First of all...Hello to everyone. I just found this forum and I'm sorry to ask for help in my first thread.

I'm making a telescope and I found a mirror set at a local astronomy shop. He gave me an awesome deal, and my only problem is that I don't know the f/ratio of the mirror, so I can't figure out the focal length. He said it was easy to find and gave me a quick explanation, but I have to admit I was lost. Anyway, can anyone tell me how to find the f/ratio or the focal length? Thank you.

I would set up a small, unfrosted light bulb and a piece of paper side by side. A flashlight should do nicely. Turn the mirror toward the light and aim the reflection of the filament toward the paper. Move back and forth until the image comes to a sharp focus and measure the distance between the mirror and the paper. That will be your radius of curvature, and the focal length will be half of that.

Hornblower's suggestion is great for finding the focal length; the f/ratio will just be the mirror's focal length divided by its diameter.

EDIT: Wait, Hornblower, why will drawing out the image to a sharp focus cause it to be at the radius of curvature? Shouldn't it be at the focal point, and thus the distance between the paper and mirror be the focal length?

Thank you Hornblower and ctcoker. I really appreciate you help. I was able to find the focal length and therefore the f/ratio . I'm not sure why the dividing by 2, either, but it worked great and I now know that I have a 6" f/8 mirror . Thank you again!

Hornblower is very correct. Focal length is defined as the distance to the image plane for an object at infinity. Note that whenever you focus on an object closer than that, the focal point moves back. When the object is at the same distance as the focal plane that is the radius of curvature of the mirror and is where many optical tests are run. It is exactly twice the infinity focal length.

For a sphere a line drawn from the center to the surface will always hit the surface exactly perpendicular to the surface. Thus a light beam is then reflected perfectly back to the center forming a precise point at the center which is, of course also at the radius, hence the term "radius of curvature". Note this is a perfect focus, no spherical aberration at all.

When the rays hit the surface of the sphere coming in parallel to each other (infinity) then the surface is at an angle to the incoming rays and focuses at only half the distance they do when the rays come from the center of the sphere. Draw it on paper and the difference becomes obvious.

More than one novice mirror grinder has missed this point and ended up with a f/3 mirror rather than f/6 as intended.

Rick