MFD equals 4x focal length? But published specs contradict that

Question

I spent the better part of this evening perusing the series of equations behind this popular magnification calculator.

Equation F10 states d ≥ 4f, where d is focus distance and f is focal length. I followed the math up to here, and it makes sense to me. I did some testing with one of my all-around lenses, and the results fit within these equations. All of this suggests that MFD is 4x a lens' focal length.

So how then can the Sony FE 90mm F2.8 macro lens have d = 280mm and f = 90mm? This would appear to violate the previously defined limit, since 280 < 4*90. What am I missing?

EDIT: I found the concept of "focus breathing" and added it below as an answer. But, I have a followup question. Does this mean after the focus breathing, the 90mm truly is focused at a focal length of 70mm? (i.e. 280mm/4) This seems like a non-trivial change; whereas the definition of focus breathing describes these changes as "small".

Answer 1

The site you reference does not state that the effect of focus breathing is small. It states (emphasis mine),

The nominal focal length applies for the lens focused at infinity, but may be shorter for small distances.

For that Sony lens, indeed, it is experiencing focus breathing. Most internal focus lenses do — focus breathing is usually a side effect of that lens geometry.

Actually, 70 mm vs 90 mm is not all that much. For instance, the Nikon 70-200mm ƒ/2.8G VRII lens, when zoomed fully to 200 mm and focused down to its minimum focus distance, has a field of view of a 120 mm lens, a 40% difference.

Answer 2

All of those formulae assume a single thin lens. Most actual lenses are compound lenses with multiple lens elements. When those elements are all moved in unison by the same amount to change the focus distance, such as is often the case with many classis lens designs, the lens will more or less act according to expectations. But when different groups of elements move by differing amounts, or even in opposite directions, as the lens is focused, then all bets are off. This is the case with all internally focusing lenses. Some of the elemnts inside the lens move to change focus, but the front of the lens does not.