Calculating the Period of Fringe Pattern for Michelson Interferometer

Thread starter cryforhelp104
Start date Feb 9, 2024
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Michelson interferometer Physics

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In a Michelson Interferometer, moving Mirror 1 by a distance Δd=λ0/2 results in a path difference of λ0, causing each fringe to shift to the position of an adjacent fringe. The relationship Δd=m(λ0/2) is crucial for understanding fringe movement. The intensity equation I0=2I0 - 2I0 cos(2kdL or 2wt) indicates that fringes shift by a phase of 2kdL or 2wt. The discussion highlights a need for clarity on how to apply the given wavelength and mirror displacement to calculate the period of the fringe pattern. Understanding these principles is essential for accurate calculations in interferometry.

Feb 9, 2024

cryforhelp104

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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