Michelson interferometer moves and bright fringes disappear

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SUMMARY

The discussion centers on calculating the distance a mirror in a Michelson interferometer is moved based on the disappearance of 250 bright fringes, with a light wavelength of 800nm. The formula used is 2d = mλ, where d is the distance moved, m is the number of fringes, and λ is the wavelength. The user concludes that the mirror was moved 0.01 cm. Additionally, the user seeks clarification on deriving the formula and understanding the impact on optical path length when the mirror is translated by fractions of the wavelength.

PREREQUISITES
  • Understanding of the Michelson interferometer and its operation
  • Familiarity with wave optics and interference patterns
  • Knowledge of the relationship between wavelength and fringe patterns
  • Ability to manipulate and derive equations related to optical path length
NEXT STEPS
  • Study the derivation of the formula 2d = mλ in the context of interferometry
  • Explore the effects of mirror displacement on optical path length in detail
  • Learn about the significance of fringe visibility and contrast in interferometry
  • Investigate applications of Michelson interferometers in measuring small distances
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Students and educators in physics, optical engineers, and anyone interested in the principles of wave interference and precision measurement techniques.

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Homework Statement


In a Michelson interferometer, as one of the mirrors is moved, 250 bright fringes disappear into the centre. If the light wavelength was 800nm, how far was the mirror moved?

Homework Equations

The Attempt at a Solution


My logic is:
If we were to count how many passing bright fringes we have, we could find the wavelength, basing ourselves off of the formula: 2d=mλ. In this case I would say 2Δd=Δmλ, where Δd is the distance that the mirror moved and Δm is the number of passing bright fringes.
So I would solve for Δd and get 0.01cm
My problem is, I am pretty sure I need to somehow derive 2d=mλ, I can't just use it. Can someone get me started on how to derive this?
Also, is my logic correct
 
Physics news on Phys.org
What happens to the corresponding optical path length if a mirror is translated over ##\lambda\over 2 ## ? Idem ## {2\lambda\over 2}, {3\lambda\over 2} ##, etc ?
 

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