Calculating the Period of Fringe Pattern for Michelson Interferometer

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SUMMARY

The discussion focuses on calculating the period of fringe patterns in a Michelson Interferometer. When Mirror 1 is displaced by Δ𝑑=𝜆0/2Δ, the path difference changes by one wavelength (𝜆0), resulting in adjacent fringes shifting positions. The relationship Δ𝑑=𝑚(𝜆0/2) is established, and the phase shift of the fringes is described by the equation I0=2I0 - 2I0 cos (2kdL) or 2wt. The key challenge is determining the implications of the beam's wavelength and the displacement of Mirror 1 on fringe movement.

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Homework Statement
Given the wavelength of the beam of light, and the displacement of one of the mirrors, how would one go about finding the fraction of a period the fringe pattern will move as a result of the mirror displacement?
Relevant Equations
Δ𝑑=𝑚(𝜆0/2), I0=2I0 - 2I0 cos (2kdL or 2wt), dL=L1-L2
In a Michelson Interferometer when Mirror 1 is moved a distance Δ𝑑=𝜆0/2Δ, this path difference changes by 𝜆0, and each fringe moves to the position previously occupied by an adjacent fringe. Δ𝑑=𝑚(𝜆0/2)

I also know from the equation for I0=2I0 - 2I0 cos (2kdL or 2wt) that the fringes shift by a phase 2kdL or 2wt(omega tau). I'm unsure what to do , though, given that I am only provided the beam's wavelength and mirror 1's displacement. I'd appreciate any help!
 

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