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Minimum angle required for resolution

  1. Apr 5, 2009 #1
    1. The problem statement, all variables and given/known data

    The radio telescope at Arecibo, Puerto Rico, has a reflecting spherical bowl of 295 m diameter. Radio signals can be received and emitted at various frequencies with appropriate antennae at the focal point of the reflecting bowl. At a frequency of 200 MHz, what is the angle between two stars that can barely be resolved?

    2. Relevant equations

    θmin= (1.22λ)/D

    θmin= minimum angle required for resolution (rad)
    λ = wavelength
    D = diameter of aperture

    3. The attempt at a solution

    Should be fairly straightforward but I'm getting hung up on what I am sure is something silly. The equation above should be all that is needed. Just do (1.22*1.5)/295 as specified by the problem for θmin (in radians). I know I must be overlooking something simple, so any help is greatly appreciated. Thanks!
     
  2. jcsd
  3. Apr 5, 2009 #2

    Redbelly98

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    Don't worry, this one really is that simple :smile:
     
  4. Apr 5, 2009 #3
    Heh. Figured as much. I'll keep looking at it, and I'm sure it will come to me eventually. Thanks.
     
    Last edited: Apr 5, 2009
  5. Apr 5, 2009 #4

    Redbelly98

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    What do you mean "it will come to me eventually"?

    (1.22*1.5)/295​

    You are just a few calculator keystrokes from having the answer. (In radians)
     
  6. Apr 5, 2009 #5
    Well, 1.22 times the wavelength (1.5m) divided by D (295m) should equal θmin in radians, no? That is how I'm interpreting it, at least.
     
  7. Apr 5, 2009 #6

    Redbelly98

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    Yes, exactly.
     
  8. Apr 5, 2009 #7
    That's what I thought. System says that's incorrect, though.
     
  9. Apr 5, 2009 #8

    Redbelly98

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    Weird. All I can think is it's either a significant figures or units problem. But with radians, expressing no units should be acceptable. I guess you have rechecked the calculation.

    Can't think of anything else, but if I do I'll post here again.
     
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