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Homework Help: How far apart are two stars

  1. Feb 7, 2009 #1
    1. The problem statement, all variables and given/known data
    Two stars 18 light-years away are barely resolved by a 68 -cm (mirror diameter) telescope. How far apart are the stars? Assume \lambda = 540 <units>nm</units> and that the resolution is limited by diffraction.
    Express your answer using two significant figures.



    2. Relevant equations
    Theta=(1.22 lambda)/diameter of the lense

    9.4605284 × 10^15 meters


    3. The attempt at a solution
    I have no clue how to do this. I plugged the give info into the equation and got theta to equal 9.6882352941176470588235294117647e-7 then i just plugged this into the Pythagorean equation to get 559491313771834207552834.45286104
     
  2. jcsd
  3. Feb 7, 2009 #2

    mgb_phys

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    Science Advisor
    Homework Helper

    Roughly from similair triangles:
    lamba/D = separation/distance

    The angle between the stars is 1.22lambda/D so you can work out this angle (remember is answer in radians) then you have the angle between two stars a distance away so getting the distance between them is easy.
    Since the angles are small you can use the apprx theta = sin theta (in radians)
     
  4. Feb 7, 2009 #3
    I have worked it out both ways and both of the answers i got were wrong
     
  5. Feb 8, 2009 #4
    Remember, as mgb_phys stated, Rayleigh's Criterion expresses the angular distance in radians.

    If you're still getting the incorrect answer I suggest you explicitly post how you're calculating the distance.
     
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