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GR9277 #68
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Comments |
tan
2009-10-31 04:48:19 | Plugging in the numbers gives a, not c. What's wrong? |  | justguessing
2009-09-29 08:13:27 | I always used that formula in degrees, not rad. I'm confused. | | ramparts
2009-08-06 21:08:19 | If you (like many people!) don't have this formula memorized, there's really only one logical way (dimensionally) to get the answer, and that's to divide the wavelength by the angle. Unless there's a dimensionless constant that's not on the order of 1 (in this case, it's 1.22, which is great), that'll give you a rough and easy order of magnitude estimation in cases like this, where the answers are off by powers of 10. | | p3ace
2008-05-11 15:32:40 | So why do we use the formula for diffraction to get the width of a mirror for resolution????
hot_dark_matter
2008-05-23 15:19:11 |
We use the concept of diffraction because when any light interacts with an optical instrument, the light diffracts. When two sources have a small angular separation, the central maxima of their respective diffraction patterns can overlap; thereby making two sources look like one.
To visualize the phenomena, consider a monochromatic source shining on a single slit and producing a diffraction pattern. Now if a second, identical source is turned on at the same position, the patterns overlap and an observer cannot discern whether there are one or two sources. If the second source is moved to one side, the second diffraction pattern appearing on the screen is also displaced.
To observe two distinct patterns we essentially need the central max of one pattern to occur, at the very least, at the first minima of the other pattern. Since the first minima occurs at  , the angular separation of the two sources must also be about  . As mentioned previously, the 1.22 is a numerical factor having to do with circular geometry rather than 1-D slits.
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student2008
2008-10-16 06:00:00 |
This is called the Rayleigh criterion.
See also http://en.wikipedia.org/wiki/Angular_resolution
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|  | hamood
2007-04-04 16:48:52 | Can anyone please tell me where the factor of 1.22 comes from, like how do we derive the formula. just curious about it....
nigelfordham
2007-04-10 12:22:21 |
the 1.22 comes from the evaluated bessel function in the derivation of diffraction of a circular aperture.
http://cnx.org/content/m13097/latest/
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