Stupid Lens Size Question

So, I got to thinking the other day (scary, right?). Why are 6x6 lenses larger than 645 lenses? If a lens projects a round circle, wouldn't 645 lenses provide coverage for 6x6, only with less wasted image circle?

The diagonal of a 6x6 frame is larger than a 645 frame by about 1 cm. However it's the lens barrel rather than the lens . After all the standard lens on a TLR is actually a lot smaller than the 80mm on my 645. It's more about ergonomics.

Ian

Imagine the 4.5x6 recxtangular, then a circle so small that it touches the four corners of that rectangle.
Then imagine this rectangle to be enlarged at two sides to form a 6x6 square. The four corners now all will be out of that circle.

The easy and inaccurate explanation is that lens size is dependent both on focal length and maximum aperture. A 50mm f2 lens needs a maximum opening of 25 mm, a 80mm f4 lens a maximum opening of 20mm.

The larger the size of the film, the larger the focal length needed to give the same angle of view. Where on 35mm 50mm is considered the standard focal length, on 4.5x6 this will be somewhere near 65 mm, on 6x6 it is 80 mm and on 4x5 it is around 150mm. All these lenses give more or less the same angel of view, comparable to the diagonal of the film format.

The consequence is that a f2.8 80mm for 6x6 needs to be bigger then a f2.8 65mm for 4.5x6. But then: a f2 65mm for 4.5x6 needs an opening of 32.5 mm and is bigger then the f3.5 80mm with its opening of 22.9 mm you can find in many TLR's. Of course there are many exeptions on this basic rule, for instance when you need retro focus contructions to clear for a mirror.

Thanks everybody. It's clear I wasn't thinking things through properly.