Resolution Limit: Rayleigh & Dawes

It’s by far one of the hardest concepts in amateur astronomy to understand. Resolution is nice to know when trying to split double stars. If the separation of two stars is less than the resolution of the telescope, then the stars cannot be resolved as two separate sources of light.

There are actually two different equations for this. One is the Rayleigh Limit, and the other is the Dawes Limit.

The Rayleigh Limit gives you a general measure of the ability of a telescope to distinctly resolve two stars of equal magnitude.

Dawes’ Limit is reached when the airy disk of one star is in the diffraction ring of another, and the stars are seen as just barely touching. At this point, the light intensity in the middle of the two stars drops 30%. Dawes figured out that the least amount of separation between two stars when this 30% drop will occur is equal to 116 divided by the diameter of the telescope.

With all that being said, while our telescopes are sufficiently capable to reach these limits, the atmosphere usually will not allow them. On the best of nights you may be able to expect 1 arcsecond resolution, and on bad nights expect worse than 4 arcseconds.

Rayleigh’s Limit Example:

Resolution [ arcseconds ] = 138 ÷ ( D_scope [ mm ] )

Or for diameter in inches,

Resolution [ arcseconds ] = 5.42 ÷ ( D_scope [ in ] )

Using my telescopes specifications, a diameter of 130 mm.

Resolution [ arcseconds ] = 138 ÷ ( 130 ) = 1.06 arcseconds

Dawes’ Limit Example:

Resolution [ arcseconds ]  = 116 ÷ ( D_scope [ mm ] )

Or for diameter in inches,

Resolution [ arcseconds ] = 4.56 ÷ ( D_scope [ in ] )

Using my telescopes specifications, a diameter of 130 mm.

Resolution = 116 ÷ ( 130 ) = 0.89 arcseconds

More information on the Rayleigh and Dawes Limits:

Diffraction-Limited Defined
Dawes’ Limit Defined
Telescope Resolution
Rayleigh Limit / Dawes Limit

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