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11/18/2011 02:21:31 PM · #1 |
I am currently reading a book about exposure that says aperture (f-stop) determines how much light is allowed to enter the lens, basically, the size of the hole. I already knew this and it makes perfect sense. It also said that f/4 means the focal length of the lens divided by the aperture equals the diameter of the lens opening (50mm lens / 4 = 12.5). I didn’t know that but it makes sense. It goes on to say that every time you halve or double that opening, you are increasing or decreasing the light by one full stop. It then says that the difference between F/4 and F5.6 is one full stop but that doesn’t make sense.
50 / 4 = 12.5
50 / 5.6 = 8.92
This is not half. What am I missing?
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11/18/2011 02:57:00 PM · #2 |
The area of a circle or pi*R squared
of 50/4=12.5 Equals 385.53
and of 50/5.6=8.92 equals 196.32
here you can see it is almost double, hense letting in twice the light...
Thank you for that post as I just taught myself something!! |
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11/18/2011 03:15:09 PM · #3 |
OK. Not sure how you got your numbers here.
If the diameter of the aperture is the focal length divided by the fstop (D=fl/fs)
Then at f4 and 50mm D=50/4=12.5
Area of a circle = pi*r^2 or pi*(d/2)^2 = 3.14159/(12.5/2)^2 = 122.72
at f5.6 and 50mm D=50/5.6=8.93
and area of a circle = pi*r^2 or pi*(d/2)^2 = 3.14159/(8.93/2)^2 = 62.61
So it's still about the same ratio of roughly half but you have to use the radius and not the diameter. |
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11/18/2011 03:24:21 PM · #4 |
To reiterate the first reply from another (essentially equivalent) view point:
Lets say you have a lens with focal length f and aperture diameter D. To keep the math simple, lets assume the focal length is 1 mm and so is the diameter (1 mm). The f-number, or focal ratio is the length (f) over the diameter (D) so, 1/1 = 1.
The area of the opening is equal to pi*r^2 or pi*(D/2)^2 which given the diameter above is 0.785398 mm^2.
Since a 'stop' is defined as changing the light by a factor of 2, to move the diameter one stop lower you will reduce the light by 1/2. To do that, you need to reduce the area by 1/2 which gives you 0.392699 mm^2.
What diameter is the aperture now? D = 2*Sqrt(Area/pi) = 2*sqrt(0.392699/pi) = 2*sqrt(0.125) = 2*0.353553 = 0.7071067.
What is the f-number? Recall that it is f/D, so 1/0.7071067 = 1.414.
Now, if you went on and on, halving the area each time, you would get the series leading to the f-ratio: 1, 1.414, 2, 2.828, 4, 5.656.
Now, square each f-ratio: 1, 2, 4, 8, 16, 32, 64....You'll notice that the f-ratio is the square root of 2^N where N(1) =0, N(2)=1, for each 'stop'.
If you notice, when N=9, the f-ratio is 22.627 but cameras are set to 22. I'll leave the explanation of that to someone with far more experience. My guess is that 22 is more intuitive than 22.6, or perhaps it has something to do with the aperture blades, I'm not sure....
Message edited by author 2011-11-18 15:25:10. |
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11/18/2011 03:29:33 PM · #5 |
Originally posted by PGerst:
If you notice, when N=9, the f-ratio is 22.627 but cameras are set to 22. I'll leave the explanation of that to someone with far more experience. My guess is that 22 is more intuitive than 22.6, or perhaps it has something to do with the aperture blades, I'm not sure.... |
I think at that end of the scale, there wasn't room to print the three-digit numbers on the edge of the lens without overlapping. ;-)
Also, because (as you mention) the aperture is a polygon and not a circle, the numbers will vary slightly from the ideal. |
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11/18/2011 06:34:39 PM · #6 |
| Opps, I squared the (pi*R) in stead of pi (r^2)... but you get the idea... |
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11/18/2011 06:55:23 PM · #7 |
@ PGerst Bravo. That was a great explanation!!! Now how do you explain a stop using shutter speed?? |
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11/18/2011 07:05:32 PM · #8 |
Originally posted by EL-ROI:
@ PGerst Bravo. That was a great explanation!!! Now how do you explain a stop using shutter speed?? |
That part's easy: think of it as plumbing. A bucket filled with liquid represents the correct exposure. The aperture is the size of the pipe, and the shutter speed is how long you have let the liquid flow out of the pipe until the bucket is filled. The bigger the pipe, the less time it takes to fill the bucket. The smaller the pipe, the longer it takes.
