Where did our magnification go to?

[Pete Andrews]

Not really a question, more a bit of a conundrum to ponder over.

We take our LF camera, say a 5x4 with 180mm lens, and our less-discerning friend Jim takes his 35mm camera with 50mm lens. We both point our cameras at a distan t scene, and both cameras take substantially the same angle-of-view (46 degrees diagonal). Now we both shoot something a bit closer, say, 5 metres distance, and the same thing applies. Our lens extensions are in proportion to their focal le ngths, and we each get a slightly smaller coverage angle of our subject than bef ore, but we both get more-or-less the same image.

Now we decide to do some macro work at 1:1. Both our lenses have been extended b y one full focal length, and again everything is in proportion. But now, the fir st day issue commemorative postage stamp that we're shooting nearly fills Jim's frame from corner to corner, while we're left with, well, a postage stamp size i mage in the middle of the frame.

I know that by definition 1:1 is life size, and it'll take a 5x4 size subject to fill my LF ground glass screen, but both myself and Jim have done everything in proportion, and he's ended up with one angle of view, and I've ended up with a much wider one. Why? I've puzzled over this and can't see where the discrepency creeps in. I think it's a geometrists conspiracy against us Large Format users.

[Pete Andrews]

Sorry, I should have said field-of-view in that last paragraph, not angle-of-view.

[David A. Goldfarb]

Less-discerning Jim's 50mm lens is going to be much closer to the subject when shooting 1:1 than your 180mm lens, no?

[Doug Paramore]

Pete: The image size is the same. If you cut out a 1x1-1/2 section of the 4x5 neg the images should match at 1-1 magnification. The magnification stays constant. The same applies at any magnification. A 90mm lens at infinity is a medium telephoto on a 35mm, it is a wide angle on 4x5. The image size remains the same, the film size is different. Much more magnification is needed to fill the frame of the 4x5. The advantage of 4x5 comes from the negative area. The largest you can go on a stamp size object without cutting part of the image out is basically 1-1. You can move closer with the 4x5 and fill the rame and have a much larger image of the stamp due to the image area. The magnification formula and the area covered formula are different. Hope I haven't confused you as much as I have confused myself.

[Pete Andrews]

True David, it's going to be 100mm from the 50mm lens' front node, but the LF lens's 180mm focal length won't allow focussing that close. So there's still a discrepancy.

[Struan Gray]

Err, Pete, life's just like that. David and Doug are both right, but David has the key to your 'paradox': with the 50 mm lens you're closer, so the stamp fills a bigger angle.

This highlights the old saw that infinity is defined by how you approach it, not by what you find when you get there. In the 1:1 case the two formats have equal magnification, but at 5 metres and infinity you talk about equal object distance. Your paradox only seems to be a paradox because you don't define the point at which you swap from one description to the other.

Imagine starting with a stamp at infinity and then moving it towards the cameras while refocussing in such a way that the lenses' centres stay still. If you move the stamp so that the object distance is always the same for the two cameras you'll lose focus on the 180 mm before the 50 mm ever reaches 1:1. If you move it so that the magnification is the same for both formats, it has to travel faster in the 50 mm case.

[David A. Goldfarb]

Or, as I was thinking of it, imagine that both lenses have the same angle of view. Make a scale diagram with each lens showing the angle the lens sees. If the stamp is 100mm from the vertex as it will be with the 50mm lens, it covers the whole arc inscribed by the angle. If the stamp is 360mm from the vertex, as it will be with the 180mm lens, it only covers a small portion of the arc inscribed by the angle.

[Pete Andrews]

Thanks for your replies David, Doug, and Struan. I can explain the logic and geometry of it to myself 'til the cows come home, but to me it still seems one of those non-commonsensical situations where practice runs counter to expectation. The intuitive part of my brain just won't accept that field-of-view doesn't scale with focal length, format, and lens extension, that's all.

[David Grandy]

I think in your last paragraph you've answered your own question but here I go anyway.

In 35 mm a stamp at 1:1 will pretty much fill the frame. That same stamp in 4X5 at 1:1 is exactly the same size on the 4X5 neg, leaving most of that neg empty. 1:1 just means life size, not "filling the frame". You're are admitting (again the last paragraph) that something would have to be 4X5 inches in real life to be 1:1 on a (fully filled) 4X5 neg, but at the same time not realizing that a stamp would have to be shot at 1:whatever to fill the frame. If you want to have the SAME angle of view then FILL THE FRAME and forget about the 1:1 or 1:20 ratios. I also suspect that when you and your friend are doing say a portrait, you are adjusting the angle of view through "filling the frame" but without the bench mark 1:1 would give you.