The Resolution Of A Telescope

The resolving power of a telescope is the ability of the device to measure the angular separation (θ) of the points in an object. θ

Light From A Star Even the nearest stars are effectively point sources of light because they are so incredibly distant.( It may be considered a surprise that we can produce an image of them at all!) The parallel light arriving through the telescope aperture (or even the eye) is subject to diffraction just like light passing through a thin slit.

Diffraction Through a Circular Aperture When light from a point source passes through a small circular aperture, it does not produce a bright dot as an image, but rather a diffuse circular disc known as Airy’s Disk (Astronomer Royal Sir George Airy, 1835-1892). surrounded by much fainter concentric circular rings. This example of diffraction is of great importance because the eye and many optical instruments have circular apertures If this smearing of the image is larger than the smearing produced by aberration, the resolution of a telescope ( effectively its ability to produce clear images) is said to be diffraction limited The size of the Airy disk is determined by the aperture of the telescope – the larger the aperture, the smaller the Airy disk.

Resolving individual images (The Raleigh Criterion) Two stars may be so close together that they cannot be resolved. (They may lie within the same Airy disk) We can caluculate the limit of resolution using Raleigh’s criterion One star or two?

The Raleigh criterion states that two images are resolved when the central peak of the second image coincides with the initial minimum of the first image More technically when the peak of the second point spread function coincides with the trough of the first point spread function Central peaks coincide with minimums.

An empirical formula was given by Lord Raleigh θ is the angular separation of the objects λ is the wavelength of the light entering the telescope D is the diameter of the objective lens or mirror Effectively because the angles are small (the small angle approximation is used) we can write: Do not get the D here mixed up with the D used as the symbol for lens power

Question from Paper 5 June 2006