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03-02-2010, 05:36 PM   #1
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How much is one stop?

Ok so if a lens is F2.8, what is 1 stop faster? F1.8?

Or do they go up/down in increments of 0.5 or 0.6?

Thanks

03-02-2010, 05:55 PM   #2
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It is a sort of exponential scale

From wikipedia this is the list of full stops

0.5 0.7 1.0 1.4 2 2.8 4 5.6 8 11 16 22 32 45 64 90 128
03-02-2010, 05:57 PM   #3
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One stop is double (or half) the light. Aperture stops are: f/1, f/1.4, f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22, f/32, etc. Shutter stops fudge a little; they are 1 sec, 1/2 sec, 1/4 (or 1/5) sec, 1/8 (or 1/10) sec, 1/25 sec, 1/50 sec, 1/100 (or 1/125) sec, 1/250 sec, 1/500 sec, 1/1000 sec, etc. You get the same exposure at f/11, 1/100 sec, as at f/22, 1/25 sec. Them's are the basics.

MORE: There's a reason for the weird numerical progression. F-stops are the ratio of the aperture to the focal length, so they're a fraction. So f/2 means the aperture size (diameter) is 1/2 the focal length (FL), f/8 means it's 1/8 the FL, etc. A larger f-stop number means a smaller fraction, just as 1/2 is more than 1/8. Since it's a ratio, f/8 delivers the same amount of light no matter the FL of the lens. This makes calculating exposures much easier.

But that f-stop is a diameter, the diameter of the (near) circle of the aperture iris blades. And doubling the AREA of a circle, which controls how much light actually passes, means increasing the diameter by the SQUARE ROOT of 2, which is 1.41414... So to get half as much light as f/1, you need a diameter of f/1.4; and to halve that, you get 1.4 x 1.4 = f/2; and to halve that you get 2 x 1.4 = f/2.8, etc. It's the old Inverse Square law, like with gravity.

"There is no gravity; Earth sucks." --anon.

Last edited by RioRico; 03-02-2010 at 06:37 PM. Reason: addendum
03-02-2010, 06:51 PM   #4
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Original Poster
Ok thanks guys.

03-03-2010, 02:35 AM   #5
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And the stop comes from old manual lenses.
You'd feel a click when turning the aperture dial on the lens in each "stop".
The was true for the shutterspeed dial.
1 stop aperture open/close = 1 stop slower/faster shutter speed.
03-03-2010, 03:25 AM   #6
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For exposure it's best to think of everything in terms of stops: aperture; shutter speed; sensitivity.

Consider F5.6, 1/125s, ISO100 = LV (Light Value) 12 approx. (An LV calculator is available here)

Now say the light dims to LV 11 (lower LV = less illumination). To compensate we could use:

F4 (+1 stop more opening of the aperture), 1/125s, ISO100 = LV 11
F5.6, 1/60s (+1 stop longer illumination time), ISO100 = LV 11
F5.6, 1/125s, ISO200 (+1 stop more sensitivity) = LV 11
F8 (-1 stop smaller aperture), 1/125s, ISO400 (+2 stop more sensitivity) = LV 11
etc.

So you can see that +1 stop = twice the aperture area/shutter duration/sensitivity.
And -1 stop = half the aperture area/shutter duration/sensitivity.

Also, if the light level drops -1 LV we need to increase the overall exposure +1 stop. And if the light level increases +1 LV, we need to reduce the exposure setting by -1 stop.

Note: F5.6, 1/125s, ISO100 is actually LV 11.9, rather then LV 12, because we are not using exact root-2 steps, but more convenient x1.4 steps. So comparing the ratio of 1/5.6^2 to 1/4^2 = 0.03189 : 0.0625, so the ratio is not 1 : 2.

Dan.

Last edited by dosdan; 03-03-2010 at 12:37 PM.
03-03-2010, 04:04 AM   #7
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QuoteOriginally posted by dosdan Quote
. So comparing the ratio of 1/5.6^2 to 1/4^2 = 0.03189 : 0.0625, so the ratio is not 1 : 2.
That comes to .51024. Dunno if this might be due to some rounding issues, but (0.03189 / 0.0625) is pretty close to a ratio of 1:2.

I had to do some math to get more precise numbers and verify. The numbers used are rounded to make life easier, but generally the numbers are not single decimal place. You don't want to say f1.41213562373095 or f5.656854249238 hundreds of times a day. :-)

Honestly I am not 100% positive on the following, but I believe the correct order of operations done above is incorrect. It is (1/5.6)^2 not 1/(5.6^2).

FYI, 1/5.6^2 ~= (SQR(2)*4)^2 ~= (5.656854249238)
So, (1/5.656854249238)^2 == .03125 (not .03189)

1/4^2 == .0625

With those numbers: .03125 / .0625 == 0.5
03-03-2010, 04:34 AM   #8
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QuoteOriginally posted by amoringello Quote
(1/5.6)^2 not 1/(5.6^2)
Same thing.

1/(3^2) = (1/3)^2
1/9 = .11111111... and 1/3*1/3 = .11111111...


1/10^2 = (1/10)^2
1/100 = .01 and 1/10 * 1/10 = .01


Dan.


