Zoom optical design question

I originally posted this in the sigma 150-600 thread, but thought that a specific thread would be better:

Take the canon 100-400 as an example : the front element is about 75 mm in diameter, in agreement with the aperture at 400mm which is f/5.6.

However at 200mm it is an f/5 lens, which needs only 40 mm of front glass theoretically.
At 100m, f/4.5 translates into only 22mm of front element. This sounds like a lot of wasted glass (and dead weight in the field).

This holds also for constant-aperture zooms. The 200-400 f/4 has enough glass to be an f/2 lens at 200mm, but however it is f/4 all over the range.

Why is the fair trade of TCs (1 stop for 40% more FL) not applicable to zooms ?

It's due to the internal design where elements have to move around and can't see the entire front element diameter as the optics move back and forth (the image circle internally moves around due to blanking off). This isn't an issue with single focal length lenses. As a crude example imagine a pipe with a washer inside that you can somehow move back and forth. When you look through it and the washer is near your eye you can see the full image circle but if you move the washer away from your eye inside the pipe you are no longer seeing the full amount of light entering the front of the pipe even though the diameter of the front hasn't changed.

Thank you EJ for this explanation.
It confirms somehow that zoom lens make use of the whole front element, only at the longest FL. And that at other FLs, you're in fact carrying unused extra weight. I presume it is the price to pay for the easiness to change FL on a zoom, compared to a prime +/- TCs.

I hope lens manufacturers come with more "onboard" TCs as the Canon 200-400. Imagine a 800/8 prime with two switchable "TC elements", providing a 560/5.6 and or a 400/4 at the touch of a finger ...

Except for the variable aperture f number, it would be similar to a leica tri-elmar: a zoom with fixed FL steps.
I mean, do we really need the intermediary focal length ? I crop files to adjust composition on a regular basis, thus I would be happy with only 400/560/800mm without the need to mount/unmount TCs.

But then you are carying the weight of the unused TC when you aren't using it

Touché, EJ !