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Angular Magnification by Astronomical Telescope
The angular magnification, M, (also sometimes called magnifying power) produced by an optical instrument is defined as
 
See here for more detail.
An expression for the angular magnification produced by a telescope can easily be found by looking at ray diagrams.
See the ray diagrams pages (ray diagrams, ray diagrams, examples, ray diagrams, focal length) if necessary.
 
An astronomical telescope consists of a long focal length convex lens (the object lens or objective) and a short focal length convex lens, the eye lens.
 
This diagram shows the long focal length lens, the object lens.
 
We imagine a distant object to be placed with one end on the principal axis of the lens.
The three rays originate from a point at the other end of the object.
These rays are parallel and so are meet in the focal plane of the lens.
We therefore have a real image formed in the focal plane of the lens.
 
This real image is now to be considered an object to be viewed with (and magnified by) the eye lens.
In "normal adjustment", the eye lens is placed so the the "object" (the real image from the object lens) is in the focal plane of the eye lens, giving a final, virtual image, at infinity.
 
The next diagram shows these two stages together, forming the complete telescope.
 
 
The angles α and β will, in practice, be very small angles, so
where h is the height of the real image.
 
Therefore, the angular magnification is given simply by
 
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