Last edited by dosdan; 03-03-2010 at 04:48 AM.
03-03-2010, 05:52 AM   #9
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alert - some esoteric math

Just a warning - the following math discussion may scar you for life, or at the very least make you want to vomit

for full stops: 2^(1/2) or 2^(-1/2), e.g 2*2^(1/2)=2.8 & 2*2^(-1/2)=1.4
for half stops: 2^(1/4) or 2^(-1/4), e.g 2*2^(1/4)=2.4 & 2*2^(-1/4)=1.7

2^(1/2) is the same as the square-root of 2, & 2^(-1/2) the same as 1 divided by the square root of 2

And yes, some rounding is involved.
03-03-2010, 07:57 AM   #10
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Aperture numbers differ by a factor of sqrt(2) or approximately 1.414.

You can figure it out for yourself. Take a 50mm lens, with a diameter of 50mm. That's an f/1.0 (50mm/50mm) lens. Calculate the area of the aperture. Remember pi * r ** 2. In this case its 3.1415926 * 25 * 25 = 1963.5 sq. mm.

Divide that by 2 (one f-stop equals half the area) and solve for the diameter. This is 35mm. The f-stop is 50mm/35mm = 1.414, usually rounded to simply f/1.4.

Halve the area again and solve for the diameter. This time, its 25mm. The f-stop is f/2.0 (50mm/25mm). Note that 2.0 is 1.414 * 1.414.

Do it again. The diameter comes out to about 18mm, resulting in an f-stop of f/2.8.
(2.8 = 1.4 * 2.0).

Yet again, the diameter is 12.5mm, resulting in f/4.0 (4.0 = 2.8 * 1.414)

Keep going. The f-stop is always 1.414 times the previous stop.

BTW, the same is true of flash guide numbers. If your flash has a GN of 120 (feet) at ISO 100, it will have a GN of 120 * 1.414 = 170 at ISO 200. At ISO 400 it will be 170 * 1.414 = 240.
03-03-2010, 10:55 AM   #11
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I read the question in terms of price. So here are my equations:

A50/1.4=$125 and A50/2=$30, so that stop is about $100

but

A50/1.2=$500, so that half-stop is about $375.
03-03-2010, 12:28 PM   #12
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QuoteOriginally posted by Just1MoreDave Quote
I read the question in terms of price. So here are my equations:
A50/1.4=$125 and A50/2=$30, so that stop is about $100
Where are you finding a reliable source for A50/1.4's at $125? I usually see them go for over $200. Even when the FA50/1.4 was only $200-ish, the A50/1.4 rarely sold for less in my experience.
03-03-2010, 12:32 PM   #13
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QuoteOriginally posted by Just1MoreDave Quote
I read the question in terms of price. So here are my equations:

A50/1.4=$125 and A50/2=$30, so that stop is about $100

but

A50/1.2=$500, so that half-stop is about $375.
DEAD ON!!!

Yeah, it's too easy to focus too narrowly on the photo factors: exposure, DOF, etc.

So look ouside the box (or whatever): cost, bragging rights, sex appeal (nothing says HEY BABY! like a huge, fast lens, eh?), weight (for Russian Jupiter lenses, the almost-a-stop of 85/2 to 85/1.5 is about half a pound, I think). How else can we judge f-stops?
03-03-2010, 03:03 PM   #14
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QuoteOriginally posted by Marc Sabatella Quote
Where are you finding a reliable source for A50/1.4's at $125? I usually see them go for over $200. Even when the FA50/1.4 was only $200-ish, the A50/1.4 rarely sold for less in my experience.
That's about the price ($125) where I lose interest. I guess I should be following them more thoroughly.

I have strongly considered selling mine. It sits in a drawer even more than all my other underutilized lenses.
03-24-2010, 05:36 AM   #15
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QuoteOriginally posted by dosdan Quote
For exposure it's best to think of everything in terms of stops: aperture; shutter speed; sensitivity.

Consider F5.6, 1/125s, ISO100 = LV (Light Value) 12 approx. (An LV calculator is available here)

Now say the light dims to LV 11 (lower LV = less illumination). To compensate we could use:

F4 (+1 stop more opening of the aperture), 1/125s, ISO100 = LV 11
F5.6, 1/60s (+1 stop longer illumination time), ISO100 = LV 11
F5.6, 1/125s, ISO200 (+1 stop more sensitivity) = LV 11
F8 (-1 stop smaller aperture), 1/125s, ISO400 (+2 stop more sensitivity) = LV 11
etc.

So you can see that +1 stop = twice the aperture area/shutter duration/sensitivity.
And -1 stop = half the aperture area/shutter duration/sensitivity.

Also, if the light level drops -1 LV we need to increase the overall exposure +1 stop. And if the light level increases +1 LV, we need to reduce the exposure setting by -1 stop.

Note: F5.6, 1/125s, ISO100 is actually LV 11.9, rather then LV 12, because we are not using exact root-2 steps, but more convenient x1.4 steps. So comparing the ratio of 1/5.6^2 to 1/4^2 = 0.03189 : 0.0625, so the ratio is not 1 : 2.

Dan.
No wonder i set my P3n on auto. I can't imagine going through the calcs. to take a shot of a setting sun or a galloping horse in morning light with fog. I desperately needed a hobby but not one that requires a mathematics degree. I'll just stick to the art and remain an amatuer; and try not to lose my lunch on the science. oohh boy.
p.s. I'm not picking on Dan feel free to bash me.
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