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I understand that the simple idea that f-stop is focal length divided by aperture really applies to a simple single-glass lens, not the compound lens systems used to provide good image quality in modern lenses.

I've heard that in this case, what matters is the ratio of the aperture as it appears through the front element. Why the front element, and not the back (which would be the "point of view" of the sensor or film)?

What about for effects such as diffraction? Does the literal physical aperture size matter, or is it the effective size?

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The difference is that almost everything you need to know as a photographer depends on the effective aperture (also known as the entrance pupil diameter) whereas the actual size of the diaphragm is only relevant in the design of the iris / lens barrel.

Diffraction is the ultimate limit to how much detail can be extracted from a photograph, and there is no free lunch here. If it depended on the physical aperture only then clever lens designs could bypass the diffraction limit and we wouldn't need electron scanning microscopes etc.

The reason the entrance pupil size is different to the physical size of the opening is the presence of lens elements in front and behind that change the magnification. Trying to cheat diffraction by using a physically larger opening, would require reducing elements in front of the aperture to make the image of the opening smaller, but also enlarging elements behind the aperture.

The smaller spread of light due to the larger physical opening would then be magnified into a larger spread equating to a blur of the same radius regardless of the physical aperture size.

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"would require reducing elements in front of the aperture to make the image of the opening smaller, but also enlarging elements behind the aperture" - out from a pure curiosity - isn't that what some of large format lenses do? –  MarcinWolny Apr 10 '13 at 8:54

The reason that effective aperture is based on the size of the diaphragm as it appears through the front element is that this is what determines what percentage of the light that falls on the front element is allowed to pass through the lens.

Why the front element, and not the back (which would be the "point of view" of the sensor or film)?

The two are not totally unrelated. If the front of a lens concentrates the light that falls on a large objective so that it may pass through a narrow central section, then the rear elements must expand it in order to throw the correct sized image circle. But how much light needs to be expanded is determined by how much was collected at the other end of the lens and what percentage of that was allowed to pass through by the diaphragm.

What about for effects such as diffraction? Does the literal physical aperture size matter, or is it the effective size?

Since diffraction is determined by how much the light passing through the aperture is collimated, it is also determined by effective aperture.

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Doesn't the diffraction depend on the wavelength of the light relative to the size of the aperture, and since the lens doesn't magnify or shrink that, wouldn't it therefore be less with a larger physical aperture? –  mattdm Apr 9 '13 at 12:41
    
No. See the end of Matt Grum's answer. –  Michael Clark Apr 9 '13 at 19:02
    
Yeah, that clears it up and makes total sense; his answer wasn't there when I wrote that comment. –  mattdm Apr 9 '13 at 19:08

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