Michelson's Interferometer Problem

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SUMMARY

The discussion centers on solving a problem related to Michelson's Interferometer, specifically focusing on the relationship between the indices of refraction and the speed of light in different mediums. The key equations utilized include Nm = 2L*n/λ and Na = 2L/λ, leading to the conclusion that Nm - Na = 2L*n/λ - 2L/λ. The final solution derived from the problem yields an index of refraction value of 1.0003, confirming the expected result. The discussion emphasizes understanding the logic behind light beam interference and the effects of medium changes on light speed.

PREREQUISITES
  • Understanding of wave interference principles
  • Familiarity with the Michelson Interferometer setup
  • Knowledge of the relationship between speed of light, wavelength, and index of refraction
  • Basic algebra skills for manipulating equations
NEXT STEPS
  • Study the principles of light interference in detail
  • Learn about the Michelson Interferometer and its applications in precision measurements
  • Explore the derivation of the index of refraction using different mediums
  • Investigate similar physics problems on platforms like Physics Forums for additional practice
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Students studying optics, physics educators, and anyone interested in understanding the principles of light interference and the Michelson Interferometer.

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Homework Statement



[PLAIN]http://img828.imageshack.us/img828/7386/physicsch3581.png

Homework Equations



Not sure

The Attempt at a Solution



the indicies of refracton are inversly related to the speeds, that is n=c/v . You find the time to go distance L in one arm t=L/v with air and the other with vacuum t=(L+dL)/c dL=(fringes)*wavelength

My substitute teacher gave us that as a hint, but I really don't see how that relates to the problem, or rather I don't see any of those equations in the section over the interferometer.

I see Nm = 2L*n/λ
Na = 2L/λ
Nm - Na = 2L*n/λ - 2L/λ

I really don't know where to begin on this problem, we never did any examples of it in class.
 
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I recommend that you focus on the logic of the Michelson interferometer. You split a light beam and then recombine it: why does interference occur?

If you have that down, think though the effects of changing the speed of the one beam by putting it through a vacuum rather than air.

You might also look at https://www.physicsforums.com/showthread.php?t=358946", which is about a very similar problem.
 
Last edited by a moderator:
Ended up using Nm - Na = 2L*n/λ - 2L/λ and solved for n. Ended up with the books value of 1.0003.
 

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