TL;DR
- To determine magnification with an extension tube you need to use the effective focal length of the lens at the minimum focus distance, which is not the number printed on the barrel. You can get that value from Canon's information, but you have to go deeper than the top-line specs.
- There's a practical limit to the length of extension tube(s) you can use – tubes shorten the working distance (front of lens to subject), as tube length gets longer the working distance gets shorter and eventually negative.
tolusina said:
The arithmetic to calculate the additional magnification provided by extension tubes is quite simple.
Start with a lens' native magnification from the lens' specification page.
Then divide the length of the extension tube(s) used by the lens' focal length, add the result to the lens' native magnification and you're done.
Not quite done... Yes, the arithmetic is simple using the formula you describe:
m' = m + (L/f) where
m' is the new max magnification (with tube),
m is the specified max mag of the native lens,
L is the length of the extension tube (or stack of tubes) and
f is the focal length of the lens. (For Doug Kerr's derivation of the formula, go
here.)
That formula works great...as long as you use the proper input values. But unfortunately, you're not. Also, it's worth noting that the arithmetic (even when done with correct values) doesn't tell the whole story.
tolusina said:
I'll give several examples, then calculate total magnification for each after adding the full 68mm stack of Kenko tubes.
- - -
Both
EF 100mm f/2.8L Macro IS USM
and
EF 100mm f/2.8 Macro USM
have 1X magnification specs.
68mm ÷ 100mm = .68X additional magnification, 1.68X total with a full tube set.
That seems simple, but unfortunately it's wrong.
Let's use your example.
---
Both
EF 100mm f/2.8L Macro IS USM
and
EF 100mm f/2.8 Macro USM
have 1X magnification specs.
Based on your simple arithmetic, with a 25mm extenstion tube
25mm ÷ 100mm = .25x additional magnification,
1.25x total with the EF 25 II tube
But in their respective instruction manuals, Canon states that with the EF 25 II tube, the magnification will be
1.37x for the 100mm L lens and
1.39x for the 100mm non-L lens.
So, either Canon doesn't know how to determine the specifications for their own products, or there's something wrong with the way you're calculating the final magnification. I'll go out on a limb and say the Canon knows what they're doing.
Now...
what is wrong with your calculation? The problem is that you're using the specified focal length of the lens, e.g. 100mm in the case above. Sure, it's printed on the barrel and all, but it's important to realize that the specified focal length is with the lens
focused at infinity. When a lens is focused, a small group of elements within the lens actually moves to achieve focus. The consequence of that is that the focal length of the lens – which is properly defined as the distance from the sensor to the second/rear nodal point – changes as the lens is focused, because the position of the second nodal point moves as the lens is focused. Thus, the resulting effective focal length of a lens when focused at the minimum focus distance is shorter than the focal length at infinity. How much shorter depends on the design of the lens, e.g. what type of focusing system is used, where the focusing group sits in the optical path and how the focusing group moves (for a
crapload of detail on that sort of thing, see Pierre Toscani's information and animations
here and
here).
I don't think many photographers are aware of this issue, which is commonly referred to as focus breathing. When you focus closer, the focal length gets shorter resulting in a wider FoV. For a still image with a subject at a 'normal' distance, it's likely that you wouldn't notice the effect at all. But in some cases, it can be quite significant. For example, if you're using a Nikon 70-200mm f/2.8 VR and take a tight close up at 200mm, you're essentially getting the framing of a 135mm lens. OTOH, videographers and cinemaphotographers are acutely aware of focus breathing, since it means that the framing/composition of the footage changes as you pull focus during a shot. One reason why cine lenses are so expensive is that they have minimal to no focus breathing.
Although I suggested not many photographers are familiar with focus breathing, I expect many macro photographers are – anyone who's tried doing focus stacking by changing the focus of the lens (manually or with something like Helicon Remote and a tethered camera) will notice that the FoV changes through the stack. That's why the better way to focus stack is to move the whole camera+lens on a focus rail.
Ok, back to the example above where the formula-generated magnification doesn't match Canon's specifications. In the case of the 100mm f/2.8L Macro IS lens, which is 100mm at infinity focus, the
effective focal length with the lens focused at the minimum focus disance is ~68mm. So, back to the arithmetic:
25mm ÷ 68mm = .37x additional magnification, 1.37x total with the EF 25 II tube, and that matches Canon's value
68mm ÷ 68mm = 1x additional magnification, 2x total with the full Kenko tube set
Ok, but how do you determine the effective focal length at MFD for a given lens? It's not listed in the specs, and although there are a few 'focus breathing calculators' and formulae out there, they're not accurate becuase the effective focal length is dependent on the position of the rear nodal point within the lens, and that is in turn dependent on lens design. One way to determine the actual focal length is to empirically measure it, but without going into exhaustive details, I'll sum up by saying it's a royal PITA (it's pretty easy for distant objects, but the math breaks down at close distances, and that's what we really need to know).
Fortunately, there is someone who knows how the lens is designed and knows exactly where the rear nodal point is at the MFD – the people who make the lens! If you look in the Canon instruction manual for most lenses, they provide value for the maximum magnification when used with the Canon EF 12 and EF 25 extension tubes. If you're using a single Canon tube, you're done – they've given you the maximum magnification. But if you're using Kenko tubes or stacking Canon tubes, you need to know the effective focal length at the MFD. You can estimate that with a rearrangement of the formula above and more simple arithmetic:
fe = L ÷ (m' – m), where
fe is the effective focal length at the MFD,
L is the tube length associated with the Canon-provided maximum magnification
m', and
m is the native magnification of the lens. You can get the
m' values for the two Canon tubes in the instruction manuals for most lenses.
For example, with the 180L Macro, the fe at 1:1 is 119mm. The effective focal length of the EF-S 60mm macro at 1:1 is 41mm.
tolusina said:
EF 50mm f/2.5 Compact Macro also has 1X native magnification.
68mm ÷ 50mm = 1.36X additional, 2.36X total.
Actually, the 50mm Compact Macro is only 0.5x native magnification, unless you add the Life Size Converter (which costs nearly as much as the lens itself) to bring it to 1x mag.
tolusina said:
EF 40mm f/2.8 STM
0.18X native
68mm ÷ 40mm = 1.7X additional, 1.88X total.
---
Notice that, with a full set of tubes, total magnification of the Shorty Forty is greater than the 100 Macros. I've no idea which combination is more suitable nor why one might be better than the other.
I'd say the 100mm macro would be a much better choice, because if you stack 68mm of extenstion tubes behind the 40/2.8 lens, the focus distance will be shorter than the resulting length of the optics, i.e.
the subject would need to be inside the lens in order to be in focus. This is one of those cases where calculating the theoretical maximum magnification gets dashed against the rocks of practical reality.
tolusina said:
TS-E 24mm f/3.5L II
0.34X native
68mm ÷ 24mm = 2.833...
3.17333...X total
- - -
I listed the TS-E 24mm primarily as an arithmetic example, I've no idea if tilt and or shift of the image circle can work together with extensions.
While the TS-E 24mm can work with tubes, including tilt and shift, this is another case of practical limitation. With a 12mm tube on the TS-E 24, you get 0.85x and the focus distance is about 3 cm in front of the lens. With a 25mm tube, you'll get a bit over 1x and the subject will need to be touching the front element (Canon doesn't recommend this, for obvious reasons). You certainly can't achieve focus with >25mm of tubes behind the lens.
