GR0177 #13


Problem


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Optics}Aperture Formula
The circular aperture formula (a.k.a. Rayleigh Criterion) is given by . Plug in the given quantities to get that.
(It's a nice formula to memorize, as it's used as common sense in a variety of engineering fields, as well as in remotesensing, such as satellitecommunications.)


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Comments 
kevintah 20151007 05:43:54  Can anyone tell me where the 1.22 comes from? I would memorize the formula with that constant, but I am just interested to know where it comes from.
NervousWreck 20170328 09:21:55 
From some accurate integration for a diffraction from a circular aperture

poopterium 20171026 00:47:57 
Just in case anyone comes across this....it comes from integrating over a circular aperture in optics. The 1.22 comes from a zero of a first order Bessel\'s function of the first kind. I believe the zero of the function is about 3.9, then dividing it by pi gives you the 1.22.

  grae313 20071101 16:19:02  "that" being 2.5 cm, or choice (B) :) thanks Yosun
ebykl 20080923 21:13:33 
I'm confused about units...which unit do we have to use as wavelength, do we need to use nanometer or sth else??

nobel 20081031 04:40:39 
use lambda in metres then u get D in metres, use lambda in cms to get D in cms.
1 nanometre is 10^(7) cm and 10^(9) m

andrew0387 20090930 21:30:14 
1 nm is 10^(11) cm. I believe nobel meant to say that 100 nm is 10^(7)m. Then when dividing by the angle in radians, you get 2.44*10^(2)m, which is 2.44 cm.

Albert 20091027 10:47:29 
Sorry andrew0387, you seem to be confused. Nobel is right, 1 nm is 10^(9)m and it is also 10^(7)cm....always remember whenever you consider smaller units, the number in the power gets bigger. In this case, 7 is bigger than 9. Therefore, 1 nm is NOT 10^(11)cm.
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