When I decided to teach, students loved how I simplify and make concepts easy but there are those peculiar students that took this a sign of incompetence. One of those topics is the topic of aperture and f-stop. In my course this was simplified for easy understanding and ready application. Although, if you’re one of those people who want a tedious explanation of concepts, well, here it is!
EXPOSURE VALUE: APERTURE
The aperture or the adjustable hole of the lens is one of the 3 exposure values. It controls the amount of light that enters the camera. The diameter of that hole can be big or small, depending on which f-stop is used. A high f-number means less light enters the camera and a low f-number means that more light enters the camera.
That doesn’t make sense at first glance. Higher number logically means more and lower number means less. People often find this puzzling. But there’s a perfectly logical explanation why this is so. I usually skip this technical part when I explain the aperture because getting the logic involves some math. Unfortunately, most people glaze over once calculations are involved. They just want to take photos! Not do physics!
F-STOPS: APERTURE, DIAMETER, RADUIS, AND AREA
The f-stops written in your camera or written on the side of your lens may not seem to follow a logical progression: f1.4, f2.0, f2.8, f4, f5.6, f8, f11, f16, f22. But there is a method to this madness!
F-stops are not a measure of light entering the camera. F-stop is the ratio between the diameter of the aperture of the lens and the focal length of the lens, usually measured in millimeter (mm). In other words, we’re talking about how big the hole is (aperture) and how long the lens is (focal length). Size and length basically. Let’s do an example...
A common prime lens with a specification of 50mm, f2.0 is just saying the length of the lens and the diameter has a ratio of 2. That means the diameter of the aperture is 25mm. That is 50:25 = 2. That's why it's f2.0.
So if you take that same prime lens and choose f1.4 instead of f2.0, you’re actually making the aperture bigger, not smaller. Because 50:35.714 = 1.4. We can see here that the diameter at f1.4 is larger than the diameter at f2.0. F1.4 with a diameter of 35.714 is larger than the diameter of 25 at f2.0. Since we’re doing this anyway, let’s add the calculation of the area of the aperture.
Since apertures are circles we need to use the formula for calculating the area of a circle that we learned in math or physics class: π * radius² or for π (pi) we can use 3.14159265. Okay, let’s do this on our 50mm, f2.0 prime lens.
So we have these values to put in our formula: 50mm length and 25mm diameter. But wait! The formula says radius not diameter (ahhh are you now seeing why I don’t want this in a basic photography course?).
To get the radius of the circle we need to divide the diameter by 2. The diameter is the distance/line going across the circle. From “end” to “end” so to speak. The radius is the distance from the center of the circle to the boundaries of the circle.
So, 25mm/2 = radius 12.5mm.
Now we can calculate the area of the circle or aperture of our lens:
3.14159265 * 12² = 490.87385 sq.mm.
If our 50mm prime lens has an f-stop of f1.4-f22 The full specs of lens will be as shown on the table
As you can see from the table, the larger the area of the aperture the smaller or lower the f-number is. That is precisely because we were dividing, squaring, and multiplying. Given that math and a lot of people don't go together, it’s no wonder why f-stops seem so dubious at first blush.
So why not use the aperture area instead of the f-stop, this way it’s clear that the hole is bigger and more light can enter? It’s more descriptive that way and don’t seem backwards like the f-stops.
Answer: it would be correct to say that you took a photo with your 50mm lens at 1/250th sec with an aperture area of 1,963 sq.mm. But not only will nobody understand this but the area of the aperture changes with each lens.
If you have a 200mm lens the calculations will be different. The area of the aperture at f1.0 will be different on the original 50mm lens versus the 200mm lens. And would again be different on a 75mm lens. We’re just talking about prime lenses here (non-zooming), how about a compound lens such as a 55-100mm lens? Can you imagine how confusing that would be to compare lenses and can you imagine the horror it would cause when using light meters in a studio environment?
Using f-stops instead of calling out the aperture area is better. It not only gives people in the industry a standard to work with, it also makes it easier for photographers to evaluate different equipment. Having f-stops, in my experience, also helps photographers develop a “feel” for exposure and DoF (depth of field) over time and that is very useful.
As you can see, there’s a very good reason not to dedicate time on this on my course. This information is not very useful for beginners. I don’t even use this and I don’t know of any pro who use this in their daily work. I tried explaining this once and people just zoned out at the mention of ratios and division!
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