What is an f/ratio?

[Ganymede12]

A basic question, I know, but the basic questions are the most important.

So what is an f/ratio?

[steppenwolf]

An F ratio is simply a mathematical indication of how fast (i.e. how much light a telescope captures) a telescope is. It is calculated by dividing the focal length by the aperture thus a 1000mm focal length telescope with an aperture of 200mm has a focal ratio of 1000 / 200 = F5

[Ags]

To slightly qualify steppenwolf's answer, the light collected by a telescope is determined only be the aperture. A 200mm scope collects 4 times as much light as a 100mm scope, regardless of F ratio.

If you are doing prime focus photography, then the F ratio is the photographic speed of the telescope. In this case an F5 telescope can use one quarter the exposure of an F10 telescope. But this is irrelevant if you are looking through the telescope using an eyepiece.

[umadog]

In practical terms the focal ratio matters for various reasons

A moderate focal ratio (e.g. below about f/6) is useful for ensuring that telescopes with larger mirrors don't become too long. For example, a 10" f/10 would have a focal length of 2.5 m. That would make it hard to use. Since magnification is defined as telescope focal length divided by eyepiece focal length, a long focal length scope will not produce low power views.

As you might imagine, based on the above there has recently been a push for short focal length telescopes. The advantage being that a large aperture can be housed in a short tube and provide a wide field of view. [Note, that SCTs have short tubes and fast primary mirrors but the focal ratio of the system is long because the secondary mirror isn't flat, but convex. They differ in other ways two and won't go into that now.] Life, as ever, isn't simple. Fast mirrors are harder to make than slower mirrors. Large fast mirrors are particularly hard to make. Consequently, such telescopes can become very expensive. Despite this, there are plenty of mass-produced instruments between f/4.5 and f/5.0 which can be bought at moderate prices and large apertures. Whether the mirror quality drops off for larger, faster, mass-produced scopes is unclear.

Mirrors below f/5 or f/5.5 are nowadays considered "fast." Even if you have a very good fast mirror there are other things to consider. The main one is coma. This an aberration inherent to parabolic mirrors: stars away from the center of the field are not focused into a point. At the edges, stars will look like little comets. In the center the view is good. Coma becomes much worse for faster telescopes as it is inversely proportional to the square of the focal ratio. Consequently, you will get less crisp views with a fast telescope unless you also invest in a coma-corrector, which adds "inverse coma" and clears up the field of view. In addition, the depth of focus decreases with fast optics. Although this doesn't alter the views (since everything you're looking at is at infinity), it does mean that you need focus just right. Dual speed focusers become important. Finally, collimation in a fast telescope is more important. If you're off by just a bit, you will notice it.