Magnification Factor Calcs and Infinity Inschminity

Hello,

I suspect I've a little conceptual hurdle to get over when it comes to magnification - maybe its just terminology - we'll see ...

I like shooting at what I call '1:1' which to me means that the image caught on film is the same size as it is in reality - quite nice in portraiture in 8x10" and above.

This usually equates to a doubling or so of the focal length of any given lens I have in terms of the bellows extension.

Magnification factor from I think the Hasselblad website is defined as the extension beyond that of focus at infinity (0mm) divided by the focal length - which works nicely with my observations as a doubling of focal length equates to a extension equal to the focal length >>> focal length / focal length = 1

1:1

So its as simple as that ?

I can always know that to get 1:1 I need to double the focal length of any lens I'm ogling on feePay (more or less) ?

Maybe I answered my own question - heh heh

Its making me ponder - I guess it depends on what is important to you, but you could if you wanted define focal length that way right ? So all focal lengths would be doubled and they would be defined as the extension required to achieve 1:1 - infinity inschminity

It's as simple as that! Reproduction ratio = extension length / lens focal length, assuming there is not internal focusing mechanism within the lens being used...focused at infinity. You can get closer (raise the repro ratio) via usage of any focus mechanism within the lens itself.

There's just something about infinity focus and 1:1 on the film that seems unrelated to me that something as simple as doubling the focal length in extension should work to get me from one to the other.

Mind you, I remember noting one day that to turn a car say left you had to turn the wheel both left and right to do that and it was the order (and timing) that you did this that determined the direction you'd end up in... Much days of furrowed brows in the passenger seat, trying to make connections withe the price of fish and the ultimate fate of the universe :rolleyes:

Maybe I need to look up the definition of focal length...

At 1:1 magnification, the bellows extension = lens-to-object distance = 2 x focal length, but that is not the same as doubling the focal length.
(Of course, this assumes a non-telephoto lens if you treat the bellows extension literally.)
The bellows factor for exposure relates to the fact that the lens is now twice as far from the film as when the camera is focused at infinity, therefore the inverse-square law results in the light hitting the film to be 4x (2 squared) less than when focused at infinity.

Yes - I understand bellows factor calcs - that's a bit off topic.

I don't understand what you mean by "2 x focal length, but that is not the same as doubling the focal length" ...

My point is not so much understanding it all per se - not to say this isn't required, and I suspect it is - my point is that there is no intuitive link for me between magnification ratios and focus (at the moment).

There's nothing jumping out at me and making it obvious that at 2xfocal length extension that the projected image will be 1:1 on the film plane. A deduction would have to be made by playing with the math or by trail and error as I did - the math as easy as it is doesn't appear to have an intuitive or trivial derivation ...

Probably a brain fart

I was looking at my old posts and saw this reply from two years ago.
Simple math for lenses: let u = object to lens distance, v = lens to film distance (bellows extension), and f = focal length of lens.
Magnification: = (size of image on film) / (actual size of object) = v / u
Focus condition: (1/u) + (1/v) = (1/f).
Note that u and v are measured from principal planes, which are close the center of the lens for non-telephotos.
From algebra, for v = u (magnification = 1), u = v = 2xf.
In English, "doubling the focal length" would mean adjusting a zoom lens to achieve a longer focal length parameter.

Conceptually that's correct... 1:1 occurs at 2x focal length. However...

The variable is the infinity focus position. This is actually measured from the rear lens node to the film, which by definition equals the optical focal length.
But the rear lens node can be located anywhere, within or without the physical lens. You generally don't know where it is, unless you have the lens spec sheet.

You need some physical reference from which to measure. With large format lenses, this is the front of the lensboard on which the lens is mounted.
With lenses for other types of cameras, you can use the leading edge of the lens barrel, or any other convenient point.

When you move that reference point forward from its infinity focus by a distance equal to the lens focal length, you have 1:1 magnification.

- Leigh

To add to what Leigh wrote, by definition the rear node is one focal length from the film plane when the lens is focused on infinity. As he'd have told you if he'd put it that way, since the number engraved on this lens as focal length is rarely the lens' actual focal length (back when, Modern Photography used +/- 5% as the limits of acceptable variation), until you go to the trouble of measuring focal length calculations that use focal length can't be counted on to give exactly the right answer. Close is usually good enough.

That said, the law is: rear node-to-film plane distance = focal length * (1 + magnification). Remember that at infinity magnification is zero.

In practice, and I suspect that Leigh wrote it early in this discussion, for lenses of normal construction --not telephoto, not retrofocus -- the rear node is usually near the diaphragm. Most, not all, LF lenses are of normal construction.

In practice, the relationship between magnification, focal length, and extension matters much only when trying to find out whether the gear at hand can possibly give the desired magnification. It matters a lot to me because from time to time I design a variation on Spiratone's MacroDapter and want to know what to expect from it before I take the tools out. This matters not at all to most photographers because very few people do closeup work with manual flash.

Yeah, in reading post #7, the wording is kinda awkward. Wish I drank... I'd have something to blame it on.

- Leigh

I was looking at the data sheets (hard to read) for Schneider lenses that cover 8x10 at x1 magnification, and the separation between the mounting plane and the two principal planes is only a few mm out of 300 mm focal length. Of course, a telephoto has a much larger displacement, since the principal planes are on the subject side of the lens.
Back in the day, before computer drafting of PC boards, we would do tape on precision-ruled mylar at maybe 4x real size and focus it on film through an Apo-Nikkor mounted in a wall. The original artwork always had fiducial marks, with the final dimension, and we adjusted the easels with respect to the wall to get focus and accurate dimension at the film plane. This is the best technique if you actually need accurate 1x magnification: place a scale at the subject position and verify dimension on the ground glass.

nick mulder said:

There's nothing jumping out at me and making it obvious that at 2xfocal length extension that the projected image will be 1:1 on the film plane.

Click to expand...

It jumps out at me every time it solve it

M = S2/S1

M = Magnification
S2 = Subject distance
S1 = Object distance.

TimFox said:

This is the best technique if you actually need accurate 1x magnification: place a scale at the subject position and verify dimension on the ground glass.

Click to expand...

This is how I was taught.
Place a ruler in the scene and then compare on the GG.

nick mulder said:

There's just something about infinity focus and 1:1 on the film that seems unrelated to me that something as simple as doubling the focal length in extension should work to get me from one to the other.

Mind you, I remember noting one day that to turn a car say left you had to turn the wheel both left and right to do that and it was the order (and timing) that you did this that determined the direction you'd end up in... Much days of furrowed brows in the passenger seat, trying to make connections withe the price of fish and the ultimate fate of the universe :rolleyes:

Maybe I need to look up the definition of focal length...

Click to expand...

At speed on a motorcycle to turn right you actually move the bars left. It's called countersteering.