Physics · Wave optics
Rayleigh criterion calculator.
Enter the wavelength and the aperture diameter. Get the diffraction-limited angular resolution and, with a distance, the smallest separation you can resolve.
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Rayleigh criterion
Two point sources are just resolved when the centre of one diffraction pattern falls on the first dark ring of the other. For a circular aperture of diameter D that angle is θ = 1.22 λ/D in radians (small-angle form). A bigger aperture or a shorter wavelength resolves finer detail. To convert radians to arcseconds multiply by 206,265.
Worked example. 550 nm light and a 100 mm aperture: θ = 1.22 × 550×10−9 / 0.100 = 6.71×10−6 rad, about 1.38 arcseconds. Two objects 1000 m away would need to be at least 6.71 mm apart to be resolved at that limit.
This is the diffraction limit of the optics. Atmospheric turbulence, aberrations and sensor pixel size usually make real images worse.
Frequently asked questions
What is the Rayleigh criterion formula?
theta = 1.22 lambda / D for a circular aperture, where theta is in radians, lambda is the wavelength and D is the aperture diameter in the same length unit.
Why 1.22?
It comes from the position of the first dark ring of the diffraction pattern of a circular aperture. A single slit uses lambda / a instead.
How do I convert the answer to arcseconds?
Multiply radians by 180/pi to get degrees, then by 3600. The tool does this for you.
Does a bigger telescope always see finer detail?
It lowers the diffraction limit, but atmospheric seeing and optical quality often set the practical limit.
Which wavelength should I use for a human eye?
Use about 550 nm as a typical mid-visible value, or your own wavelength. Pupil diameter sets D, so the answer changes with lighting.
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OpenStax gives theta = 1.22 lambda/D. Arcsecond conversion (1 rad = 206,264.8 arcsec) and the small-angle separation (theta times distance) are arithmetic. Runs entirely in your browser. Nothing you type is sent or stored.
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Idealised diffraction limit for a circular aperture. Not a substitute for tested optical specifications.