aperature number vs f number

guinness2 wrote:

A 10 inch f/5 telescope has an aperture of 10 inches (254mm) and a focal length of 50 inches (1270mm). A 10 inch f/10 scope would have twice the focal length and therefore twice the magnification with the same eyepiece, but it collects the same amount of light.

It is interesting numbering, is it different than in the world of a common photography?
10 inch f/10 usually means here the lens ~250 f/10 where the first is the focal length and the latter the lens speed= maximal aperture=maximal hole the lens is capable to open to.

So I feel your example is a bit misleading, despite it is physically correct.

I mean , it is worth to mention, that the lens with the speed f/5 collects more light than the one with speed f/10 of the same focal length, when both are full open.

I was hoping to provide an illustration of other slightly different but related applications of focal ratios. But you're correct, it could be potentially confusing if the basic principle isn't understood. My apologies for being potentially misleading.

That said -- To follow my tangent regarding telescope f-ratios and light gathering...

Remember we're talking about a ratio, which can be affected by changing any of the factors involved: aperture or focal length. Also FYI, telescope magnification is the ratio between the eyepiece focal length and the telescope focal length. E.g., a 10mm eyepiece in a 1000mm (focal length) telescope will be 100x, regardless of that telescope's focal ratio.

Broadly speaking, you can think of it this way: With telescopes the difference in focal ratio is due to differing focal lengths at the same aperture. With camera lenses, it's due to different apertures at the same focal length. So while you're correct that a camera lens at f/5 will collect twice as much light as one at f/10 (given the same focal length), that's not true for telescopes in my example. I was speaking the other way: constant aperture with varying focal length.

A 10" f/10 telescope has the same aperture (and therefore, the same light gathering ability) as a 10" f/5 telescope. It just brings the light to a focus at a distance twice as far away as the f/5 scope. So at the same magnification, the image will be equally bright in both scopes regardless of focal ratio. However, the same eyepiece will yield twice the magnification in the f/10 scope as in the f/5 scope so therefore with the image being twice as large, it will be one fourth as bright.

So you're right that a 'faster' telescope will yield brighter images than a slower scope of the same aperture with the same eyepiece (i.e., at different magnification), but at the same magnification they're equally bright.