I've located some automatic extension tubes for my Olympus OM-D E-M1. I've had extension tubes for my Pentax for decades, but they're useless for Olympus lenses, because the lenses don't have a manual diaphragm: it has to be set electrically. And that's what these new tubes promise.
One problem is that there are only two tubes, 10 mm and 16 mm. My old Pentax tubes were a set of 3, 11 mm, 20 mm and 30 mm, double as much as the new tubes, and with them you can get a 1:1 magnification with a 50 mm lens set on . How much magnification can I get with my Zuiko Digital ED 50 mm F2.0 Macro? That depends on how close it can focus without tubes.
And then I got thinking. What's it like with zoom lenses? Clearly extending a 9 mm zoom lens by 26 mm will create a magnification of roughly 3:1. And at closest focus (0.25 m) it's even more. But how do you calculate these things? The lens formula states:
1/f = 1/u + 1/v
where f is the focal length, u is the distance from the centre of the lens to the subject, and v is the distance from the centre of the lens to the sensor. So both focusing and extension tubes increase v. But the formula assumes thin lenses, and zooms are magic. According to the formula, changing the focal length when focusing close changes u, the distance to the subject (the point on which the lens is focused). But it doesn't, because that would be inconvenient.
Things got complicated enough that I wrote a program to calculate the focus distances and magnifications with the lens set at and its closest setting. The magnification is relatively simple: it's u/v.
And even that went through several iterations while I considered the ramifications of zoom lens design. What do people mean by closest focus distance? It's reasonable to assume that they're measuring from the subject to the sensor, so the value is effectively u + v. But even that doesn't seem to work. The 50 mm macros is specified as focusing to 0.24 m and having a maximum magnification of 0.52. But those values don't match.
Part of the problem is that the specs are vague. The inaccurate depth of field table on the product description page shows different values: a depth of field of 0.236-0.237 m when the camera to subject distance is 0.24 m. At 0.236 m, v is 0.071913 and u is 0.164087, so the magnification is still only 0.4383.
Another part of the problem could be that the lens, though fixed focal length (prime), is not thin. The theoretical distance for a magnification of 0.52 is 0.222 m, only 14 mm shorter. That's a lot less than the real thickness of the lens from front to back.
Spent much of the day pondering what information is useful and what isn't. In the end came to the conclusion that there's not enough accurate information about the closest focus distance that you can rely on it, so it's just a vague indication of the real u and v. My current version takes these parameters:
extension-tubes tube-length near-focus shortest-focal-length [longest-focal-length] [step]
And it produces output like this for the 9-18 mm lens:
=== grog@eureka (/dev/pts/28) ~ 9 -> extension-tubes 26 0.25 9 18 3
Tube extension: 26 mm
Near focus: 0.25 m
Shortest focal length: 9 mm
Longest focal length: 18 mm
Focal length Near limit Extension Magnification Far limit Extension Magnification
9 0.0474 0.0353 2.9277 0.0121 0.0260 2.8889
12 0.0560 0.0386 2.2199 0.0175 0.0260 2.1667
15 0.0654 0.0420 1.8018 0.0237 0.0260 1.7333
18 0.0753 0.0455 1.5292 0.0305 0.0260 1.4444
Near limit and far limit are the minimum and maximum camera-to-subject distances with this extension. In this case, they're ridiculously inaccurate: the difference between near limit and extension at 9 mm is only 12 mm, far less than the length of the lens. Maybe I should just give up these columns as being meaningless.
Other information is more useful. I get the biggest magnification (3.3×) from my Olympus Zuiko Digital ED 8 mm f/3.5 fisheye lens. The main question is whether it will then be focused inside or outside the front element. A more practical possibility is the M.Zuiko 12-40 mm f/2.8 Pro, which would have a magnification of 2.2 when set at 12 mm.
Getting back to the original question: what magnification can I get with both tubes and the 50 mm macro? 20 cm and a magnification of only 1.04×. Much depends on the image quality that I can get from the 12-40 under these circumstances.
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