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Confused about this Optics problems Solution

  1. Dec 3, 2011 #1
    1. The problem statement, all variables and given/known data
    The Lick Observatory has one of the largest refracting telescopes, with an aperture diameter of 36 in. and a focal length of 56 ft. Determine the radii of the first, second, and third bright rings surrounding the Airy disc in the diffraction pattern formed by a star on the focal plane of the objective.


    2. Relevant equations
    [tex]\frac{\pi}{\lambda}Dsin\theta=\gamma[/tex]
    Where \gamma is either the maxima (bright fringes) or minima (dark fringes) of the bessel function which occurs in the solution to the diffraction through a circular aperture.
    [tex]r=f \theta[/tex]
    Where f is the focal length.
    Maxima of Gamma function: 5.136,8.417,...

    3. The attempt at a solution
    This is not an attempt, this is part of the actual solution. I do not understand a certain aspect of it though.

    So using the first equation above and solved for sine. I came into a problem though. The problem doesn't give the wavelength! The solution just says..
    "Thus for wavelength of 550nm..."
    And then they plug it in. Where did this come from?!

    Thanks :D
     
  2. jcsd
  3. Dec 3, 2011 #2

    Simon Bridge

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    550nm is green light - right in the middle of the visible spectrum and thus in the middle of the fringes/rings.

    This sort of thing is common - IRL you are unlikely to have all the information you need to do a calculation right then and there. It may be difficult to get a figure too. So you have to make a reasonable guess. If you knew the spectra of the star in question, you would pick a different wavelength perhaps but you are only told that it is visible.
     
  4. Dec 3, 2011 #3
    Thank you very much! That makes perfect sense :]
     
  5. Dec 3, 2011 #4

    Simon Bridge

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    No worries then - have fun :)
     
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