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Diffraction patterns and lasers!

  1. Feb 25, 2012 #1
    1. The problem statement, all variables and given/known data
    A laser with monochromatic light of frequency 6.33 × 10^14 Hz is fired through a diffraction grating.

    If the first minimum in this diffraction pattern coincides with the position of the second order that was seen in the previous diffraction pattern, what is the width of the slit?


    2. Relevant equations
    [itex]w=\frac{\gamma}{\sin\theta}[/itex]

    [itex]n\gamma=d\sin\theta_{n}[/itex]

    3. The attempt at a solution
    Here are my results from a previous question to which it refers

    Using the following values: [itex]\gamma=633nm[/itex]
    and [itex]\theta=39.3^{o}[/itex]
    and the equation [itex]n\gamma=dsin\theta_{n}[/itex]

    Rearranged for distance between the slits [itex]d=\frac{n\gamma}{sin\theta_{n}}[/itex]
    then [itex]d=\tfrac{5*633x10^{-9}m}{sin(39.3)}=5\mu m[/itex] or 5.00E^{-6}m

    Now to answer this question I've calculated the distance between the slits:

    First calculate the distance between the slits second order using the equation [itex]d=\frac{n\gamma}{sin\theta} = \frac{2*633E^{-9}m}{sin(39.3)}=2\mu m[/itex] or 2.0E{}^{-6}
    m.

    This is where I don't know where to go... I know I need w... but how? Please help, I've had a thought:
    by combining the two equations and substituting for [itex]\sin\theta[/itex] then maybe [itex]\frac{n\gamma}{d}=\frac{\gamma}{w}[/itex] so [itex]w=\frac{\gamma d}{n\gamma}=\frac{d}{n}[/itex]
     
    Last edited by a moderator: Feb 25, 2012
  2. jcsd
  3. Feb 25, 2012 #2

    Redbelly98

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    Hello,

    I'm getting confused in trying to follow what you did, so let's start by clearing some things up.

    (I'll not worry that you're using [itex]\gamma[/itex] for wavelength when λ is the conventional symbol used by maybe 99.9% of all physics teachers and textbooks :smile:)
    Okay, for starters, diffraction gratings do not produce well-defined minima. Since you mention "the width of the slit", I am wondering if the current problem is actually for a single slit, whereas the previous problem did use a diffraction grating. Can you confirm this, or clarify what the setup really is for the two problems?

    That is either the 1st order minimum for a single slit of width w -- or possibly the 1st order maximum of a diffraction grating (or double slit) of grating (slit) spacing w.

    Looks good. That gives the nth-order maxima of a diffraction grating (or double slit) of grating (slit) spacing d.
    It looks like the problem was to find d for a diffraction grating, if the 5th-order maximum makes an angle of 39.3° for light of wavelength 633 nm. Can you confirm my guess?
    What slits? If it's the same diffraction grating, the grating spacing doesn't change and is still 5.00 μm. Or is it really supposed to be some other grating? :confused:

     
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