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I have a Canon EOS 7D Mark II (1.6x crop factor), and I have a Canon EF 100-400 IS USM. Working with just 400mm for the purposes of this question, my understanding is that my 35mm-equivalent focal length is 640mm (400 X 1.6 = 640). Now, if I purchase a Canon Extender EF 1.4X III, does it take my 35mm-equivalent focal length to 896 (400 x 1.6 x 1.4 = 896)? It seems like I'm missing something!

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    Please do note that 896 is excess precision. None of the other numbers in your calculation are so precise — not 400mm, not 1.6× crop factor, and not the 1.4× of the extender. Just say "900mm". – mattdm Apr 11 '16 at 21:48
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Well, the main thing is that crop factor doesn't really affect focal length. It just affects the field of view by making it narrower. So, what you really have is a 400x1.4x => 560mm lens combination on a crop body, which has the same FoV that an 896mm lens would have on a full frame body. So, unless you shoot full frame enough to translate focal lengths to given fields of view, the 896mm figure may be kinda meaningless to you.

See the Canon Field of View Comparator tool to get a sense of what crop factor on a given lens means.

You also should be aware that the 1.4x teleconverter (TC)+ 100-400L combination, while it will work on a 7DMkII, wouldn't work on a lot of other Canon crop bodies. Using a TC is not exactly the same as using a longer lens. The TC, while it increases focal length, by the very act of doing so, reduces the lens's maximum aperture. A 1.4x TC reduces it by one stop, so once you put it on, the 100-400@400mm effectively becomes an f/8 lens. And most Canon crop bodies can't autofocus at apertures that small--they mostly stop autofocusing once the max. aperture of the lens hits f/8.

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    Only the center focus point will work with f/8 lens/extender combinations on the 7D Mark II. The EF 100-400mm f/4.5-5.6 becomes an f/6.3-8 lens with the EF 1.4X III. Since the aperture is narrower than f/5.6 at all focal lengths, the center focus point may be the only one that will work at any focal length. – Michael C Apr 11 '16 at 22:21
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    @MichaelClark, actually, center point, or with reference to the surrounding 4 points if AF point expansion is turned on, according to Chuck Westfall. the-digital-picture.com/Comparisons/… – inkista Apr 12 '16 at 1:16
  • I guess I could have phrased it more accurately by saying that AF only works on the 7D Mark II with an f/8 lens/extender combination when the center focus point is selected as the focus point. – Michael C Apr 12 '16 at 15:11
  • The four surrounding points are only usable as assist points in AF point expansion (Manual selection, 4 surrounding assist points) when the center point is chosen as the focus point. They are not independently selectable as Single-point Spot AF or Single-point AF focus points. Nor are they selectable as the primary point in AF Point expansion (Manual selection, 4 surrounding assist points). They only work when the center point is chosen as the primary. Please see pages 21 and 35 of the EOS 7D Mark II AF Setting Guide Book downloadable from learn.usa.canon.com/resources/articles/2014/ – Michael C Apr 12 '16 at 15:27
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Yes, placing a teleconverter on a crop works exactly the same as on a full frame – you multiply the teleconversion factor by the lens focal length, and since it's on a crop, you factor in the 1.6x crop factor of a Canon APS-c to get an effective focal length of 896.

Keep in mind that placing extenders on any lens will decrease its effective aperture. For the 100-400 which is already fairly slow, this could bring the aperture down past f/8, which I seem to recall is the minimum allowed for the central focus points on a 7dII.

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Yes many people do exactly what you suggest and end up with a field of view that is equivelent to an 896mm lens on a full frame camera.

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