Rayleigh criterion

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The limiting resolution of a telescope set by diffraction; also known as the Rayleigh limit. The image of a star in a telescope consists of the Airy disk surrounded by diffraction rings. The English physicist Lord Rayleigh (1842–1919) defined the limit of resolution as the separation of two stars when the centre of one image lies on the dark interval between the Airy disk of the other and its first diffraction ring. This separation is 1.22 λ/a radians, where λ is the observing wavelength and a is the telescope aperture. For visual light this corresponds to 13.8/a seconds of arc, where a is the telescope aperture in centimetres. Thus a 30-cm telescope should resolve double stars with separations 0″.45 or greater, given good optics, steady air, and adequate magnification. (For comparison, the Dawes limit above which two 6th-magnitude stars should be resolved with this aperture is 0″.39.) Rayleigh also investigated how accurately the objective should be figured to avoid serious degradation of the size of the Airy disk; he found the limit to be a quarter of the wavelength of light.

Subjects: Astronomy and Astrophysics.

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