Airy Disc Formula: Why Does it Include 1.22?

[agentas]

Why Airy disc formula has 1.22 in front of it?Does it depend on aperture diameter?Thanks

 

[Andy Resnick]

The factor 1.22 is there because an Airy disc is comprised of a Bessel function:

http://en.wikipedia.org/wiki/Airy_disk
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/cirapp2.html

the 'diameter' of the first dark ring is equal to 1.22*l/d, where l is the wavelength of light and d the diamater of the entrance pupil. If the aperture was not circular, the factor 1.22 would be different, reflecting the difference in far-field diffraction pattern.