Largest possible aperture

Started Feb 10, 2004 | Discussions thread
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Doug Kerr Forum Pro • Posts: 20,898
Largest possible aperture

Sometimes, when a newcomer has asked about the signficance of the f/-number, respondents will include in their reply the comment that, "the largest theoretically possible aperture is f/2.0".

But that's not so - the laregst theoretically-possible aperture is f/0.5.

We can easliy demonstrate why that is so.

If we have a simple lens both of whose surfaces are portions of spheres with radius r, the focal length, f, will in fact equal r.

If we increase the overall diameter of the lens, maintaining this radius of the surfaces, the largest we can go is until the two surfaces become hemispheres - the whole lens becomes a sphere.

The diameter of the lens, D, will then be 2r, but this is also 2f.

The "clear aperture" of the lens will also be its diameter, D, which is 2f

The relative aperture , a (expressed as an f/-number), is the ratio of the focal length to the diameter of the clear aperture.

Thus:

a = f/D = f/2f = 1/2 = 0.5

That is, this largest relative aperture is f/0.5.

Of course, it is not normally practical to achieve this largest theoretically possible apreture and still accommodate other realites iof lens design, primarily the mitigation of various aberrations. But apertures larger than f/1.0 are in fact found in practice.

Interesting, wot?

Best regards,

Doug

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Leica V-Lux 4
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