Transcript The Resolution Of A Telescope

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
sin   1.220

D
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:


D
Do not get the D here mixed up
with the D used as the symbol for
lens power
Question from Paper 5 June 2006