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Aperature vs f

As I understand it the f=focal length/aperture. My question is why does a longer focal length lead to a higher f (via intuition not equation). What about focal a longer focal length makes stars less bright? If I am collecting light through 80mm diameter where is it getting lost en route to the ccd. For example if I have two refractors that are 80mm but one is f6.5 and the other f7.5 I would need longer exposures for the same image on the latter. Where is the light lost?
if you use the same magnification, for example 100 times, you obtain the same "amount of light" in f6.5 and f7.5 (eyepiece f=5.2mm for 80/520 and f=6mm for 80/600)..
You need longer exposure time for photo in primary focus 80/600 because of the size of object is bigger. For Jupiter is size 0.116 mm in 80/600 and 0.101 mm in 80/520. You pay with light for bigger square size.
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The brightness of stars, and any point source, depends on the aperture only. Whether it's an 80mm f/4 or an 80mm f/15, stars will have the same brightness on the detector and will record to some particular limit in equal time. (the differing sky brightness, and relative contribution of camera noise can lead to small differences, but they're minor.)

The surface brightness of an extended object depends on the solid angle subtended by the objective as seen from the focal surface. An f/4 objective will have twice the subtended diameter as will an f/8 objective, and so will present 4X the area and hence an image having 4X the surface brightness.

And this applies equally to any aperture. If the f/4 objective is, say, 80mm and the f/8 objective is, say, 200mm, the former will still offer an image having surface brightness 4X that of the latter.

Think of it this way. Imagine you're a tiny bug sitting on the CCD, looking up toward the objective. To you, this illuminated circle is like a skylight in the ceiling. The bigger the skylight, the more brightly lit will be the floor you're standing on. If the skylight is twice as high but at the same time is twice as wide, it will provide the sane illumination. This is like two telescopes, one having twice the focal length but also twice the aperture, thus working at the same f/ratio.

This should provide the foundation of understanding exactly why it is that f/ratio alone controls image surface brightness in an imaging system.
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So in essence aperture alone is not king. You want the widest and fastest system?
Which is weighed more heavily? A small gain in aperture should increase sa by piR^2
How much foes focal length effect light collection? Any formula?
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So in essence aperture alone is not king.

For visual use and afocal photography, it is. For starters you'll get better resolution but let's disregard that for now and focus (pun intended) on light intensity.

The aperture determines the absolute amount of light that can enter your telescope and the focal length determines magnification, all very basic. But now consider this thought experiment: you have two telescopes of the same aperture but different focal length, say f/4 vs f/9, and they're both looking at the same object. Since they have the same aperture they can gather the same amount of light - but this amount of light will have to come from different amounts of sky:

So if you keep the aperture constant, increase the focal length and project the resulting image onto the same sensor area you'll need the same amount of light to come from a smaller patch of sky if image brightness is to remain constant. Since that's not going to happen you'll end up with a larger but dimmer image instead.

So it's not a matter of light getting "lost", you're just gathering it from a smaller patch of sky and the supply is limited. With visual observing and afocal photography, you'd simply adjust magnification to compensate but for prime focus you'll need to increase exposure time or sensitivity.

This is of course a gross oversimplification but you get the general idea.
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Jarno, that is a superlative explanation.
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The "f number" is a ratio of (focal length of the telescope) divided by (aperture of the objective), so yes, as focal length increases so does focal ratio (aka "f number").

Stars are not made less bright in a scope with a longer focal length. It is exit pupil that determines star brightness, not focal length. However, as focal length increases the magnification produced by a given eyepiece also increases, and exit pupil decreases. Smaller exit pupil and higher magnification result in dimmer images. At equal exit pupil, though, any two scopes of a given aperture will produce an equally bright image, even if they have different focal lengths and focal ratios.




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Great explanations - thank you all!
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