, how many fringes will pass across the detector if mirror 1 is moved just 1.140mm? If you can easily detect the passage of just one fringe, how accurately can you measure the displacement of the mirror?

Explanation / Answer

The path difference associated with the mirror movement of d is 2d, i.e if the mirror is moved a distance d , the path difference will be 2d

this path difference 2d = m where m is the number of fringes that pass across and is the wavelength

So, for d = 1.14 mm

2 x 1.14 x 10-3 = m x 639 x 10-9

m = 3568.075 So, approximately 3568 fringes will pass across the detector if mirror 1 is moved just 1.14 mm

For, one fringe, m = 1

So, 2d = 1 x 639 x 10-9

d = 319.5 nm

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