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Calculating the Number of Lines on a Diffraction Grating

  1. Jun 19, 2016 #1
    1. The problem statement, all variables and given/known data
    A diffraction grating gives a second-order maximum at as angle of 31° for violet light (λ = 4.0 × 10^2 nm). If the diffraction grating is 1.0 cm in width, how many lines are on this diffraction grating?

    2. Relevant equations
    d = (m)(λ)/sinθm

    3. The attempt at a solution
    d = (m)(λ)/sinθm
    d = (2)(4.0 x 10-7 m)/sin(31°)
    d = 1.6 x 10 x 10-6 m

    0.01 m / 1.6 1.6 x 10 x 10-6 m = 6250 lines

    Many thanks in advance! :smile:
     
    Last edited: Jun 19, 2016
  2. jcsd
  3. Jun 19, 2016 #2

    Charles Link

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    You need to use the equation ## m \lambda=d \sin{\theta} ## for the location ## \theta ## of an interference maximum. From this equation and the info they gave you, you can compute "d"=the distance between the lines on the grating. (The grating is filled with these lines. Item of interest=your computed "d" is going to be very small=on the order of a wavelength of light.) The width of the grating is w=1.0 cm so you need quite a large number N of these closely spaced lines to make 1.0 cm. Do you know what the letter "m" represents?
     
  4. Jun 19, 2016 #3
    Is this what you mean? I was in the process of editing as you posted.
     
  5. Jun 19, 2016 #4

    Charles Link

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    Yes. Your d=1.6 E-6 (meters) is what it should read. I believe your answer is correct N=6250 but I would need to doublecheck the arithmetic. (And your m=2 is correct.)
     
  6. Jun 19, 2016 #5
    Yes, whoops, got a little overzealous with the scientific notation there, haha.

    Thank you Charles! :smile:
     
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