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Highest order of spectrum given two wavelengths

  1. Feb 10, 2014 #1
    1. The problem statement, all variables and given/known data

    I've attached the problem

    2. Relevant equations

    d*sinθ=mλ

    3. The attempt at a solution

    I've tried a couple of methods. I considered solving for m when θ=90 degrees => sinθ=1 because 90 degrees is the highest possible angle and will (in my mind at least) yield the highest order of spectrum by rounding the resultant value of m down to the nearest integer. But I don't know how to factor the two given wavelengths into all this.

    I then considered fiddling about with approximations like, at small angles, tanθ=sinθ=θ=y/L but to no avail.

    Can anyone help me on how to solve this? I don't even know how to picture the problem and draw a diagram.
     

    Attached Files:

  2. jcsd
  3. Feb 10, 2014 #2

    Simon Bridge

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    To get a fringe at a position you need constructive interference at that position.
    What is the condition for constructive interference?

    Note: you probably have not been given the final equation for this situation, you will have to work it out for yourself.
     
  4. Feb 10, 2014 #3

    ehild

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    Last edited: Feb 10, 2014
  5. Feb 11, 2014 #4
    Thanks for the replies.

    Constructive interference would occur when m=some integer.

    Thanks, but it appears that when I work through (with the assumption that θ=90) I get m=5 for the 410nm wave, whereas the OP of that topic arrived at m=4. Is the assumption I'm working with wrong (about θ being equal to 90 degrees)? And what's the reason for choosing m=3 over m=4?

    Also, how do I go about working out the second part of the question?
     
  6. Feb 11, 2014 #5

    ehild

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    d*sinθ=mλ, and θ<90°. The 5th order maximum does not appear for the 410 nm wave.
    Also, the maximum order is 3 for the red light, and the problem asked the number of full spectra.

    Determine the angles of both the violet and red light for m=1, 2, 3, 4 and arrange them in increasing sequence.

    ehild
     
  7. Feb 11, 2014 #6

    Simon Bridge

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    Kinda - that's not the whole story.

    This means you need to understand the physics:

    Consider - if you had white light incident on the slits, you get a series of rainbow fringes.
    Each fringe is a whole spectrum, but the highest order spectrum may be incomplete ... so you can end up with more blue fringes than red ones.

    Originally I thought you were looking at something like water waves with a different frequency at each slit.

    You should certainly do the exercise that ehild suggests at the end of post #5
    Determine the angles of both the violet and red light for m=1, 2, 3, 4 and arrange them in increasing sequence.
     
  8. Feb 11, 2014 #7
    Aha, thanks a bunch Simon Bridge and ehild, I'll finally got the answers!
     
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