1. ## F < 1

Someone educate me here, because I am puzzled.

My basic understanding of lens aperture is that the F stop directly correlates with the amount of light that goes through the lens. I do understand that the f stop is actually a fraction, 1 over the square root of <something>, which means that f1.4 [1.4 ~ srq(2)] gives twice the light of f2 [2 = sqr(4)], which gives twice the light of f2.8 [2.8 ~ srq(8)], and so on.

Now, take the Noct 0.95.

Shouldn't the aperture of 0.95 mean that effectively, there is more light coming out of the back of the lens than actually entered?

My misunderstanding of math / physics or a marketing ploy?

Someone enlighten me.

2. ## Re: F < 1

f number is a fraction, derived from

diameter of aperture
focal length

so f:2 or f/2 for a 50 mm lens means that the diameter of the aperture is 25 mm --

25
50

= 1/2 or f2 or f:2 or f/2

The area of the aperture determines how much light = how many rays/how many photons pass through. The diameter of a circle -- apertures are usually considered to be circles -- is

a = pi*r^2

a = area
pi = 3.14159, a constant
and r = radius of the circle -- r^2 = r squared.

to half the area of a circle:

1/2a = pi*(r-x)^2 as the radius is smaller by a value x

1/2(a/pi) = (r-x)^2

sq root1/2(a/pi) = r-x

the square root of 2 = 1.414..., the sq root of 1/2 = 1/1.4.4

so that halving [or indeed doubling] the area invloves the factor 1.4 (rounded from 1.414...)

which gives the series: 0.5, 0.7, 1, 1.4, 2, 2.8, 4, 5.6...

lens with f/0.95 means that the aperture is larger than the focal length -- no more than this; more light doesn't leave than enter.

It's not possible to have f less than about 0.5 because there ain't enough room for all the rays to pass through the [restriction of the] aperture.

3. ## Re: F < 1

Don't know if anyone has ever developed a working f/0.5 lens, but Zeiss has produced f/0.7 lenses.

Stanley Kubrick used Zeiss 50mm and 36.5mm f/0.7 lenses for the candlelit scenes in Barry Lyndon. Here's info on how they were adapted for film: http://www.visual-memory.co.uk/sk/ac/len/page1.htm.

4. ## Re: F < 1

Robert, David, I don't know how to thank you for your most informative replies.
Kind regards,
Osman

5. ## Re: F < 1

Another way to think of this is the inverse square law -- it's the same thing, expressed a bit differently.

If you are at a certain distance from the Nuke and move twice as far away, you get one quarter of the radiation [because the area of the circle quadruples if the radius doubles].

6. ## Re: F < 1

Originally Posted by DavidE
Don't know if anyone has ever developed a working f/0.5 lens, but Zeiss has produced f/0.7 lenses.

Stanley Kubrick used Zeiss 50mm and 36.5mm f/0.7 lenses for the candlelit scenes in Barry Lyndon.
f/0.7 seems to be the fastest so far made; f/0.5 is the [approximate] theoretical maximum possible -- perhaps not actually attainable.

7. ## Re: F < 1

The real confusion comes from the rather loose way that manufacturers and others describe lenses -- as f4-5.6 for example. The f number is a ratio, and is easier to understand when written f/4 - f/5.6 or f:4-5.6

"Make the aperture smaller with bigger f numbers" is a description often found, and very confusing; the fractional numbers are actually getting smaller.

8. ## Re: F < 1

Originally Posted by Robert Campbell
The real confusion comes from the rather loose way that manufacturers and others describe lenses -- as f4-5.6 for example. The f number is a ratio, and is easier to understand when written f/4 - f/5.6 or f:4-5.6

"Make the aperture smaller with bigger f numbers" is a description often found, and very confusing; the fractional numbers are actually getting smaller.
Leica lists f-stop in f/# nomenclature.

Good point, though. Shutter speed numbers share this same confusion. Higher numbers have shorter durations because they are fractions. 1/500th not 500.

Thanks for laying out the math for the rest of us. In the immortal words of Teen Talk Barbie, "Math is hard! Let's go shopping!"

David

9. ## Re: F < 1

Originally Posted by Robert Campbell
f/0.7 seems to be the fastest so far made; f/0.5 is the [approximate] theoretical maximum possible -- perhaps not actually attainable.
f/0.5 is theoretical limit for a conventional photographic lens that has to form an image on a flat plane.

The reason (cribbed from an explanation in one of Rudolf Kingslake's books) is that for the lens to be well-corrected, all the light "rays" that form each image point have to travel the same distance from the equivalent refracting surface (an imaginary surface from which the light rays emanate.) The only way for all the rays to travel the same distance is if the equivalent refracting surface is a partial sphere with a radius equal to the lens' focal length.

The bigger the f/number, the bigger a portion of the sphere this "surface" has to be... and as the aperture diameter approaches twice the focal length (f/0.5) the "surface" approaches intersecting with the image plane! So that's as far as you can go even in theory -- and in practice, it would be pretty tough to get that far.

One aspect of this that until recently has been only a curiosity is that if you DON'T need to form the image on a plane, you could go farther. For example, I have a vague recollection of reading back in the 1960s about a projection television system in which the image source was a part-spherical CRT, allowing the lens that focused the CRT image onto the projection screen to have an aperture of f/0.33.

And now that most imaging is done on a digital receptor rather than a flat sheet of film, it seems as if it would be possible to form that receptor onto something other than a flat surface -- which would open up the possibility of designing faster lenses. Don't hold your breath, though...