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What is the light's wavelength?

  1. May 23, 2012 #1
    1. The problem statement, all variables and given/known data
    A diffraction grating having 500 lines/mm diffracts visible light at 30°. What is the light's wavelength?

    d = 1/500(lines/mm) = 2x10-6(m)
    θ = 30° = pi/6 rad⇔
    2. Relevant equations
    d*sin(θm) = mλ

    3. The attempt at a solution
    when i rearranged the equation, i got λ = d*sin(θm)/m
    And the problem was how can i find what is the order of the diffraction?
    I assumed it to be the first order, so m=1, and i got the wavelength was 1000nm but the answer was 500nm, so it must be the second order, m=2. But i have no idea how to get m=2
     
  2. jcsd
  3. May 24, 2012 #2

    cepheid

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    Gold Member

    It says the grating diffracts *visible* light. The order m = 2 is the only one for which you get an answer for lambda that is in the visible range. A wavelength of 1000 nm is too large, and the wavelengths for all orders higher than 2 are too small.

    That's one way I can think of to arrive at the answer. I could also be missing something else. But for now, this is what I can come up with.
     
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