Airy Disk Angular Diameter Back | Up | Next

Formula 7    Angular Diameter of the Airy disk to the First Interspace

D = (2.44 * Lambda * 206265) / A

The first interspace is the middle of the first dark space between the Airy disk and first light ring.

Where

  • D is the Angular Diameter of the Airy disk
  • 2.44 is a constant
  • Lambda is the wavelength of light in millimeters
  • 206265 is the number of arcseconds in a radian
  • A is the aperture or diameter of the telescope objective in millimeters

Example: What is the angular diameter of the Airy Disk for yellow-green light where the eye is most sensitive at 550 nanometers (0.00055 millimeters) for a 5 inch telescope (127 millimeters aperture)?

D = (2.44 * 0.00055 * 206265) / 127
D = 276.80763 / 127
D = 2.18 arcseconds

The angular diameter of the Airy Disk for a 5 inch telescope for light at 550nm is 2.18 arcseconds.

From this we can see that the angular diameter of the Airy disk depends only on the diameter of the objective for any given wavelength of light. Larger apertures form smaller stars.

For other size objectives, the angular diameter of the first interspace is:

5" objective = 2.18 arc sec
4" objective = 2.72 arc sec
3" objective = 3.63 arc sec
2" objective = 5.44 arc sec
1" objective = 10.9 arc sec

Don't be misled by the apparent size of the front element of a camera lens such as a wide angle or fish-eye. The actual working aperture is tiny compared to the huge hunk of glass in the front element.

Angular Diameter of the Airy Disk for Various Camera Lenses
Focal Length F/Ratio Aperture Angular Diameter
300mm f/2.8 107mm 2.58 arc sec
200mm f/2.8 71.4mm 3.8 arc sec
100mm f/2.8 35.7mm 7.7 arc sec
85mm f/2.8 30.7mm 9.0 arc sec
50mm f/2.8 17.8mm 15.5 arc sec
35mm f/2.8 12.5mm 22.1 arc sec
24mm f/2.8 8.5mm 32.5 arc sec
20mm f/2.8 7.1mm 38.9 arc sec
15mm f/2.8 5.3mm 52.2 arc sec

Our guiding tolerances become much less critical as the focal length of the lens gets shorter because the spot star size in the imaging lens is so large compared to the size of the star in the guidescope.


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