John, I'm not trying to be argumentive, so please have some
patience while us lesser technical endowed, who are trying to sort
through your post.
I didn't take your post as argumentative. In fact, I love explaining things and listening to explanations. Occasionally I get something wrong and I love it when I'm corrected because it furthers my understanding of how things work - something in me likes to learn.
OK, maybe I'm missing something here. My understanding was that 1
stop increase = current aperture / 1.414. Why 1.414? Because it's
the square root of 2.
Ummm... where did the "2" come from? Again, please be patient,
you're dealing with some one who thinks that a click on their lens
equals an F stop.
OK, let me take a step back and see if I can make this make sense. Please don't take this as "talking down" to you - I just want to make sure we're all on the same page and if I cover something you already know I apologize.
If you halve the shutter speed, say from 1/30th of a second to 1/60th of a second the film (or sensor) only gets half of the light it was getting at 1/30th of a second. Half the light is a 1 stop decrease in light (or exposure). So, every halving of the light the film sees is a 1 stop decrease in exposure and every doubling of the light the film sees is a 1 stop increase in exposure. So what is a half stop increase? Well, it's half of a 1 stop increase. ;-) If we have two half stop increases we get a full stop increase so a shutter speed of 1/60 times 1.414 (first half stop increase) times 1.414 (second half stop increase) = 2/60 = 1/30. A half stop increase from 1/60 of a second is 1/42.433 of a second but in the world of cameras it's OK to round so we say that 1/45 is a half stop increase in shutter speed from 1/60 second.
Now, on to aperture. For all intents and purposes the aperture is a circular hole (it's not really perfectly circular but for our discussion it's close enough). The amount of light the aperture lets in is based on the area of the hole. The area of a circle is pi time the radius of the circle squared. If we double the radius of the circle we actually let in 4 times as much light - orignal radius squared (r^2) = 1/4 of doubled radius sqaured (2r^2 = 4 times r^2). So, once again the square root of two (1.414) helps us out. If we increase the radius of the aperture by 1.414 then we double the area of the hole and thus double the amount of light reaching the film (sensor): 1.414r^2 = 2 times r^2.
Now, on to the magic f numbers and what they mean. If we take a picture at 1/60 of a second and f8 then we get the same exposure regarless of the focal length of the lens used. If this weren't the case then it would be very hard for a camera or a human to meter because they would have to set their exposures differently depending on the lens they used. So, what is f8? Well, the f stop number is the focal length of the lens divided by the diameter of the aperture . Ever notice how the 200mm f2.8 lens is much bigger around then the 28mm f2.8? The longer the focal length the physically bigger the aperture has to be for an exquivalent f number. In the case of the 200mm f2.8 the aperture has to be 200/2.8 = 71.4mm while the 28mm f2.8 only needs an aperture 10mm in diameter. Now, packaging all the elements in a lens greatly increases it's size which is why the wide angle low f number lenses are still pretty big around but the apertures in them are actually significantly smaller.
So, as the diameter of the aperture decreases (is stopped down) the f stop number gets bigger. Lets suppose we decrease the diameter by a factor of 1.414. That means the f stop number increases by a factor of 1.414. When the diameter is decreased by a factor of 1.414 the radius of the aperture is also decreased by a factor of 1.414. Since we square the radius of the aperture to get the area (and hence the amount of light it lets through) we halve the light when we decrease the diameter/radius by a factor of 1.414.
OK, let's take a more practical look at it. Increasing the exposure by 1 stop doubles the amount of light. The f number is the ratio of focal length to aperture diameter. The smaller the aperture the larger the number. 1 stop decreases are achieved by halving the area of the aperture which means multiplying the f number by 1.414. So, starting at f1 the full stop progression for an aperture is 1, 1.4, 2, 2.8, 4, 5.6, 8, 11 (ok, actually 11.2 but remember we said it was OK to round here and there), 16, 22, 32, 44...
If you've made it this far I congratulate you!
. The f stop is a measurement of the radius of
the aperture and area of a circle is pi X radius squared.
I didn't know that the radius of the aperture was an constant, from
lens to lens that is, could you define this a little further?
Actually the aperature is a ratio of focal length to diameter of the aperture - that's why f2.8 is a different physical aperture size from lens to lens. The thing that's constant is how much light a lens allows through at a given f number.
if the radius decreases by a factor of 1.414 then you have half the
light. All this is just a way to say my understanding is that 1.2
is approximately 1 stop faster than 1.8 (1.2 X 1.414 = 1.7).
Ok, than a F 1:1.4 lens is only a half stop faster? I didn't know
Canon would manufacture so many lenses in half stops. The constep
of "stops" is some what of a mystery to a lot of us, and any light
you could shed would be greatly appreciated.
Thanks,
No, thank you. If you do manage to read my whole post please let me know if I wasn't clear on something.
John Engstrom
Plano, TX
