A221210 -id:A221210 - cp's OEIS frontend

A245461 Decimal expansion of constant in the Rayleigh criterion: first zero of J_1, divided by Pi.

1, 2, 1, 9, 6, 6, 9, 8, 9, 1, 2, 6, 6, 5, 0, 4, 4, 5, 4, 9, 2, 6, 5, 3, 8, 8, 4, 7, 4, 6, 5, 2, 5, 5, 1, 7, 7, 8, 7, 9, 3, 5, 9, 3, 3, 0, 7, 7, 5, 1, 1, 2, 1, 2, 9, 4, 5, 6, 3, 8, 1, 2, 6, 5, 5, 7, 6, 9, 4, 3, 2, 8, 0, 2, 8, 0, 7, 6, 0, 1, 4, 4, 2, 5, 0, 8, 7

Offset: 1

Charles R Greathouse IV, Jul 22 2014

The angular resolution (diffraction limit), in radians, is this constant times the wavelength of the light used divided by the aperture diameter. That is: objects closer than this angle cannot be resolved as separate objects.
Note that the small angle approximation sin(theta) =~ theta can be used. Also, a commonly used approximation to this constant is 1.220. - John W. Nicholson, Jul 29 2014
For example, a radio telescope with a 300-meter aperture observing at the hydrogen line (21.106... cm) can distinguish objects at most 0.04916... degrees apart. - Charles R Greathouse IV, Mar 08 2018

			1.21966989126650445492653884746525517787935933077511...

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
COSMOS - The SAO Encyclopedia of Astronomy, Rayleigh Criterion
Rene Kay, Todd Kay, Planet Seeker Interferometer (PSI), hal-02870885v2 [astro-ph.IM], 2020.
Wikipedia, Angular resolution
Wikipedia, Diffraction-limited system
Index entries for transcendental numbers

Cf. A115369, A221210.

RealDigits[ BesselJZero[1, 1]/Pi, 10, 111][[1]] (* Robert G. Wilson v, Jul 23 2014 *)

PARI
```
solve(x=3,4,besselj(1,x))/Pi
```

besseljzero(1)/Pi \\ Charles R Greathouse IV, Aug 09 2022

Equals A115369/A000796.

cp's OEIS Frontend

A245461 Decimal expansion of constant in the Rayleigh criterion: first zero of J_1, divided by Pi.

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