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Light and Diffraction Gratings

  1. Jul 25, 2008 #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
    Last edited: Jul 25, 2008
  2. jcsd
  3. Jul 26, 2008 #2
    interference in thin films:

    A transparent oil (n=1.29) spills onto the surface of water (n=1.33), producing a maximum of reflection with normally incident orange light, with a wavelength of 6.00 x 10^-7 m in air. Assuming the maximum occurs in the first order, determine the thickness of the oil slick.

    n[oil] = λair/λoil

    where n is the index of refraction of oil

    λoil = n[oil]λair
    = 1.29(6.00 x 10^-7)
    λoil = 7.74 x 10^-7


    t = λoil / 4

    where t is the thickness of the oil and λ/4 is when the first maximum occurs

    t = 7.74 x 10^-7/4
    t = 1.935 x 10^-7 m = 193.5 nm

    the answer is supposed to be 233 nm.
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