Note: this article is still under construction
Magnification, in terms of telescope optics, is the process by which an object's apparent size is increased to allow the viewer to see smaller details. The common unit of measurement used for magnification is the ratio of apparent size increase, often referred to as "magnification factor" or "times" and abbreviated with the letter X. Thus a magnification of 2X would mean that the apparent size of the image is twice as large as with the unaided eye, or two times as large.
For visual observation, the magnification factor can easily be calculated by dividing the focal length of the telescope itself by that of the eyepiece being used. Thus if a telescope with a focal length of 1,000mm is used with a 25mm eyepiece, the magnification factor is 40x. If the eyepiece is exchanged for a 10mm eyepiece, the magnification factor is then 100x.
Impact on Field of View
There are two different types of Field of View, Apparent Field of View (AFOV) and True Field of View (TFOV). AFOV describes the eyepiece's field, regardless of the telescope used. TFOV refers to the angular size of the field of view - essentially the size of the piece of sky the observer can see through the telescope with the given eyepiece. The common method for calculating TFOV is to divide the eyepieces's AFOV by the magnification factor. Thus, if two eyepieces have the same AFOV, then if you double the focal length of the eyepiece, you double the field of view, making the object appear 1/2 as large.
When it comes to photography, magnification is not the term typically used. Instead, field of view is the consideration, which is analogous to visual magnification, but not the same.
Since visual magnification is based on the apparent increase in visual size, it is based on human sight and how the telescope's optical elements increase or decrease the apparent size of the object.
But this doesn't apply to camera sensors in quite the same way. While human eyes are all roughly the same size and capability, camera sensors are available in many different sizes. While it would be appropriate to say that doubling the focal length of a telescope will increase the magnification of an image 2x for a given camera, two cameras with different image sensors will not show the same image size. 1X for visual observing is defined by the naked-eye view. But for cameras, different cameras produce a different 1x image scale.
Thus magnification simply doesn't have the same meaning in the photographic real. For this reason, for astrophotography the field of view is typically the measure to be considered, and this is based on the telescope's focal length and the dimensions of the image sensor.