# F factor and speed of a lens



## Vuorilla (Dec 6, 2009)

Hi there,

I wonder if there is a direct relation between the "f number" and the speed of a lens. Is there a way to quantify how faster a f number is as compared to another f?

For example, how many times faster is F1.2 compared to F3.5?
And F1.2 to F1.4?

I don't know if the term "faster" is the correct one here. Maybe I should say "how much more light does F1.2 let in as compared to F3.5?"

I enjoy night photography, but my lens, at F3.5, sometimes is too slow to capture a crystal-clear photograph.


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## jnm (Dec 6, 2009)

Vuorilla said:


> Hi there,
> 
> I wonder if there is a direct relation between the "f number" and the speed of a lens.



yes.  when someone says a lens is 'fast' or 'slow' they are referring to the max aperture, i.e. f number.



Vuorilla said:


> Is there a way to quantify how faster a f number is as compared to another f?
> 
> For example, how many times faster is F1.2 compared to F3.5?



the standard f-stops are 1.4 > 2 > 2.8 > 4 > 5.6 > 8 > 11.2 > 16 > etc.

each jump is one full stop, or a doubling of light. there's probably a way to tell how much faster 1.2 is in relation to 3.5 but i dont know it. what i do know is 1.2 is a hell of a lot more light than 3.5. ex. if you had asked how much faster 1.4 is than 4 i could tell you that 4 > 2.8 is twice the light, 2.8 > 2 is twice the light, and 2 > 1.4 is another twice the light.

twice * twice * twice = 2 * 2 * 2 = 8x more light, i.e. f 1.4 allows 8x more light than f/4 does. i suspect the jump from 1.2 to 3.5 is in a similar range.

Aperture - Wikipedia, the free encyclopedia


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## rufus5150 (Dec 7, 2009)

> Is there a way to quantify how faster a f number is as compared to another f?



That's precisely why it's expressed how it is -- the f-number is a pure number. All of the units have been factored out, which allows us to compare the amount of light let in by lenses with radically different physical sizes.


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## Garbz (Dec 7, 2009)

Wikipedia has another good article on this too: F-number - Wikipedia, the free encyclopedia


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## Vuorilla (Dec 7, 2009)

Oh, I see. Could I say, for example, that if in a certain situation, with certain settings (ISO speed, etc.) the slowest shutter speed that would enable me to get a clear picture would be 1/10 at F4, then at F1.4, I could use 1/80 and I would get the exact same picture?


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## Shockey (Dec 7, 2009)

tripod.....
F2.8 lets in light fast and large opening, short depth of field great for action....handhold

F14 lets in light slow and small opening, large depth of field great for landscapes...tripod

Shutter speed is a function of f-stop combined with ISO.


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## jnm (Dec 7, 2009)

Vuorilla said:


> Oh, I see. Could I say, for example, that if in a certain situation, with certain settings (ISO speed, etc.) the slowest shutter speed that would enable me to get a clear picture would be 1/10 at F4, then at F1.4, I could use 1/80 and I would get the exact same picture?



exposure wise yes.  depth of field wise no.  you could also do something in between, such as upping the iso one stop and using 1/40 or upping iso 2 stops and using 1/20.  exposure is a math problem really.  each one of the variables (shutter speed, iso, aperture) does something different to the picture though.


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## raptorman (Dec 11, 2009)

Vuorilla said:


> Is there a way to quantify how faster a f number is as compared to another f?



(1/(2*largest_aperture))²/(1/(2*smallest_aperture))²

So if you compare 1.4 with 4 you get this:

(1/(2*1.4))²/(1/(2*4))² = 8.1633 -> F/1.4 allows 8.1633x more light then F/4

If you compare 1.2 with 3.5 you get this:

(1/(2*1.2))²/(1/(2*3.5))² = 8.507

So jnm's suspection was pretty much correct.


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## Dao (Dec 11, 2009)

Vuorilla said:


> Oh, I see. Could I say, for example, that if in a certain situation, with certain settings (ISO speed, etc.) the slowest shutter speed that would enable me to get a clear picture would be 1/10 at F4, then at F1.4, I could use 1/80 and I would get the exact same picture?



Go here
Exposure value - Wikipedia, the free encyclopedia

Take a look at the EV table from the link. (Table 1)

On the far left column, that is the EV value.  For example, EV=8, every settings (shutter speed and aperture) on that row are equal to EV 8. So you can say (F/4, 1/15) settings will yield the same exposure as (F/11, 1/2)


Let take another example.
Shooting in "Areas in open shade, clear sunlight", according to wikipedia, you can take a photo with EV 12 settings (based on ISO100).   So if you want to have more objects in focus in the photo, you may take the photo with (F/11, 1/30)
,  but if you are taking a photo of a kid running around, you may need a faster shutter speed such as (F/4, 1/250).  Both should give you the same exposure.


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## Stosh (Dec 11, 2009)

raptorman said:


> (1/(2*largest_aperture))²/(1/(2*smallest_aperture))²
> 
> So if you compare 1.4 with 4 you get this:
> 
> ...


As I understand it, f/1.4 is *exactly *8x more light than f/4.  Your math is likely correct, but the beginning number is wrong.  It would technically be f/1.4142135........ or the easier way is the square root of 2.  Of course this would be cumbersome to print on a camera lens.


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## Josh66 (Dec 11, 2009)

Stosh said:


> raptorman said:
> 
> 
> > (1/(2*largest_aperture))²/(1/(2*smallest_aperture))²
> ...



It could just say "50mm f/&#8730;2" instead.


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## KmH (Dec 11, 2009)

Stosh said:


> raptorman said:
> 
> 
> > (1/(2*largest_aperture))²/(1/(2*smallest_aperture))²
> ...


Yep, there's a bit of rounding for the f-numbers.


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## Garbz (Dec 12, 2009)

You're assuming photographers at large have brains. I know first hand that this is largely not the case, the sqrt button will likely just confuse them


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## djacobox372 (Dec 12, 2009)

Vuorilla said:


> Hi there,
> 
> I wonder if there is a direct relation between the "f number" and the speed of a lens. Is there a way to quantify how faster a f number is as compared to another f?
> 
> ...



I'll skip the crazy math and make it simple:

A smaller F # is faster, here's the scale in 1 stop increments (each stop doubles the speed of the lens):

1 - 1.4 - 2 - 2.8 - 4 - 5.6 - 8 - 11 - 16 - 22 - 32

F 1.2 is about three times "faster" then f3.5, which means you'll get the same exposure at 1/90th of a second at f1.2 as you'd get at 1/30th at f3.5.


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## spudgunr (Dec 12, 2009)

Actually, 1/30th at 3.5 would be 1/60th at 2.5, 1/120th at 1.8, and 1/240th at 1.2. 

3 stops is 8 times as much light (2^3).


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