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# why do larger lens telescopes have a larger F number

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just cant figure this out surely more light gathering should reduce the F,thanks

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F Number = Focal length / Diameter of the lens, so it's a fixed number depending on how that specific scope is made.

So if you had 2 scopes exactly the same length but one had an objective lens twice the size it's F number would be half the other scope.

Edited by Dinglem
To clarify the point

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It also depends on the style of scope. With an SCT for example the light hits the primary mirror, bounces the the secondary and then back again out of a hole in the middle of the primary.

So in effect the light path - eg the focal length is much longer than the scope’s tube length would suggest.

To illustrate I have a SW 150P 750mm focal length tube (which physically is a bit more than 750mm long to account for the space required behind the primary mirror for the collimation mechanics and the space required in front of the secondary for the spider etc but close enough). 750/150 = 5 so the scope is f5.

I also have a 250mm (10”) Meade SCT which has a tube of a very similar length  to the SW but because the light travels to the back of the scope then to the front and then out the back it has a focal length of 2500mm. 2500/250=10 so the scope is f10.

In other words we have two scopes of a very similar length but the larger one is twice as slow. If they were both newtonian reflectors the larger aperture scope would be twice as fast.

All nice and simple

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The key point here is probably relating to managing chromatic abberation in refractors. This is proportional to f/D^2 where f = focal length and D = aperture (diameter). The attached quote explains a little more.

For Newtonian, larger apertures do often have faster focal ratios in order to keep the eyepiece height manageable. They do not suffer from CA so this is not an issue, but coma is so a coma corrector is likely needed under around f4.5.

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Talking solely about refractors, which a layman photographer (as opposed to an astro-photographer) would recognize as a "normal-style" lens, the f-number represents the simple geometry of the lens: roughly the length of the lens divided by its width at the front. In other words, the "opening-out" angle from the back to the front is the same for lenses of different focal-lengths but same f-number.

But also bear in mind that an object of twice the linear dimensions of another same-shaped one will weigh 8 times as much (2x2x2): the weight increases by the cube of the focal length for a given f-number*. So refractors (normal lenses) get very unwieldy (and hence expensive) very quickly.

As an example: I own some big Canon prime lenses, including a 300mm f/2.8 and a 400mm f/2.8. Although the 400 is only 33% longer than the 300, it weighs more than twice as much!

Cheers, Magnus

* edit: that's assuming everything is scaled up pro rata. In practice the configuration of something like a lens is somewhere between a 2-D object and a 3-D one: lens tubes inparticular are likely to be thinner in a bigger lens, to try to offset this effect. So pone probably should be thinking of a power of perhaps 2.5ish rather than 3 when scaling up like for like

Edited by Captain Magenta

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I suspect you are confusing the variable aperture of a camera lens with the fixed aperture of a telescope. Yes, a fast, wide open lens at f2.8 will be faster than a lens stopped down to f22 but with a scope, the aperture is fixed (unless you apply an aperture mask. E.g. my 16" f4 dob becomes an 6" f10 if I use a mask with a 6" hole cut in it. This reduces brightness due to lost aperture compared with the 16" but the focal length (1600mm) remains the same and the view is tighter on e.g. double stars etc than with full aperture, perhaps partly at least due to no diffraction via the secondary spider.

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