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Seperation for third order maxima for two wavelengths - help please

  1. Jan 25, 2014 #1
    1. The problem statement, all variables and given/known data


    A grating has 1070 lines per centimetre, and a flat screen is perpendicular to the ray that makes the central peak of the diffraction pattern. The screen is 3.20 m from the grating. If light of two wavelengths, 630 nm and 705 nm, passes through the grating, what is the separation on the screen between the third-order maxima for the two wavelengths?


    2. Relevant equations

    mλ = dsinΘ

    3. The attempt at a solution


    d = 1/1070 = .000935 * 10 000 000 = 9345.79nm

    λ1 = Θ1 = sin^-1(3*705 / 9345.79) = 13.0796°
    λ2 = Θ2 = sin^-1(3*630 / 9345.79) = 11.6674°

    [3.2tan(13.0796°)] - [3.2tan(11.6674)] = .082673 * 1000 = 82.67 nm


    My answer is incorrect, can anyone see where I'm going wrong here?

    Also, where I multiplied my numerator by 3 above, I did that due to the third order maxima, is that correct? I was impatient and also tried multiplying it by 2 instead, also incorrect.

    Please help me out here.
     
  2. jcsd
  3. Jan 25, 2014 #2

    Doc Al

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    Check your arithmetic.
     
  4. Jan 25, 2014 #3
    oops.

    Then shouldn't using (1/107) * 10000000 as my new value be right?

    It's still wrong.
     
  5. Jan 25, 2014 #4

    Doc Al

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    Two things:
    (1) That should be (.1/1070)
    (2) 1 nm = 10^-9 m
     
  6. Jan 25, 2014 #5
    I still got it wrong.

    I'll show you once more what I'm doing now


    d = .1/1070 = .000093 * 10 000 000 = 934.579nm

    λ1 = Θ1 = sin^-1(3*705 / 934.579) = x1°
    λ2 = Θ2 = sin^-1(3*630 / 934.579) = x2°

    [3.2tan(x1°)] - [3.2tan(x2)] = z

    z*1000 = ans


    still wrong though


    Where exactly do i need to make changes, and what are those changes? I have 6 tries left.
     
  7. Jan 25, 2014 #6

    Doc Al

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    .1/1070 = 0.0000934579 m. So far, so good.
    Why do you then multiply by 10 000 000? Instead, multiply by 109.
     
  8. Jan 25, 2014 #7
    im doing all of this and still getting it wrong
     
  9. Jan 25, 2014 #8

    Doc Al

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    Post each step, just like you did before.
     
  10. Jan 25, 2014 #9
    Most previous try:

    d = .1/1070 = .000093 * 10^9 = 93457.9 nm

    λ1 = Θ1 = sin^-1(3*705 / 93457.9) = 1.297°
    λ2 = Θ2 = sin^-1(3*630 / 93457.9) = 1.159°

    [3.2tan(1.297)] - [3.2tan(1.159)]

    = .0077 nm
     
  11. Jan 25, 2014 #10

    Doc Al

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    That answer in is meters, not nm. What units do they want the answer in? mm makes sense.
     
  12. Jan 25, 2014 #11
    Well the units don't matter, hold on I will convert it and give it a try!
     
  13. Jan 25, 2014 #12
    7.7mm didn't work
     
  14. Jan 25, 2014 #13

    Doc Al

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    I don't see an obvious error, unless it's just a significant figures issues. Often those systems want 3 sig figs no matter what.

    Otherwise I will look at this more carefully later and see if there's another error that I missed.
     
  15. Jan 26, 2014 #14
    Sounds great. Thank you very much for your help this far.
     
  16. Jan 26, 2014 #15

    Doc Al

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    I don't see any errors in the calculation.

    Did you try using 3 sig figs in your response? (I assume this is some online system, not a textbook problem, right?)

    If all else fails, it might help to take a screenshot of the question so that we can check that there's no ambiguity. (Though it seems pretty clear.)
     
    Last edited: Jan 26, 2014
  17. Jan 26, 2014 #16
    I did try 3 sig figs.. still wrong. In my angle calculation (second step), I multiplied each wavelength by 3, is that correct?
     
  18. Jan 26, 2014 #17

    Doc Al

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    Sure.
     
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