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Diffraction Grating problem (waves and optics)

  1. Mar 13, 2014 #1
    1. The problem statement, all variables and given/known data

    Visible light passes through a diffraction grating that has 900 slits per centimeter, and the interference pattern is observed on a screen that is 2.58m from the grating. In the first-order spectrum, maxima for two different wavelengths are separated on the screen by 3.16 mm . What is the difference between these wavelengths?

    2. Relevant equations

    d*sinΘ=mλ

    3. The attempt at a solution

    d = 1/90000 = 1.111*10-5

    d*sin(Θ1)=λ1 and d*sin(Θ2)=λ2

    using subtraction d*ΔsinΘ=Δλ (and using small angle approx d*ΔΘ=Δλ)

    But im not sure how to find ΔΘ (or how even to visualize ΔΘ)

    thanks in advance.
     
  2. jcsd
  3. Mar 13, 2014 #2

    BvU

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    This help ?
    Azd61G7.jpg
    On the left is the grating, on the right is the screen.
    (grating details not shown on this scale)
     
  4. Mar 13, 2014 #3
    Thank you for making it clearer! i was originally thinking this but i didn't think i could calculate it since i didn't have all of the distance of the opposite side (the screen).

    Is this the correct way to go about it?

    Sin(ΔΘ) = sin(Θ2) - sin(Θ1)
    = x/2.58 + (3.16*10-3-x)/2.58 (where x is the total distance on the screen)
    = (3.16*10-3)/2.58
    ΔΘ=0.001225

    and λ=1.225*10-3*1.11*10-5
    =1.36*10-8
     
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