Answer:
The distance is [tex]d = 0.00029065 \ m[/tex]
Explanation:
From the question we are told that
The first wavelength is [tex]\lambda _1 = 588.9950 nm = 588.9950 *10^{-9} \ m[/tex]
The second wavelength is [tex]\lambda _2 = 589.5924 nm = 589.5924 *10^{-9} \ m[/tex]
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
[tex]2 * d = [\frac{\lambda _1 * \lambda_2 }{\lambda_2 - \lambda _1 } ] * n[/tex]
Here d is the mirror M 2 must be moved
substituting values
[tex]2 * d = [\frac{(588.9950*10^{-9} ) * (589.5924 *10^{-9}) }{(589.5924 *10^{-9}) - (588.9950*10^{-9} ) } ] * 1.0[/tex]
[tex]d = 0.00029065 \ m[/tex]
