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Homework Help: Diffraction gratings

  1. Jul 23, 2015 #1
    1. The problem statement, all variables and given/known data

    A diffraction grating produces a third-order maximum, at an angle of 22 degrees, for red light (694.3 nm). Determine the spacing of the lines.

    2. Relevant equations

    for maxima:

    sin θm = mλ/d

    where m is the order of the maxima, λ is the wavelength in nm, and d is the spacing of the lines

    3. The attempt at a solution

    λ = 694.3 nm
    θ = 22
    m = 3

    d = mλ / sin θ
    d = 3 (694.3) / sin 22
    d = 5560 nm

    but the answer in the textbook is 7400 nm. what have i done wrong?

    and this one:

    Calculate the highest spectral order visible when a 6200-line/cm grating is illuminated with 633-nm laser light.

    d = 1/6200 cm
    λ = 633 nm = 6.33 x 10^9 cm
    n = ?

    how do i find n without θ? i'm probably missing some obvious things
  2. jcsd
  3. Jul 24, 2015 #2


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    Education Advisor
    Gold Member

    Are you sure they didn't mean 4th-order maximum?

    I'll look at the second question in a few.
  4. Jul 24, 2015 #3


    User Avatar
    Education Advisor
    Gold Member

    You're setting up an inequality for the second problem, what are the constraints on theta?
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