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How wide is a single slit that gives its first minimum at 90°?

  1. Aug 31, 2014 #1
    1. The problem statement, all variables and given/known data
    How wide is a single slit that gives its first minimum at 90°?


    2. Relevant equations
    øp=p(λ/a)



    3. The attempt at a solution
    Not quite sure what the answer is looking for but I'd guess I would need to solve for "a." So...

    90°=(λ/a)


    Is there any more information I can gather from this problem? Any guidance would be a big help.

    Thanks guys!
     
  2. jcsd
  3. Aug 31, 2014 #2

    BvU

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    Hello JMM and welcome to PF,

    The answer isn't looking for anything. You've given a problem statement, but suppose I didn't know any of the symbols appearing in your equation; then: how could I help you ?

    Do you know what the answer is to "How wide is a single slit that gives its first minimum at 30°?" or 45 or 60 ? Can you express that in a formula ? Then moving on to 90 shouldn't be too dificult, right ? Or... ?
     
  4. Aug 31, 2014 #3
    Hi BvU,

    I do not know the answer to that question. No matter the angle, I'm not quite sure how to express it in a formula. I apologize if I have not asked my question in the proper form for this website.

    I know the equation øp=p(λ/a) will tell me where the dark bands are on the screen. I assume øp = 90 since that is given. I do not know λ. It appears I need to solve for a, which is the width of the slit.
     
    Last edited: Aug 31, 2014
  5. Sep 1, 2014 #4

    BvU

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    Let me rephrase:
    What is ø and what are the units ?
    What is p and what are the units ?
    What is λ (ok, the wavelength in m)
    What is a and what are the units ? Ah we know now: the width of the slit. Also in m.

    Your expression doesn't look like what I see coming by when I simply google the title of this post. So it comes from your book or your notes, right ? What is it based on ?
    (Note that in many treatments a small-angle approach is used, where ##\sin\theta=\tan\theta=\theta##. This is something you can't have in this exercise!)

    In an exercise like this, it is OK to express the answer in units of λ .

    Oh, and:
    makes me wonder where in the equation the multiplicity ("dark bands") appears?
     
  6. Sep 1, 2014 #5
    Sorry to waste your time with stupid questions. I will seek help elsewhere.
     
  7. Sep 1, 2014 #6

    BvU

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    I'm fully prepared to provide the best possible assistance. But your cooperation is indispensible.
     
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