Your opinions, please...

Alan W. Craft wrote:
Correct me if I'm wrong, but shouldn't the focal length of the telescope
in conjunction with the f.l. of the eyepiece, that is, the magnification,
determine whether or not a telescope is fast or slow?

The terms "fast" and "slow" come, as you may know, from photography,
where they roughly express how quickly a lens will properly expose
film. The lower the f-ratio (or t-ratio, if they differ significantly),
the shorter the exposure need be.

There are two factors involved:

1. The light-gathering power of a lens or telescope is, to
first order, proportional to the area of the aperture.
There are secondary considerations--light throughput,
central obstruction, and so on--but these probably do not
equate to more than a 25 percent difference in linear
aperture.

2. The image scale--that is, the linear size of the image at
the focal point (more properly, focal plane) of the lens
or telescope--is proportional to the focal *length* of the
lens or telescope.

With these two factors in mind, consider two telescopes: a 4-inch
f/12 and an 8-inch f/6. Both telescopes have a 48-inch focal length,
so they both have identical image scales. For example, if you were
to put a piece of ground glass at the focal plane of both telescopes,
and you pointed them at the Moon, both pieces of ground glass would
depict a little Moon approximately 0.4 inches across. Since the
Moon is about half a degree across, we might say that the image scale
is 0.8 inches per degree in both scopes; more usually, we use mm and
say that the image scale is 20 mm per degree.

However, because the 8-inch has twice the aperture, it gathers about
four times (2 squared) the light. Four times as much light is put
into the same size image, so that the image of the Moon on the ground
glass in the 8-inch scope is four times as intense as the image on
the ground glass in the 4-incher. If you were to put pieces of film
in place of the ground glass, the film would be exposed four times as
quickly in the 8-inch scope as it would be in the 4-inch.

Next, consider a third scope: an 8-inch f/12. (A fairly long scope,
unless it's a folded design like an SCT, but never mind that for now.)
This scope has a focal length of 96 inches, twice as long as the other
two scopes, so its image scale is twice that of the others. A piece
of ground glass at its focal plane will show an image of the Moon
about 0.8 inches across. Its image scale is therefore about 1.6 inches
or 40 mm per degree.

Now, in comparison with the 8-inch f/6, it gathers just as much light,
but because the image of the Moon covers four times as much area, the
image is only one-fourth as intense. On the other hand, in comparison
with the 4-inch f/12, it gathers four times as much light, but that
larger amount of light is spread out over four times the area, so that
the image at the focal plane is just as intense in the 8-inch f/12 as
it is in the 4-inch f/12.

To summarize, then, scopes of the same focal *length* have the same
image scale. In contrast, scopes of the same focal *ratio* have the
same image intensity. This in turn determines how fast they will
expose a piece of film and gives rise to the terms fast (low focal
ratio, meaning more light spread out over a smaller image, so more
intense illumination) or slow (high focal ratio, meaning less light
spread out over a larger image, so less intense illumination).

While an 8" f6 would be considered fast when compared to an 8" f10,
the same 8" f6 would at the same time be equitable in "speed" to a 4" f12,
and therefore considered slow.

To continue my thought: However, when a scope is used visually, the
chief consideration is aperture, not focal ratio. The larger the
aperture, the more light gathered, and the brighter the image at any
particular magnification. To be sure, an 8-inch f/6 requires an
eyepiece half as long in focal length as an 8-inch f/12, in order to
achieve the same magnification, but what of that? A simple 2x Barlow
will suffice.

The image will look pretty much the same in an 8-inch f/6 at 100x and
an 8-inch f/12 at 100x, all other things such as optical quality being
equal. On the other hand, at 100x, the view in the 4-inch f/12 will
look significantly dimmer--one-fourth as bright, in fact.

Such slowness is precisely what I am trying so desperately to avoid,
and in order to use the telescope for comet-hunting and widefield DSO
observation, while at the same avoiding glaring instances of coma
and exacting collimations.

If what you want is wide true field of view, and you are willing to
live with less aperture, then you want a combination of short focal
length and wide focuser. For example, the Pronto has a focal length
of just 480 mm and a 2-inch focuser. That yields a maximum true field
of view of around 5 degrees--quite wide. Of course, the larger the
aperture, the more you will see in any given field of view, but it is
pretty hard to make a high-quality fast scope of significant aperture.

Brian Tung
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