How are lenses faster that F1.0 possible?

Chris Keth · December 7, 2004

I noticed in another thread a mention of a F0.7 Zeiss lens used in a feature. How is that possible? I was under the impression that the fastest possible lens, theoritically, would be a F1.0 because it would allow all of the available light in without loss.

I was also under the impression (this was my own guess at the origen) that F-stops are really the denominator of a fraction of available light they let through the lens? I.E.- An F1.4 would let 1/1.4 of the light throu8gh, the rest would lost to internal reflections/refractions. Is this right? If it's not, what is the right math behind F-stops?

Dominic Case · December 7, 2004

There's nothing magic about a value of F/1 - it's not like breaking the sound barrier or anything.

The F/stop is simply the ratio of the focal length of the lens divided by the effective diameter. It turns out if you do all the optical formulae, that this gives you a precise measure of the brightness of the image. (A longer focal length produces a larger image, therefore less bright: a larger diameter admits more light, leading to a brighter image).

So any F/4 lens for example, will produce an image requiring the same exposure, as the two properties of the lens that affect image brightness cancel each other out.

In practice, both the focal length and the effective diameter of a complex imaging lens are a little hard to measure, but you get the idea if you think of a simple magnifying glass type of lens.

In practice also, multi-element lenses tend to absorb a bit of light, which isn't allowed for in this simple theory: so T-stop values are used, which factor in the loss of light.

The practical limit is really to do with the curvature of the lens. To get a really small F/number, you need a large diameter lens with a short focal length. Powerful means the lens is very convex: big diameter means it is very very thick in the middle. At F/1, light rays from the edge of the lens are coming in to the film plane at 45 degrees - it's hard to design a lens that will do this without distortion and aberration. Then you get to a point where the rear element comes into contact with the film plane (and before that of course, the rotating shutter). Using glass with a higher refractive index buys you space, but simply makes it harder to deal with aberrations.

Chris Keth · December 7, 2004

There's nothing magic about a value of F/1 - it's not like breaking the sound barrier or anything.

The F/stop is simply the ratio of the focal length of the lens divided by the effective diameter. It turns out if you do all the optical formulae, that this gives you a precise measure of the brightness of the image. (A longer focal length produces a larger image, therefore less bright: a larger diameter admits more light, leading to a brighter image).

So any F/4 lens for example, will produce an image requiring the same exposure, as the two properties of the lens that affect image brightness cancel each other out.

In practice, both the focal length and the effective diameter of a complex imaging lens are a little hard to measure, but you get the idea if you think of a simple magnifying glass type of lens.

In practice also, multi-element lenses tend to absorb a bit of light, which isn't allowed for in this simple theory: so T-stop values are used, which factor in the loss of light.

The practical limit is really to do with the curvature of the lens. To get a really small F/number, you need a large diameter lens with a short focal length. Powerful means the lens is very convex: big diameter means it is very very thick in the middle. At F/1, light rays from the edge of the lens are coming in to the film plane at 45 degrees - it's hard to design a lens that will do this without distortion and aberration. Then you get to a point where the rear element comes into contact with the film plane (and before that of course, the rotating shutter). Using glass with a higher refractive index buys you space, but simply makes it harder to deal with aberrations.

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I see. I was told a definition of f-stops that is entirely wrong. That's kind of disappointing, but it wasn't from the best source, either. Very cool information. Thank you, Dominic. :)