This is a subject that for a long time has caused a lot of confusion in my head. Also, I the feeling that very few people actually know what’s they’re talking about when refering to f-stops or apertures in photography. Because I’m a geek I decided to go a little deeper and finally cleared all my doubts. Well at least almost all of them. I’ll try to explain here what I’ve learned in the most simple way in the hope of making someone happier, and also to test my own knowledge. First things first…
What’s the aperture?
I assume you have a slight clue on this, but anyway, simply put the aperture is the actual hole that sits in your lens and lets light go through it until it reaches the sensor (or film plane). The size of the hole can be controlled by the photographer if the lens (on older systems) or the camera allows it. The f-stop scale that we see in most lenses has this kind of progression:
f/1.4 – f2 – f2.8 – f4 – f.5.6 – f8 – f11 – f16 – f22 – f32
Most lenses nowadays have a slightly longer scale because they offer some steps in between.
How does it really work?
This is the question I have asked myself for a long time. Obviously there is a logical reason behind it, but it’s not that easy to get there just by looking. You probably heard that each f-stop represents exactly half the light that you’d get in relation the previous f-stop (considering that every other variable remains the same – speed and ISO). So, f/2.8 is half the light of f/2. Why didn’t they make it f/4 then? Would be easier to have a linear scale. Let’s go a littler deeper. First of all, it’ important to know what an f-stop actually means, besides being a hole that lets light go through. Every f-stop number represents a ratio of the focal distance of the lens (take 50mm for example) to the actual diameter of the diaphragm opening (the hole, remember?).
The diaphragm is the device that controls effective diameter of the lens opening. It’s usually formed by a series of blades that form an almost circular shape.
So, f/2 is = Focal Distance / 2 = 50mm / 2 = 25mm (diameter of the aperture or diaphragm) Still following? Ok, so for a 50mm lens at f/2 the diaphragm has a 25mm diameter. If you take a 100mm and do the same math, you can easily see that the same f/2 aperture results in a 50mm diameter. You must asking “well if the hole’s bigger, how come the aperture is the same (f/2)?”. Indeed a great question that haunted me for a long time! And if you go shoot a photo with both lenses at f/2 you will conclude that the amount of light that makes up your photo is the same. More on that later. At this point we know the size of the opening in the lens, and we know that the f-stops are directly related with focal distance. What you may not know is that to determine the amount of light we need to consider the area of the opening (and not the diameter). Remember how to calculate the area of a circle? Ok, I’ll give you a little help: π * radius² So the area of our 25mm diameter (50mm lens @ f/2) is = 3,14 * 12,5² = 490,6 mm² Also, the area of our 50mm diameter (100mm lens @ f/2) is = 3,14 * 25² = 1962,5 mm² 1962,5 / 490,6 = 4
Why did we double the focal length and the aperture area is 4 times bigger?
It’s math! There’s a rule that says that the area varies as the square of the radius. So, if you double the radius that’s the same as saying 2² which is 4.
If the opening is 4 times bigger how can it be the same amount of light (f/2) on both situations?
The answer has to do with the focal distance, once more. And also some physics: the inverse square law. Wikipedia says:
In physics, an inverse-square law is any physical law stating that some physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity.
Read the rest of the article here.
Why the odd progression of the f-stop scale?
- The amount of light is related to the area of lens opening not the diameter
- The f-numbers represent the diameter of the opening
- If you double the area, you double the amount of light
- The area varies as the square of the diameter and consequently:
- The diameter varies as the squared root of the area
So if each f-stop (moving backwards from right to left in the scale) represents double the light as the previous number that means it’s opening has double the area as well (for the same subject in the same light conditions, if you double the area you double the light). What happens to the diameter? It varies as the squared root of the area. Because we doubled the area, the diameter will be 1,414 (which is √2 – square root of 2 – double) times as great. And that’s how the scale is built, by using this multiplication factor: f/2 * 1,414 = f/2.8 f2.8 * 1,414 = f/4 f/4 * 1,414 = f/5.6 and so on… If you are reading this you reached the end. Thank you for the patience and I really hope I have made it easier for you to know what you’re doing next time you pick up the camera 
Feel free to comment and leave me your feedback or your doubts if you still have them!