Leaving the shutter open twice as long allows twice as much light to "flow into" the sensor at a given aperture.
R.
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11/18/2011 07:22:19 PM · #9 |
Originally posted by Bear_Music:
Originally posted by EL-ROI:
@ PGerst Bravo. That was a great explanation!!! Now how do you explain a stop using shutter speed?? |
That part's easy: think of it as plumbing. A bucket filled with liquid represents the correct exposure. The aperture is the size of the pipe, and the shutter speed is how long you have let the liquid flow out of the pipe until the bucket is filled. The bigger the pipe, the less time it takes to fill the bucket. The smaller the pipe, the longer it takes.
Leaving the shutter open twice as long allows twice as much light to "flow into" the sensor at a given aperture.
R. |
So if you are shooting at f4 with a shutter speed of 1/320, one shutter stop would be f4 @ 1/640 and or f4 @ 1/320? Which way is one stop higher or one stop lower? (just FYI you must know the questions about achieving one stop through a combination of aperture and shutter changes is coming up...) |
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11/18/2011 08:54:35 PM · #10 |
f/2.8 @ 1/500
f/4.0 @ 1/250
f/5.6 @ 1/125
f/8.0 @ 1/60
f/11 @ 1/30
f/16 @ 1/15
f/22 @ 1/8
f/32 @ 1/4
f/45 @ 1/2
f/64 @ 1 sec
These are the "normal" increments. Reading from the top, each aperture lets in half the light of the one before it (f/16 is a smaller aperture than f/11), and each shutter speed lets in twice the light of the one before it (1/15 sec is twice as long as 1/30 sec), so the quantum is constant: each of those combinations produces the exact same "exposure", allowing the exact same amount of light to reach the sensor.
R.
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11/19/2011 10:02:35 AM · #11 |
Also, don't forget ISO as well as that completes the exposure triangle. Though, there is a bit more to ISO as its response is not linear and is bounded. But, within normal exposure limits, the calculations are valid.
For example, lets say you want to take a long exposure and you are not sure what shutter speed to use and lets say you wanted to shoot ISO 100 to reduce the amount of noise. A 10 minute exposure is a bit long to wait to see if you got it right. So...you could increase the ISO to 3200 and do an 18 second exposure.
ISO 100 -> 200 -> 400 -> 800 -> 1600 -> 3200 = 5 stops.
time (min) 10 -> 5 -> 2.5 -> 1.25 -> 0.625 -> 0.3125 = 5 stops as well.
Then, once you found the right exposure time, you can drop the ISO, and set the exposure for that ISO.
One note, don't be confused by settings on your camera. Most allow 1/2 and 1/3 stop increments for aperture and shutter speed, but some camera may only have full stop settings for ISO. So, if you are changing ISO and counting "clicks" of shutter or aperture, be aware of that. |
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11/19/2011 10:17:54 AM · #12 |
It's a convenient correlation that if you change one corner of the triangle by one "click" then one of the other two has to be changed by one "click" , no matter if your camera is set to change by 1/3 stop, 1/2 stop or in full 1/1 steps.
They can share too, if you change shutter by 2 clicks, you can change aperture 1 click, and iso by 1 click and get the same exposure value.
That's a good time saving suggestion about shooting night long exposure test shots in high iso, then dropping back to lower iso and longer exposure for the keepers. If you were shooting 10 minute exposures at low iso as test shots, the scene could change a lot by the time you had 4 or 5 shots.
Fortunately, digital "film" does not have the old "silver film" bug of reciprocity failure, so no need to increase exposure in time exposures, as exposure time gets longer.
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11/19/2011 01:20:51 PM · #13 |
Right..but not all cameras change ISO by 1/2 or 1/3.
Originally posted by MelonMusketeer:
It's a convenient correlation that if you change one corner of the triangle by one "click" then one of the other two has to be changed by one "click" , no matter if your camera is set to change by 1/3 stop, 1/2 stop or in full 1/1 steps. |
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