Here's a topic I'm barely qualified to write about, but want to talk through as part of the process of understanding it better myself. I'm talking about F-numbers/F-stops/F-ratios. They all mean the same thing. And for many photographers, they mean a spec that you associate with the "speed" of a lens, or a setting on a camera to adjust your depth-of-field. If someone asked me "what's the f-number mean?", my explanation would be in terms of what changing it does as opposed to what the number stands for. Lower the F-stop to get more bokeh, raise it for landscape photos, etc. That's how I've been thinking about it for the past year, meaning that I had a functional understanding of what the F-number meant for my photos, but not a technical understanding of why that number has its intended effect. Let's work together to change that.
If you Google for explanations of the F-number, there are plenty of great guides and videos that do the job well. I don't want to rehash their words; it's more useful and interesting to talk through the salient points that I took away from reading those primers and the practical effect they've had on my photography. The best guide I read was this one by Matthew Cole. It's thorough and walks you through the technical derivation of the F-number, concluding with some tips for metering light using a combination of F-number and shutter speed. That last part is a little more advanced than what I want to get into today, but the following are my three biggest takeaways from reading about F-numbers to understand how it's calculated.
Exposure as a Water Bucket Analogy
A good analogy for understanding how the exposure of a photo is determined is using the idea of a bucket of water. Think of a bucket as representing the amount of exposure (or brightness) you want a photo to have, and that to achieve that target exposure, you need to fill it completely full of water. Water, in this, case, represents light. If you have a smaller target exposure (eg. want an image to be darker), you'll use a smaller bucket, which will require less water/light to fill. Conversely, if you want to overexpose your photo, you need more water/light to fill that bigger bucket. Pretty simple so far.
In photography, three technical attributes work together to determine the exposure of a photo: aperture, shutter speed, and ISO. In the water bucket analogy, each of these attributes has a corresponding element. In photography, the aperture refers to the opening in the lens that allows light through to the camera sensor or film. So in the analogy, think of this as the opening of a funnel through which you pour water into the bucket. The larger the funnel opening, the more water you can pour during a specific amount of time. That time, then, is analogous to the shutter speed--how long you keep that aperture/funnel open. The faster the shutter, the less light can get through.
And then there's ISO, which in my mind is thought of as a compensating factor for the aperture and shutter speed. In the water bucket analogy, it's like pre-filling the bucket with sand. More sand in the bucket (higher ISO) means you need less water (light) to fill it for your target exposure, but it also means that your image will be less clear--literally grainy. Trading off these three attributes is a fine balancing act, which is why it's useful to set your camera to different priority modes to automate one or more of those settings.
So how does this relate to the F-number? Well, the F-number corresponds with the lens aperture; the effect of changing it is what opens or closes the aperture to allow more or less light into your bucket. But if you think of that opening as a circle, the F-number is not a standard geometric variable. It's not the radius or diameter of that aperture opening, nor is it the circumference. It's not even the physical area of the aperture opening, which would seem to make the most sense in the water bucket analogy. And that leads to my second takeaway point: