The element sodium can emit light at two wavelengths, λ1 = 588.9950 nm and λ2 = 589.5924 nm. Light in sodium is being used in a Michelson interferometer. Through what distance must mirror M 2 be moved if the shift in the fringe pattern for one wavelength is to be 1.00 fringe more than the shift in the fringe pattern for the other wavelength?

The distance is  

Explanation:

From the question we are told that

    The  first wavelength is  

     The  second wavelength is  

     The  difference in the  fringe pattern is  n =  1.0  

Generally the equation defining the effect of the movement of  the mirror M 2 in a Michelson interferometer is mathematically represented as

Here d is the mirror M 2  must be moved

substituting values

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this would be about 43%