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Question/Comments on Primer - Focal Lengths and Ratio's

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Nice one CC :D

Aperture

More aperture means that you are collecting more light and more light makes the image appear brighter. Bright things are easier to see and to photograph. More is better.

You are also collecting more information: More aperture = more resolution.

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When I started out it took me a long time to get my head round one thing above all: the higher the focal length of the objective or mirror, the higher the potential magnification of the telescope will be; but increase the focal length of the eyepiece and you will get a lower mag. I think I'm there now - more or less.

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Here's something else to think about. The exposure time for imaging is deterimined directly by the focal ratio. so an F6 60mm aperture scope requires the same exposure time as a 300mm scope. Image scale is directly related to focal length.

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:nono: :nono: :nono: :D

See thats the problem with these sort of posts, just digesting CC's excellent "primer" and it is sort of sinking in....then out of nowhere more posts to totally confuse me again.....

Stop it, stop it now :D

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:D :D Chub, don't get confused or try to work it out, just accept what I have just written. It is true! Actually it's dead simple really. An F6 60 mm scope will give a much wider field than a 300mm scope. As you know from visual work, higher magnifications give a dimmer image. So the 300mm scope magnifies more because of its longer focal length, the dimming of higher magnification is exactly matched by the brightening form the larger aperture. So exposure time is the same, wish everything was that simple.

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Here's something else to think about. The exposure time for imaging is deterimined directly by the focal ratio. so an F6 60mm aperture scope requires the same exposure time as a 300mm scope. Image scale is directly related to focal length.

Yeah I know, but try to put it into words WHY it is the case. That's one for tomorrow evening. I'm off for a kip soon and when I wake up I'll have it sorted. A bit like the guy who invented Benzine by drinking it or something.

Captain Chaos

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Yeah I know, but try to put it into words WHY it is the case. That's one for tomorrow evening. I'm off for a kip soon and when I wake up I'll have it sorted. A bit like the guy who invented Benzine by drinking it or something.

Well I thought I had just done it! Sleep well. I wouldn't recommend the benzine thing :shock:

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Its BenzEne apparently, and yes Martin you did it, but its the square of the f/ ratio number, not just the number so a 'scope at f/8 needs four times what a f/4 'scope needs. It was getting muddy when the area of the front lens / mirror bit started go get a bit "Open University" so I backed off on that one for now. I'll get it sorted out though.

Thanks for the nice words folks,

Captain Chaos

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Its BenzEne apparently, and yes Martin you did it, but its the square of the f/ ratio number, not just the number so a 'scope at f/8 needs four times what a f/4 'scope needs.

Yes I know - cos it's the area of the objective that matters not it's diameter. Now go to bed :D

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More of the same...

Background and definition

The f/ ratio of an optical system like a telescope is also known as the speed of the system. This is from photographic systems where the photograph’s exposure is calculated by using the f/ number so the exposure length is shorter when using a smaller f/ ratio.

The actual number is derived from dividing the focal length of the system by the aperture of the system so a ‘scope with a 200mm aperture and focal length of 1000mmm would be 100/200 =5 . The focal length is represented by f which is where the f/ designation comes from. Most ‘scopes are described the other way round so that it would be described as a 200mm f/5 instrument.

What does it mean?

The f/ ratio determines how bright something appears when viewed through the ‘scope or how long an exposure will be necessary when imaging. Because the ratio depends on the diameter of the aperture and not the area, the sums get a tiny bit more complicated. An f/5 ‘scope will have four times the area of an f/10 ‘scope for a given focal length. This equates to four times as much light getting in therefore the view will be four times as bright or the exposure time will be reduced by a factor of 4.

How does it really work?

The magnification of the object depends purely on the focal length of the system and has nothing to do with the f/ ratio.

Now the magnification bit has to come into play. Adjacent stars in the same field of view are spaced apart according to the magnification of the system which is worked out from the focal length. The distance between the images of two stars at the point of focus of the system can be worked out using a pinhole camera analogy. In this system there is a pinhole at the aperture end of the ‘scope through which all the light enters. The light travels in a straight line until it hits the imaging chip where it forms a bright spot. Taking the three belt stars of Orion as an example, there would be three points of the chip lit up by light from these three stars. Moving the chip towards the pinhole would put the star images closer together and conversely moving the chip away from the pinhole would spread them out more. Thus the magnification is fixed by the focal length of the system, which is the distance from the pinhole to the imaging chip. With a real ‘scope, the focal length is fixed because the lens or mirror will only form an image at one distance from objective lens or mirror to the chip.

Light flux.

Each star or bit of nebula out there emits light towards us which can be imagined as leaving the star in all directions equally. This can be imagined as a series of spherical shells of light, like onion skins, each expanding away from the star at the speed of light and coming towards us. The “shells” are made up of photons (particles of light) starting out crowded closely together and getting more and more spread out as the shell expands. When the “shell” gets to us the photons are spread very thinly as they pass into the ‘scope. The ‘scope collects light according to the area of the aperture therefore a bigger aperture collects more photons from each of these “shells” as they arrive.

All the photons are aimed at a single point within the ‘scope, so that for the bigger aperture ‘scope, the image of the star has correspondingly more photons and appears brighter.

Back to the f/ ratio bit now. As the distances between two stars’ image on the chip is fixed, the only thing that the f/ ratio can do is alter the brightness of each image. From the above “shell” analogy each image gets more photons from a bigger aperture or lower f/ ratio.

More stuff.

If the ‘scope is pointed at a distant galaxy which has loads and loads of stars close together, the star images crowd together on the image chip and are close enough to overlap. This lights up the whole chip if the magnification is sufficient, or all the light is concentrated onto a section of the chip. Whichever way, the number of photons is the same, i.e. the same total passing through the ‘scope’s aperture. Spread out by high magnification, the photons per pixel is lower than if they are all crowded together with low magnification.

The bottom line.

The photons per pixel can be increased by shortening the focal length to reduce magnification, or widening the aperture to collect more photons. To get the same level of illumination of the chip, measured in photons per pixel, depends on the focal length and aperture. The way this works out means that the best measure for determining how bright the image will be can most easily be written as f/.

Visual version.

When we use a ‘scope visually, the light comes in the front and is focused in thin air just in front of the eyepiece. The lens in the eyepiece is then used to look at the “aerial image” just as a jeweler examines a gemstone with his magnifying glass. The image is formed in exactly the same way as if it were on an imaging chip but the method of examining it is different.

I think that’s quite enough for a Sunday afternoon ramble?

Captain Chaos

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Chaos,

It's a while since you created this post, but i've got to say it's one of the most useful I've seen so far. I've been wondering what the f/ malarky was all about for a while - it makes sense now, thanks a ton for flicking the switch between my ears 8)

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Excellent post. Been trying to get my head around this stuff for a few weeks now.

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I think I nearly understand this now - might have to read it again though. Great post - thanks

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Great informative articles.

Definitely some of the clearest explanations I have read.

Andy

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