What is an easy way to remember the full stop scale?
If you were teaching someone new to photography the full stop scales, is there a better way then flat out memorizing these values? Does anyone have an easy way that they remember the scale? Would it make more sense as a type of mathematical equation without getting overly complex?
Aperture Full Stops:
1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32, 45, 64
Shutter Full Stops:
1/1000s, 1/500s, 1/250s, 1/125s, 1/60s, 1/30s, 1/15s, 1/8s, 1/4s, 1/2s, 1s
Obviously the shutter stop scale is very easy to remember, but how can I use the square root to determine the aperture easily in my head?
This has been said in answers already, but for me it has been as simple as memorizing "3". I take a base aperture and know that three cliks up or down is a full aperture stop. In My case I use 5.6 since that is the max that my current zooms have at max focal length. Constantly using only full stop apertures has led me to remembering them whithout specifir effort on memory. Ultimatelly I use f5.6, f.8 and f.11 the most, so they are in my head all the time, if I need to go somewhere else, I go three clicks every time...
I'm probably missing something, but why is it even important to memorize these exact values? And even if it is, why is it important for someone just starting to learn photography?
@Roel I wanted to know the values because I've got an adapted lens with an AF confirm chip. Since cameras meter at the widest aperture, I can still use my camera to gauge the metering, but then if I want to use a different aperture, I have to calculate an equivalent exposure. For example, although a scene may be exposed correctly at `f/1.4 1/1000s ISO 200`, if I narrow the aperture to `f/5.6`, the exposure will be _4x darker_, which means I need to compensate. `1000 / 2^4 ~= 1/60s`. As for a complete beginner, unless they're shooting film, it's probably not useful. 3 clicks is easier, though..
F-stops deal with doubling/halving the amount of light hitting the sensor. Everything revolves around twos.
With the shutter speed, it's easy to understand, as you say. Every shutter f-stop is (roughly) half/double the amount of time as the previous one. Personally, I don't even bother paying attention to the numerator ("1/") part of the shutter speed; I've drilled it into my head that bigger denominator = faster = less light = darker exposure.
Note that shutter speeds aren't exactly doubles/halves. I think that this is just because manufacturers think people like to see "round" numbers. At the fast end, that means 1000, 500, 250. At the slow end, you need more accuracy, so you have true halving of speed (1, 2, 4, 8). Then, they have to make the numbers meet in the middle, so they start to fudge the numbers a bit (15 is almost 8 * 2, 125 is almost 60 * 2). (I'm a programmer, so personally, I'm fine with seeing a shutter speed of 1/1024s :-) )
Aperture is a bit trickier. Double the light means doubling the area of the aperture, which is where the squares/roots come into play (Area of a circle = pi * r^2). That's a pain to mentally calculate, but there is an easier trick to consider: every two stops represents a doubling (or halving) of the aperture's f-number:
1, 2, 4, 8, 16, 32, 64.
If you know those, then you can guesstimate the in-between stops by calculating slightly less than the average of the surrounding f-stops:
1.5 -> 1.4, 3 -> 2.8, 6 -> 5.6, 12 -> 11, 24 -> 22, 48 -> 45.
As with shutter speed, bigger number = smaller aperture = less light = darker exposure.
Something similar happens with ISO. Each doubling of the ISO value represents a stop, which you can trade off (with consequences) with stops of shutter and aperture. Note that this transition is reversed though: bigger number = more sensitive = more light = brighter exposure. The common ISOs are:
50, 100, 200, 400, 800, 1600, 3200, 6400, 12800
And just to be complete, there's another similar scale with flash power:
1 (Full power), 1/2 power, 1/4 power, 1/8, 1/16, 1/32, 1/64, 1/128
This is very much like shutter: bigger denominators (forget the numerators) = less power = less light = darker exposure. (Note that true powers of two is fine here).
Honestly though, I don't bother with any of these mnemonics myself. I usually do "three clicks of my control wheels on my camera" when I want to go up/down one stop. (My camera, and many others, set one click of the control wheel to be 1/3 of a stop.) The absolute numbers aren't usually as important as the amount of change relative to "where you are now".
Another key point in the round numbers is that the actual physical reality of optics and aperture blades and mechanical shutters isn't that precise anyway, so in a sense it's more honest to round off. (And we really should do the same thing with high ISO values. Say 250k rather than 256,000.)