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Spacing between interference maxima

  1. Oct 13, 2008 #1
    1. The problem statement, all variables and given/known data
    a) Light of wavelength 651 nm illuminates a grating with 3,424 slits per cm. If the screen is 1.08 m away, what is the spacing between the interference maxima?

    b) A laser cavity of length 0.2400 m, has reflecting mirrors at each end. What is the frequency, in GHz, of the 20-th allowed mode? Answer to at least 3 significant figures. Assume that the speed of light in the cavity is 2.998E+8 m/s. First find the fundamental frequency for standing waves in this cavity. This is a basic standing waves question!


    3. The attempt at a solution
    a) So far I have tried this:
    d=1/N=1/342400=2.92e-6m

    then dsinθ=mλ
    I know d and λ, but now I have two unknowns in m and theta. Where to from here?

    b) I used 3 formulas, namely

    L=mλ/2 (1)
    V=mc/2L (2)
    and f=v/λ (3)

    where m = mth mode = 20
    L= length of laser cavity = 0.24m
    c=2.998e8

    I calculated λ from equation 1 to be = 2L/m = 2*0.24/20 = 0.024m and velocity using equation 2 to be = 20*2.998e8/2*0.24 = 1.24e10m/s
    Then using equation 3, f = 1.24e10/0.024

    I get an answer of 520GHz as opposed to the correct answer of 12.49GHz.
    Am I using the wrong formula/formulae?
     
    Last edited: Oct 13, 2008
  2. jcsd
  3. Oct 13, 2008 #2

    Redbelly98

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    Staff Emeritus
    Science Advisor
    Homework Helper

    Hmmm. They're asking for the spacing between different interference maxima. Maybe calculate θ for the 1st two maxima, and see how far apart they are on the screen?

    The velocity is c.

    Equation (2) is actually giving "nu", a Greek letter that resembles v, but is often used for frequency.
     
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