Define the resolving power of astronomical telescope. Write the expression for it and state, on what factors it depends
Answers
The quick, simple answer is that the resolving power, if you are comparing, for instance refractor telescopes, depends on the aperture of the telescope. Larger aperture, the ability to resolve finer detail. Others, I hope, will explain all the other complications.
Here is some information from:
Diffraction Limit
The bending of light which causes this interference pattern is known as "diffraction", and the Airy disk is also known as the diffraction pattern of the scope.
The radius of the central disk of this pattern, in radians -- let's call it "R" -- is given by the formula
where λ is the wavelength of light, which happens to be 550x10
-9
m for green light, and D
scope
is the diameter of the objective in meters (so really the same thing as D
O
, but to emphasize this is in meters, not millimeters).
With regard to your telescope, what is important in this equation is that the size of the Airy disk depends on the diameter of the objective ONLY, and as the diameter of the objective gets bigger, the Airy disk gets smaller.
This means as the diameter of your scope gets bigger, you can see smaller and smaller detail -- or equivalently, you can split stars that are closer together. Conversely, this means that there is a limit to the detail you can see with your scope. That limit is dictated ENTIRELY by the diameter of the scope, and it is due to the diffraction effects caused by the scope opening.
For this reason, the radius of the Airy disk, as calculated above, is known as the "diffraction limit".
Resolving power depends solely on aperture. It is directly linear to aperture, which is if you double the aperture increases by two. i.e. a Telescope with an aperture of 4 inches has a resolution about 1 arc second, a 40 inch Telescope can resolve 0.1 arc seconds. The real test of resolving power is splitting double stars. Epsilon Lyrae is often used as a base line of an amateur scope quality. It is a double double. If you can see it with you naked eye you have good dark skies. With a Telescope the two stars are actually two doubles separated by 2.3 arc-seconds. Now just about any amateur telescope can split those doubles based on any equation you use, Dawes or Reyleigh. Yet many can’t. So what are the other factors that determine resolving power?
The first big problem and one completely out of our control is the atmosphere. Three basic problems are turbulence, transparency, and sky glow. The first two can limit a scope of any size resolving power.
The next problem is optics. If you scope is out of alignment you will have limited performance. If the lenses or mirrors are not properly ground your scopes performance will be limited.