# Is the 100-400 shy of 400 mm at the long end? Photos

Started Mar 9, 2015 | Discussions thread
Re: Is the 100-400 shy of 400 mm at the long end? Photos
4

photonius wrote:

Normally, if one takes the simple single thin lens formula, the lens moves further and further away from the sensor plane, as one focuses closer; at infinity the distance would be exactly the focal length of the lens, but at 1:1 macro, the distance would actually be double. In old, non-internal focusing macros, this is easily visible (e.g. an old FD 100mm f4 macro). However, if you take a modern 100mm f2.8 macro, they are internally focusing, they do not extend. Well, simplistically, a single thin 100mm lens would be at infinity 100mm from the sensor, a 50mm lens would be at 1:1 when 100mm from the sensor. So, what the internal focusing lens is doing in a large part is to change the focal length so as not to have to extend during focusing. The 100mm f2.8 macro has actually an angle of view like a 60mm focal length at 1:1. With zooms the same thing. Especially high zoom factor lenses suffer from this, e.g., the 18-200mm drops substantially at close-focus distance, maybe to about 135mm. Again, at the long focal length, the lens would have to extend a lot to focus close at its long end, it is compensated in part with reducing focal length that does not need to extend as much. This is of course a rather simplistic explanation, there are complex things going on a lenses with many elements.

It's actually not difficult to calculate the focal length at MFD using the thin lens formula and Canon's published figures for magnification at minimum focusing distance:

1/a + 1/b = 1/f
- where a is the distance from the subject to the thin lens, b is the distance from there to the sensor, and f is the focal length.

b/a gives the magnification of the lens (just from 'similar triangles').

The published "focusing distance" is the total distance from the sensor to the subject - which is simply a + b.

So for the 100-400L II:

b/a = 0.31 (magnification)
a = 1/0.31 x b = 3.226 x b

a + b = 980 (MFD, working in mm)
(3.226 x b) + b = 980
b = 980/4.226 = 232 mm
a = 980 - 232 = 748 mm

1/f = 1/748 + 1/232
(interlude to use calculator...)
1/f = 0.0056
f = 177 mm

So the true focal length of the 100-400L II at maximum zoom and MFD is an astonishing 177 mm. So low that you might wonder if the calculation is correct but I can assure you it is. If you compare that magnification of 0.31x at a focusing distance of 980 mm with other lenses you soon see that it is a low magnification for a supposedly 400 mm lens and the 177 mm figure becomes quite credible.

This calculation does make one important simplifying assumption. It is based on a thin lens, where the internodal distance is zero. A real lens won't have a zero internodal distance, but it should be fairly small and shouldn't have a profound effect on the result.

Putting the figures for the 400/5.6L into the same calculation (I'll skip the workings this time) gives us a focal length at MFD of 335 mm so you see it too suffers from focus breathing.

At first glance that seems to suggest the 100-400L II has only half the focal length of the 400/5.6L but that's because it has a *MUCH* closer MFD so we are not comparing like with like. What we would need to compare is the magnification of the 100-400L II at the 400/5.6's MFD of 3500 mm and that can't be calculated, only measured. This is where the OP's shots of the bird bath come in - they show us the actual difference, if they are at MFD.

Apologies to anybody who finds this really dull. Unfortunately if you are one of those people you won't have read far enough to see the apology...

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