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Single slit help?

  1. Feb 21, 2013 #1
    1. The problem statement, all variables and given/known data

    A beam of light of unknown wavelength is incident on a screen with a single-slit. Observing the interference pattern on the projection screen that is 1.7 m away, the 4th minimum is 27 cm away from the central line. The width of the slit is 15 μm.
    a) What is the wavelength (in nm) of the light used?

    b) How wide(in cm)is the central maximum?

    2. Relevant equations
    Single slit equations


    3. The attempt at a solution
    I plugged everything in, stuck on the first step.

    Xn= n*Lλ/w
    = 4*1.7λ/1.5x10-5


    Help?
     
  2. jcsd
  3. Feb 21, 2013 #2

    TSny

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    Hello, alittlelost.

    To me, it's not clear what you're stuck on. Are you having trouble doing the math steps to solve for λ or is it something else?
     
  4. Feb 21, 2013 #3
    Hey TSny, actually that is what I'm having trouble with. My brain is absolutely fried. It's probably so simple, but I can't seem to figure it out right now.
     
  5. Feb 21, 2013 #4

    TSny

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    If you have the equation a = x/b and you need to solve for x, what would you do?
     
  6. Feb 21, 2013 #5
    divide a by b to isolate x?
     
  7. Feb 21, 2013 #6

    TSny

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    No. Consider a simple equation where you can easily see what the answer should be. Such as 4 = x/2
     
  8. Feb 21, 2013 #7
    Well for that I would just multiply the 4 and 2 to find x...Sorry, I misread. I'm a little tired. I just don't know how to rearrange this equation to find λ.
     
  9. Feb 21, 2013 #8

    TSny

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    Good. So to solve 4 = x/2 you multiply both sides by the denominator 2. Going back to your equation for λ, what would you multiply both sides by?
     
  10. Feb 21, 2013 #9
    by 1.5x10-5?

    So it should look like this then?

    (4)(1.5x10-5) = (4)(1.7)(1.5x10-5
     
  11. Feb 21, 2013 #10

    TSny

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    Not quite. Let's work in symbols before plugging in numbers.

    You have the equation X = n*L*λ/w. What does this become after you multiply both sides by w? (Note that I wrote your symbol Xn as just X because I think Xn looks like X multiplied by n which could get confusing.)
     
    Last edited: Feb 21, 2013
  12. Feb 21, 2013 #11
    You would get X*w= n*L*λ right?
     
  13. Feb 21, 2013 #12

    TSny

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    Yes. Good. Now you need to isolate λ. How are you going to (legally!) "get rid" of n and L on the right?
     
  14. Feb 21, 2013 #13
    Could I move n and L to the other side of the equation?
     
  15. Feb 21, 2013 #14

    TSny

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    Yes! Can you think of something you an do to both sides of the equation so that n and L disappear on the right and appear on the left?
     
  16. Feb 21, 2013 #15
    Divide both sides by n and L which would cause them to disappear?
     
  17. Feb 21, 2013 #16

    TSny

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    Right, that will cause n and L to disappear on the right and appear somewhere on the left. Then you can evaluate λ.
     
  18. Feb 21, 2013 #17
    Since I'm bringing over n and L they would become negative on the left side correct?
     
  19. Feb 21, 2013 #18

    TSny

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    No, dividing both sides by n and L does not cause n and L to change sign.

    If you wanted to solve a = x*b for x, you would divide both sides by b to get a/b = x. Note that b does not change sign.
     
  20. Feb 21, 2013 #19
    after everything gets cancelled out, should I only have X*w =λ? If so, I got 60000nm
     
    Last edited: Feb 21, 2013
  21. Feb 21, 2013 #20

    TSny

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    No that's not the correct formula for λ. Remember, if you solve a = x*b for x by dividing both sides by b, you get a/b = x. So, the b disappears on the right, but it now shows up on the left.

    So, when you divide both sides of X*w = λ*L*n by L and n, L and n will then appear somewhere on the left side. On the left side you will have an expression that represents dividing X*w by L and n.
     
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