Neil,
The short answer is that there really isn't any simple formula for determinging the image circle of a lens based on focal length, f/#, etc. For example, two lenses with the same focal length and maximum aperture could project very different image circles depending on the details of their respecive lens designs. Factors such as the diameter of the elements (especially the front and rear elements) and the length of the overall assembly relative to those diameters come into play; but there is a lot more to it and there is no simple relationship.
If you want to empirically determining how big the image circle is for a given lens, I think someone already suggested putting together a sort of camera obscura setup to test it. This should be relatively simple to do.
For multi-element photographic lenses, you may be able to get a manufacturer's spec for image circle or projection angle (or alternatively, infer a minimum value from on the format for which the lens was designed since the image circle usually has to be at least as big as the diagonal of that format). But the idea of an image circle usually isn't applied to single element lenses. The reason is that light can make its way through a singlet lens at almost any angle - basically, there just isn't anything that prohibits light being transmitted through the lens until you get to pretty extreme angles (approaching 90 degrees, half angle). Of course that doesn't mean you can get sharp results at those more extreme angles! For a singlet lens the angle over which you can get
acceptable image quality tends to be much smaller than whatever the maximum angle is, with increasing blur at larger angles. Just how blurry it is depends on the relative aperture (f/#).
large vs small lens - as I see it from what you said above - given two lenses identical in quality and performance - I would pick a larger lens be able to keep my subsequent range of useful apetures larger i.e a low f of say 1.2 vs f4.5 or something?
Yes and no (as usual with optics!).
Generally the larger aperture buys you better low light capability, higher shutter speeds for less subject or camera movement, shallower depth of field , etc. But as as you implied with the notion of a minimum
useful f/#, a lens may have prohibitively high aberrations at low f/#'s and the meniscus lens certainly needs to be stopped down big time if your goal is to produce detailed images. Having said that, it is surprising just how good your image quality can be with only a meniscus lens when stopped down sufficiently. For what it is worth, my experience in medium format (6x6 usually) is that stopping down to the range of roughly f/16 to f/32 produces sharper results than most people would expect, even approaching the edges of the frame.
I think another criteria you should be thinking about is what your ultimate goal is as far as image characteristics. On the one hand, you may be looking to produce images of high technical qualiity and detail which you can print large. But at the other extreme, maybe reasonably sharp in the center of the image is "good enough" and you value image artifacts such as vignetting and blurring of the edges on artistic grounds. For the latter objective, the meniscus lens you mentioned would be a great place to start. However for the former, you might be somewhat disappointed in the results.
If you do experiment with a meniscus lens, there are some image characteristics you can play with in your design. For example, depending on whether you place your aperture stop in front of or behind the lens, you will get either barrel or pincushion distortion (I forget offhand which gives which). There may also be an optimal spacing between the lens and the aperture to consider.
Finally, you might be interested to know that the lens you mentioned was produced by Melles Griot (I recognize the numbering system). Actually, they are now called CVI-MellesGriot and use a new numbering sequence for their lenses. But they are still the same lenses and if you are interested about the application and use of their meniscus lenses you can find some interesting information here:
http://www.cvimellesgriot.com/Products/Documents/Catalog/MENN_MENP.pdf
I hope that helps,
Jeff
)
