1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Michelson Interferometer problem

  1. Sep 15, 2008 #1
    1. The problem statement, all variables and given/known data
    A Michelson interferometer operating at a 600nm wavelength has 2.00 cm glass cell in one arm. To begin, the air is pumped out of the cell and mirror M2 is adjusted to produce a bright spot ant the center of the interference pattern. Then a valve is opened and air is slowly admitted to the cell. The index of refraction of air at 1 atm of pressure is 1.00028. How many bright-dark-bright fringe shifts are observed as the cell fills with air?

    2. Relevant equations

    3. The attempt at a solution

    To start out the problem, in order to form a bright spot at the center, I think that there must be an equal number of wavelengths going through both arms.

    The number of wavelengths in the evacuted glass tube is (.02/6.0e-7)= 33,333

    The wavelength of the light in the air is: (6.0e-7)/1.00028 = 5.998e-7

    The length of the other arm must then be adjusted to be:

    33333= L2/(5.998e-7) L2= 0.01999 m

    When the glass tube is filled w/ air, the number of wavelengths will be (.02m)/(5.998e-7) = 33344 wavelengths.

    But I'm not sure how to put this into equation form to calculate the number of shifts I will see. Can someone explain this to me? I'm really having a tough time visualizing
  2. jcsd
  3. Sep 15, 2008 #2
    Ok... I think I have it... first I need to multiply both 33333 and 33344 by 2, then I will subtract them.

    2(33344-33333) = 22. Is this right?
  4. Sep 15, 2008 #3


    User Avatar
    Homework Helper

    The procedure you are following looks right to me; everytime you "fit" in an extra half-wavelength into the air cell you get a transition from bright to dark fringe (or vice versa).

    However, numerically I believe you might need to be more careful. Subtracting two numbers that are close together causes a loss of precision. If you let your calculator keep all the digits it can (intead of rounding off during the problem) I think you'll find that the answer 22 has a large percent error.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Michelson Interferometer problem