Formula for Image Circle Size in Relation to Magnification/Bellows Extension

[r.e.]

Hi,

I don't have access to my copy of Strobel at the moment and I need to determine the point, between infinity and 1:1, at which two of my lenses, one of which covers 4x5 at infinity and one of which covers 5x7, will cover 8x10.

Does anyone know the formula to determine this, either in terms of magnification or length of bellows extension or both?

Thanks.

[EdWorkman]

A little geometry will solve it. But you will probly want to work with the actual circles of acceptable definition, which I assume may be larger than the minimums to cover the formats. Probly you can work it out by similar triangles without resort to functions

[r.e.]

Thanks, I need to determine at what point a lens whose image circle is x (let's say 200mm) at infinity projects an image circle of about 315mm. I know that both lenses will cover 8x10 with plenty of room to spare at 1:1. It's the point where the circle reaches 315mm that I need to determine.

Regrettably, words like geometry and function are but hazy memories of the distant past.

[Stephane]

Need the focal length of your lens(es) to draw this triangle.

[r.e.]

Hi Stephane,

The lenses are a Rodenstock APO-Sironar-S 150mm, with an image circle at infinity and f/22 of 231mm, and a Docter Optic Tessar 210mmm, which the manufacturer said was 250mm at infinity/f22, but which Arne Croell in an article on this site questioned, based on computations that he did suggesting that it is actually 219mm.

As much as I want to know the answer to the question, I don't want to put people to the trouble of drawing diagrams. I assumed, apparently wrongly, that there is a straightforward formula for figuring this out.

[Peter K]

You will only need the circle of coverage for one bellows-extention as you can see here explained by Ole.

[Stephane]

formula is:
bellow draw = (8x10 image circle of 330mm) / (image circle of lens at infinity) * (focal length)
so the 150mm lens need 212mm extension, and the 210mm needs 315mm.
Hope this is right...

[jb7]

Funny, just today, I was using a 150mm Symmar S on 8x10.
Not the same as yours, obviously, but small world, nonetheless-

It has an ic of 210mm at f/22, I had a total extension of 290mm to cover 8x10,
with a lens to subject distance of about 70cm.

You should be able to get a little bit further away than that- 10% further?
I presume that's the distance that's actually most useful to you...

I could have used my 210, but that's a Fuji W, and that covers at infinity, and more-
would have been much too easy-

Anyway, just a little real world experience...

[r.e.]

Thanks very much Peter and Stephane.

Joseph, I wish that I had the 8x10 camera in hand, which would let me work this out by trial and error, but it is in New York at the moment and I'm not. Your hands-on experiment helps.

[Stephane]

Looked at the other formulas. Sunday night, bed time for me...
I just did minimum extension for the circle to cover the format. Anyway, tomorrow is another day...