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B Focal spot size limit??

  1. Jun 19, 2016 #1
    Did not know how to word this properly.

    Looking for an equation to show the behaviour of how EM can be "lensed" as a function of wavelength/frequency.

    ie RF waves can not be lensed/focussed to a spot.

    what equation determines the minimum spot size a lens can focus EM radiation as a function of frequency?
  2. jcsd
  3. Jun 20, 2016 #2

    Simon Bridge

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  4. Jun 20, 2016 #3


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    Is this what you are asking about? The Abbe diffraction limit of a microscope, which is r = λ/2.8. Shine a light thru the eyepiece and that is the minimum obtainable spot radius.
  5. Jun 20, 2016 #4


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    I believe you're asking about the Airy Disk. Try the math in this article: https://en.wikipedia.org/wiki/Airy_disk
  6. Jun 20, 2016 #5
    thanks guys. this is precisely the physics I was looking for.

    haven't read through it all in detail but am I right in thinking the spot size is purely a function of the hardware transforming the light?

    in the airy pattern, which is what is caused by diffraction from a circular aperture, would that increase the beam diameter after the aperture ie in general the smaller the aperture will cause greater spreading ie more diffraction. so therefore, if I am thinking right, a smaller beam will be achieved by a transparent lens than an aperture via diffraction.

    I am going to try link the beam waist formula to the airy disc radius, but not sure if I am messing up the wrong two concepts.
  7. Jun 20, 2016 #6


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    You're right in that a lens will make a smaller airy disk than an open aperture, but there's still a fundamental limit to how small the airy disk can be which is based on the size of the aperture and the wavelength of the incoming light/radiation. A larger aperture and/or smaller wavelength gives a smaller airy disk.
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