Airy Disc Formula: Why Does it Include 1.22?

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The factor 1.22 in the Airy disc formula arises from the properties of Bessel functions, which describe the diffraction pattern of circular apertures. Specifically, the diameter of the first dark ring in the Airy disc is calculated using the formula 1.22*l/d, where l represents the wavelength of light and d is the diameter of the entrance pupil. If the aperture shape changes from circular to another form, the 1.22 factor would also change, indicating a different diffraction pattern in the far field. Understanding this factor is crucial for accurately predicting the behavior of light as it passes through various apertures. The discussion highlights the importance of aperture shape in optical physics.
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Why Airy disc formula has 1.22 in front of it?Does it depend on aperture diameter?Thanks
 
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